The 
NAm(ONSTRUCTOR 


GSIMPSON, 

M-I-N-A 


I 


THE 

Naval  Constructor: 

A    Vade    Mecum 

OP 

SHIP  DESIGN  FOR  STUDENTS,  NAVAL  ARCHI- 
TECTS, SHIPBUILDERS    AND    OWNERS, 
MARINE  SUPERINTENDENTS,  ENGI- 
NEERS AND  DRAUGHTSMEN. 


GEORGE   SIMPSON, 

Member  op  the  Institution  op  Naval  Architects, 
Assoc.  Member  American  Society  of  Naval.  Engineers. 


Third  Edition,  Revised  and  Enlarged, 


NEW  YORK. 

D.  VAN   NOSTRAND   COMPANY. 

LONDON. 

KEGAN  PAUL,  TRENCH,  TRUBNER,  &  CO.,  LTD. 

h  Broadway  House,  68-74  Carter  Lane,  E.C. 
1914. 


A^ 


Copyright,  1904, 

BV 
D.  VAN  NOSTRAND  COMPANY. 


Copyright,  1914, 

BY 
D.  VAN   NOSTRAND  COMPANY. 


Stanbopc  press 

r.    H.    QILSON     COMPANY 
BOSTON.      U.S.  A, 


PREFACE   TO   FIRST   EDITION. 


This  handbook  has  been  prepared  with  the  object 
of  supplying  a  ready  reference  for  those  engaged  in  the 
design,  construction,  or  maintenance  of  ships,  —  such  a 
work  as  should  give  simply  and  concisely,  information 
on  most  of  the  points  usually  dealt  with  in  the  theory 
and  practice  of  marine  architecture,  and  in  addition 
much  that  is  new  and  original.  Under  the  latter  head- 
ing should  be  included  the  chapter  on  Design  and 
many  of  the  tables  of  standardized  fitting  details,  etc. 

The  Freeboard  tables  have  been  explained  and  their 
application  simplified  by  working  out  examples  embrac- 
ing the  various  types  to  which  freeboards  are  assigned, 
including  the  modern  shelter  decker,  for  which  rules 
have  recently  been  issued. 

While  it  would  have  been  possible  to  enlarge  greatly 
on  what  the  author  has  attempted,  it  has  been  deemed 
prudent  at  present  to  restrict  somewhat  the  scope  of 
the  book,  although  at  that,  it  will  be  found  much  more 
comprehensive  in  its  character  than  existing  works  on 
naval  architecture. 

It  has  been  the  author's  aim  to  eliminate  all  obsolete 
matter  and  antiquated  data,  and  to  bring  the  book  right 
in  line  with  present  day  requirements. 

How  nearly  he  has  come  to  this  ideal  will  be  shown 
by  the  reception  accorded  by  the  profession. 

His  thanks  are  especially  due  to  Ernest  H.  Eigg, 
A.  M.  I.  N.  A.,  for  valuable  assistance  in  the  prepara- 
tion of  the  chapter  on  Freeboard,  to  Jas.  A.  Thomson, 
M.  I.  N".  A.,  for  aid  in  the  reading  of  proofs,  and  to 
the  publishers  for  their  hearty  co-operation. 

GEORGE    SIMPSON. 

647  Richmond  Terrace,  Mariner  Harbor, 
New  York  City,  May,  1904. 

3431'53 


PREFACE   TO   THIRD   EDITION. 


The  preceding  editions  of  this  handbook  were  received 
so  favorably  that  it  was  decided  to  enlarge  the  third 
edition  by  the  addition  of  further  "unified"  details 
such  as  made  the  earlier  editions  noteworthy.  There 
has  also  been  included  much  new  matter  dealing  with 
ventilation  and  other  subjects,  while  other  portions  of 
the  book  have  been  revised  and  brought  up-to-date. 

It  is  hoped  that  in  its  enlarged  form  "  The  Naval 
Constructor  "  will  continue  to  occupy  its  present  position 
as  a  daily  book  of  reference  for  those  engaged  in  the 
design,  construction  and  maintenance  of  ships. 


GEORGE   SIMPSON. 


17  Battery  Place, 
New  York  City, 
1st  Mat,  1914. 


CONTENTS. 


Section  I.  —  Ship  Calculations. 

Symbols  —  Algebraical  Signs  —  Displacement  —  Simpson's 
First  Rule  —  Multipliers  for  Subdivided  Intervals  —  Proof  of  Simp- 
son's Rule  —  Displacement  Sections! —  Bottom  Half -breadth  —  Dis- 
placement Table  —  Area  of  Water  Plane  —  Tons  per  Inch 
Immersion  —  Coefficient  —  Immersion  Passing  from  Salt  to  Fresh 
Water  —  Area  of  Midship  Section — Coefficient  £ — Prismatic 
Coefficient  —  Centre  of  Buoyancy  —  Approximate  Rule  for  Cen- 
tre of  Buoyancy  —  Centre  of  Buoyancy  Longitudinally  —  Trans- 
verse Metacentre  —  B.  M.  — Moment  of  Inertia  of  Water  Plane  — 
Longitudinal  Metacentre  —  Centre  of  Flotation  —  Approximate 
Rule  for  L.B.M.  — Moment  to  Change  Trim  —  Change  of  Trim  — 
Moment  to  Alter  Trim  One  Inch  —  Approximate  Rule  for  M. — 
Alteration  in  Trim  through  shipping  a  small  weight  —  Tchiby- 
scheff's Sections  for  "  Lucania ' '  —  Displacement  Sheet  by  Tchiby- 
scheff's Rule  —  Centre  of  Buoyancy  by  Tchibyscheff's  Rule  — 
L.M.C.  and  Centre  of  Flotation  by  Tchibyscheff's  Rule  —  Trans- 
verse Metacentres  by  Tchibyscheff's  Rule  —  Effect  of  Form  of 
Water  Line  on  Position  of  Longitudinal  Metacentre  —  Effect  of 
Form  of  Water  Line  on  Position  of  Transverse  Metacentres  —  Ex- 
planation of  Tables  on  Position  of  Metacentres  —  Stability  Calcu- 
lation by  Tchibyscheff's  Rule  —  Tchibyscheff's  Sections  for  Sta- 
bility Levers  —  Calculation  of  G.Z.  by  Tchibyscheff's  Rule  — 
Cross  Curves  of  Stability  —  Stability  Curves  —  Design  —  Block 
Coefficient  —  Relation  Coefficient  e  —  Mid  Area  Coefficient  fi  — 
Prismatic  Coefficient  —  Area  of  L.W.L.  Coefficient  a —  Inertia 
Coefficient  "i"  —  Centre  of  Gravity  Coefficient  "g"  —  Bilge 
Diagonal  Coefficient  —  Element  Coefficient  —  Relation  of  the  Co- 
efficients to  one  another  —  Element  Coefficients  for  various  Types 

—  Coefficients  for  Centre  of  Gravity  —  Moment  of  Inertia  of 
Waterline  Coefficient  —  Sheer  —  Contour  of  Stern  —  Figureheads 
and  Lacing  Pieces  —  Rail  Half-breadths  —  Load  Line  Half-breadths 

—  Diagram  of  Bilge  Diagonals  —  Diagram  of  L.W.L.  Half-breadths 
— Body  Plan  of  "Oceanic"  —  Designing  the  Bossing  —  Fairing 
the  Bossing  —  Fairing  the  Oxter  —  Elements  of  Marine  Engines  — 
Engine  Room  Lengths  —  The  Preparation  of  Specifications 

—  Specification    Headings — Freeboard  —  Length  —  Breadth  — 


vi  Contents 


Depth  of  Hold  —  Coefficient  of  Fineness — Moulded  Depth  — 
Freeboard  —  Vessels  oi  Extreme  Proportions  —  Breadth  and  Depth x 

—  Erections  on  Deck  —  Sheer  —  Round  of  Beam  —  Explanatory 
Notes  on  Application  of  Freeboard  Tables  —  Additional  Freeboard 
for  Winter  North  Atlantic  for  Well-deck  Vessels — Rules  for 
Depth  of  Loading  of  Turret-deck  Vessels — Rules  for  Shelter- 
deck  Vessels  —  Load  Draught  Diagrams  —  Types  of  Vessels  — 
Freeboard  Marks — Freeboard  Tables — Freeboards  for  Freight- 
ers—  Freeboards  for  Spar  Deckers  —  Freeboards  for  Awning 
Deckers — Sailing   Vessels  —  Kirk's  Analysis  —  Analysis  Data 

—  Wetted  Surface  Formula — Launching  —  Launching  Periods 

—  Launching  Curves — Camber  of  Ways — Declivity  of  Ways  — 
Pressure  on  Dog  Shoes  —  Length  of  Ways  —  Tables  of  Launch- 
ing Data — Calculation  of  Hull  Weights — Ditto  by  Johnson's 
Method  —  Johnson's  Curves  —  Complete  Tables  of  Weights  of 
Steel  Shapes  —  The  Transport  of  Cattle  —  Arrangement  of 
Stalls  and  Pens -1— Dimensions  of  Stalls  and  Pens  —  Board 
of  Agriculture  Regulations — Detailed  Weights  of  Cattle  Fittings 

—  Rudder  Formulae  —  Spectacle  Frames  —  Proportions  of 
Spectacle  Frames  —  Propeller  Struts  —  Simpson's  Formula  for 
Propeller  Struts  —  Proportions  of  Brackets  —  Centre  of  Gravity 
by  Experiment  —  Centre  of  Gravity  by  Calculation  —  Strength 
of  Ships  —  Hogging — Sagging  —  Curve  of  Weights  —  Curve  of 
Buoyancy  —  Curve  of  Loads  —  Curve  of  Shearing  Stresses  — 
Curve  of  Bending  Moments  —  Specimen  Calculations  for  Mo- 
ments of  Inertia  —  Diagram  of  Strength  Curves  —  Resistance 
of  Ships  —  The  Admiralty  Constant  —  Table  of  Constants  for 
various  Types  —  Froude's  Investigations  —  Law  of  Comparison 

—  Application  of  Froude's  Law — Speed  and  Power  Curve  — 
Standard  Curves  of  Power  —  I.H.P.  by  Independent  Method  — 
Skin  Resistance  —  Residuary  Resistance  Power  — Form  of  Least 
Resistance  —  Middendorf's  Method  —  Table  of  Angles  of  Entrance 
and  Run  —  Table  of  Steamers'  Data. 

Section  II.  —  Strength  of  Materials. 

Strength  of  Materials  —  Ultimate  Strength  —  Working  Load 

—  Proof  Strength  —  Stress  aud  Strain  —  Tensile  Stress  —  Compres- 
sive Stress — -Shearing  Stress — Bending  Stress  —  Torsional  Stress 

—  Resilience  —  Elasticity — Modulus  of  Elasticity — Permanent  Set 

—  Moment  of  Inertia  —  Neutral  Surface — Section  Modulus  — 
Moment  of  Resistance  —  Radius  of  Gyration  —  Various  Stresses 
and  their  Factors — Elements  of  Sections  —  Beam  Bending 
Moments  —  Elements  of  Circular  Sections  —  Moment  of  Inertia 
of  Circular  Sections  —  Strength  of  Columns  —  Johnson's  Formula 
for  Columns  —  Least  Radius  of  Gyration  for  various  Sections 


Contents  vii 


—  Values  for  Johnson's  Formula  —  Pipe  Pillars  —  Standard  Pipe 
Elements  —  Steel  Columns  —  Strength  of  Metals  and  Alloys  — 
Physical  Properties  of  Timber  —  Strength  of  Timber  —  Weight 
and  Strength  of  Wire  Rope  —  Notes  on  the  Use  of  Wire  Rope  — 
Strength  of  Chain  Cables  —  Proof  Load  for  Chains  —  Strength 
of  Guard  Chains — Weight  of  Chain  Cables — Breaking  Strength 
of  Chains  —  Elements  of  Angles  —  Elements  of  Bulb  Angles  — 
Elements  of  Deck  Beams — Elements  of  Tees  —  Elements  of 
Z  bars  —  Tees  as  Struts  —  Bending  Moments  of  Pins  —  Strength 
of  Special  Shackles  —  Riveting  U.  S.  Navy  —  Standard  Rivets  — 
Lloyd's  Riveting  Table  —  Tables  of  Strength  of  Riveting  — 
Ordered  Lengths  of  Rivets  —  Shearing  and  Bearing  Tables  of 
Rivets. 

Section  III.  —  Fittings  and  Details. 

Structural  Details  —  Keels  —  Bar  Keel  —  Keel  Scarphs  —  Tack 
Rivets  in  Keels  —  Universal  Bar  —  Flat  Plate  Keels  —  Centre 
Keelson  —  Keel  Doublings  —  Stems  —  Stern  Frames  —  Braces  — 
Gudgeons  —  Pintles  —  Riveting  of  Boss  —  Rudder  Post  —  Body 
Post  —  Rudders  —  Single  Plate  Rudder  —  Norman  Head  —  Rud- 
der Arms  —  Coupling  Palm  —  Coupling  Bolts  —  Rudder  Stock  — 
Cast  Steel  Rudder  —  Balanced  Rudders  —  Heel  Bearing  —  Emer- 
gency Chains  —  Types  of  Rudder  Carriers  —  Rudder  Trunks — ■ 
Tail  Plates  —  Propeller  Struts  —  Area  of  Propeller  Brackets  — 
Boss  Barrel  —  Spectacle  Frames  —  Bossing  around  Shafts  — 
Tube-end  Castings  —  Framing  —  Resistance  of  Frames  —  Cut 
Frames  —  Pressed  Plate  Chocks  —  Stapled  Collars  —  Frame  Doub- 
lings —  Spirketting  Plate  —  Framing  of  Superstructure  —  Reverse 
Frames  —  Floors  —  Stresses  on  Floors  —  Flanged  Floors  —  Chan- 
nel Floors  —  Water-tight  Floors  —  Floor  Brackets  —  End  Floors 

—  Inner  Bottoms  —  Water-tight  Compartments  —  Centre  Vertical 
Girder  —  Side  Girders  —  Margin  Plate  —  Ceiling  on  Tanks  — 
Bitumastic  Cement  —  Manholes  —  Tank"  Bleeders  —  Beams  — 
Beam  Camber  —  Welded  Beam  Knees  —  Bracket  Knees  —  Stand- 
ard Beam  Knees  —  Strong  Beams  —  Carlings  —  Deck  Girders  — 
Beam  Collars — Hold  Pillars  —  Built  Columns  —  Pipe  Pillars  — 
Standard  Solid  Heads  and  Heels  —  Fitting  of  Pillars  —  Heels  on 
Inner  Bottoms  —  Staggered  Pillars  —  Hatches  —  Size  of  Hatches 

—  Hatch  Corner  Doublings  —  Corner  Angles  —  Hatch  Fore  and 
Afters  —  Bridle  Beams  —  Standard  Hatch  Cleats  —  Battening 
Bar  —  Hatch  Wedges  —  Hatch  Ledges  —  Hatch  Lashing  Rings  — 
Hatch  Covers  —  Lifting  Rings  —  Web  Frames  —  Keelsons  —  In- 
tercostal Plates  —  Side  Stringers  —  Bulkhead  Collars  —  Longitudi- 
nals—  Ending  of  Keelsons  —  Bulkheads  —  Collision  Bulkheads 

—  Bulkhead  Liners —  Bottom  Plaiting  Bhd.  —  Stiffeners —  Stresses 


viii  Contents 


on  Bulkheads  —  Deep  Framing  —  Caulking  —  Chafing  Pieces  — 
Shell  Plating — Arrangement  of  Strakes  —  Plate  Lines  —  Fairing 
the  Lines  on  Model  —  Shift  of  Butts  —  Furnaced  Plates  —  Land- 
ings—  Butts  of  Plating — Garboard  Strake  —  Sheerstrake —  Shell 
Riveting  —  Stealers  —  Jogging  —  Scarphs  of  Overlaps  —  Liners  at 
Overlaps — Scarphing  of  Landing  Edges  on  Stem  and  Stern  Post 

—  Holes  through  Shell — Doubling  Plates  —  Hood  End  Plates  — 
Doublings  at  Breaks  —  Pitting  Details  —  The  Preparation  of  De- 
tails—  Standardizing  Details  —  Bill  of  Material —  Standard  Hatch- 
ing—  Graphic  Division  of  One  Inch  —  Baldt  Anchors  —  Ingle- 
field  Anchors  —  Hall  Anchors  —  Admiral  Anchors  —  Anchor 
Cranes  —  Formulas  for  Bevel  and  Mitre  Gear  Blanks — Naval 
Anchor  Crane  —  Stress  on  Auchor  Cranes  —  Dimensions  of  An- 
chor Cranes  —  Ship's  Bells — Weight  of  Bells  —  Belay  Pins  — 
Balanced  Armor  Hatch  —  Standard  Bollards  —  Weights  of  Bol- 
lards—  Wire  Rope  Snatch  Blocks  —  Diamond  Rope  Blocks  —  25- 
Ton  Block  —  Standard  Iron  Blocks  —  U.S.  Standard  Bolts  and 
Nuts  —  Chain  Plates  —  Cast  Steel  Cleats  —  Catting  Hooks  — 
Crane  Hooks  —  Navy  Boat  Crane —  Boat-handling  Arrangement 

—  Rotating  Davit  —  Mallory  Davit  —  Swan-neck  Davit — Mine 
Davit  —  Board  of  Trade  Rules  for  Round  Davits  —  Davit  Heads  — 
Weights  of  Boats  and  Davit  Diameters  —  Standard  Hinged  W.  T. 
Doors  —  Standard  Sliding  W.  T.  Doors  —  Details  of  W.  T.  Doors 

—  Standard  Eyebolts  —  Standard  Fairleads  —  Weight  of  Fair- 
leads —  Flanges  for  Lead  Pipes  —  Standard  Pipe  Flanges  —  Stand- 
ard Flanges  for  Ventilation  —  Standard  Hand  Wheels  (Iron)  — 
Standard  Hand  Wheels  (Brass)  —  Hawse  Pipe  Proportions  — 
Weights  of  Hawse  Pipes  —  Hooks  —  Cargo  Hooks  —  Swivel  Hooks 

—  Trip  Hooks  —  Keys  and  Key  ways  —  Reversible  Pad  Eye  — 
Lewis  Bolt  —  Accommodation  Ladders  —  Lashing  Triangles  — 
Mooring  Pipes  —  Strength  of  W.  I.  Pipes — Plug  Cock  Keys  — 
Standard  Pad  Eyes — Strength  of  Rings  —  Proportions  of  Rings 

—  Ordered  Lengths  of  Rivets — Diagrams  for  Rivets  —  Ring  Plates 

—  Dimensions  of  Wood  Screws  —  Areas  of  Sea  Anchors  —  Detail 
of  Sea  Anchor  —  Sisterhooks — Slip  Shackles  —  Trade  Shackles  — 
Standard  Shackles  —  Standard  Worked  Eyes  —  Towing  Bitts  — 
Steering  Chain  Springs  —  Screw  Steering  Gears  —  Deck  Seats  — 
Weights  of  sidelights  —  Proportions  of  Chain  Slips — Boom  Mount- 
ings—  Spider  Bands  —  Torpedo  Net  Details  —  Gaff  Mountings  — 
Stuffing  Boxes  and  Glands  —  Thimbles  for  Wire  Rope  —  Standard 
Toggle  Pins — Admiralty  Turnbuckles  —  Trolley  Block  —  Uni- 
versal Joints  —  Low  Pressure  Valves —  Heavy  Pressure  Valves  — 
Friction  Brake  for  Cranes  —  Ventilation  —  Chart  for  Ventilation 
Pipes  —  Terminals  for  Exhaust  Pipes  —  Adjustable  Terminals  — 
Terminals  with  Dampers — Standard  Sizes  of  Ventilators  and 
Cowls — Weight    of  Cowls  —  Elswick    Guns  —  Vickers  Guns  — 


Contents  ix 

Schneider  Guns  —  Krupp  Guns  —  Bethlehem  Guns — U.  S.  Naval 
Ordnance. 

Section  IV— Rigging  and  Ropes. 

Standing  Rigging  —  Table  of  Wire  Rope  —  Splices  —  Thimbles 

—  Sheaves  —  Turnbuckles  —  Running  Rigging  —  Manila  —  Hemp 

—  Coir  —  Blocks  —  Standard  Blocks,  U.  S.  N. — Cargo  Blocks  — 
Tackles — Power  gained  by  Blocks  —  Whip  —  Double  Whip  — 
Gun  tackle  Purchase  —  Burton  —  Double  Spanish  Burton  —  Luff 
Tackle  —  Rigging  Derricks. 

Section  V.  —  Equipment. 

Anchors  and  Chains  —  Lloyd's  Equipment  —  Lloyd's  Table  — 
Hawsers  and  Warps  —  Tables  of  Equipment  —  Weights  —  Moor- 
ing Swivel  —  Blake  Stopper  —  Senhouse  Slip  —  Admiralty  Cables 

—  Chain  Cable  Links  —  Club  Shackle  —  Chain  Swivel — Renter 
Shackle  —  Boats  —  Notes  on  Construction  —  Diagram  of  Propor- 
tions —  Lifeboats^ —  Cutters —  Dinghies  —  Gigs  —  Barges  — Galleys 

—  Table  of  Scantlings  for  Rowboats  —  Sail  Area  —  Drawing  of 
Standard  Lifeboat  in  Detail  —  Lifting  Rings  and  Slings  —  Board 
of  Trade  Requirements — Supervising  Inspector's  Requirements 

—  Sea  Anchors — Axes,  Buckets,  etc. — Light  Screens  —  Ton- 
nage—  Various  Tonnage  Rules  —  Y.  R.  A.  and  N.  Y.  Y.  C. 
Rules  —  Windlasses  —  Towing  Machines,  etc. 

Section  VI.  —  Miscellaneous. 

Tables  of  Weights  —  Measures  —  Oil  Fuel  Data  —  Weights  of 
Bolts  and  Nuts  —  Tank  Capacities  —  Unit  Equivalents  —  Squares, 
Cubes,  and  Fourth  Powers  of  Fractions  —  Powers  and  Roots  — 
Speed  Tables — Foreign  Weights  and  Measures  —  Stowages  of 
Merchandise  —  Cold  Storage  Temperatures  —  Distances  from 
Colon, 

Section  VII.  — Tables. 

Complete  mathematical  tables  specially  arranged. 


SYMBOLS     COMMON    IN    NAVAL    ARCHI- 
TECTURE   USED    IN    THIS   BOOK. 


A  . 
S.A. 
C.E. 


b  .  . 
Bm 
Bx  . 
Bw. 

0.   • 

B  . 
C.B. 

0  . 
C.G. 
H  . 
D  . 
V  . 
D  + 
D- 

S- 

t  . 
F 
Fr 

g  ■ 

A. P. 
F.P. 

X  • 


Area  of  load  water  plane. 
Sail  area  in  square  feet. 
Centre  of  effort  of  sail  plan. 

Distance  of  centre  of  effort  forward  of  centre  of  im- 
mersed lateral  plane. 

^4 
Coefficient  of  fineness  of  load  water  line  = 


Bilge  diagonal  coefficient. 
Moulded  breadth  of  ship. 
Extreme  breadth  of  ship. 
Water-line  breadth  of  ship. 

Coefficient  of  midship  section  area : 


LxB 


XA 


Bxd 

.  Centre  of  gravity  of  displacement  (centre  of  buoyancy). 
.  Centre  of  gravity  of  displacement  from  aft  perpen- 
dicular. 
.  Centre  of  gravity  of  ship  above  base. 
.  Centre  of  gravity  of  ship  and  engines. 
.  Moulded  depth  to  upper  deck. 
.  Displacement  in  tons  of  salt  water  (gross). 
.  Displacement  in  cubic  feet  (volume). 
.  Displacement  in  tons  at  load  draught. 
.  Displacement  in  tons  at  light. 
.  Displacement  of  fore  body. 
.  Displacement  of  after  body. 

.  Coefficient  of  fineness  of  displacement  (block  coefficient). 
.  Relation  coefficient. 
.  Freeboard  from  statutory  deck  line. 
.  Freeboard  to  top  of  rail  amidship. 

G 


II 


Coefficient  of  centre  of  gravity  = 

After  perpendicular  (after  side  of  rudder  post). 
Forward  perpendicular  (fore  side  of  stem  at  upper  deck). 
Indicates  the  half-length  between  perpendiculars  and  is 
the  sign  of  the  mid-section  or  "dead  flat." 
xi 


The  Naval  Constructor 


X-4  .  .  •  Mid-section  area. 

M.  C.     .  .  Height  of  transverse  metacentre  above  base. 

G.Z.  .  .  .  Stability  lever. 

G.M.    .  .  Height  of  transverse  metacentre  above  centre  of  gravity. 

B.M.     .  .  Height  of  transverse  metacentre  above  centre  of  buoy- 
ancy. 

L.M.C.    .  Longitudinal  metacentre  above  base. 

*cT  .  .  .  .  Centre  of  gravity  below  L.W.L. 

G  .  .  .  .  Centre  of  gravity  above  L.W.L. 

p    .  .  .  .  Prismatic  coefficient. 

I.H.P.     .  Indicated  horse  power. 

E.H.P.    .  Effective  horse  power. 

N.P.     .  .  Nominal  horse  power. 

B.P.  .  .  .  Length  of  ship  between  perpendiculars. 

W.L.    .  .  Length  of  ship  on  load  water  line. 

wl  .  .  .  .  Water  line. 

O.A. .  .  .  Length  of  ship  over  all. 

R    .  .  .  .  Placed  before  dimensions  indicates  that  these  are  the 
registered  or  tonnage  dimensions. 

I Moment  of  inertia  of  load  water  plane. 

M  .  .  .  .  Metacentre  and  moment. 

M "    ...  Moment  to  alter  trim  one  inch  at  load  line. 

0    ....  On  drawings  locates  the  intersection  of  projected  water 

line  with  the  elevation. 

O   .  .  .  .  Centre  of  gravity,  or  moment  about  centre, 

(w)     ...  Centre  of  gravity  of  water  line. 

.  Centre  of  gravity  of  mid-section  area. 

.  Centre  of  gravity  of  sail  plan,  or  centre  of  effort. 

.  Ordinates  or  stations. 

x Common  interval  or  abscissa  between  ordinates. 

W.S.    .  .  Area  of  wetted  surface.  « 

JB    ....  Eesistance. 

\  G,  or  U,  Half-girth  of  midship  section  (Lloyd's). 


d 
-*rd 

■e-. 

P    . 

V  . 


Draught  of  water  moulded  (mean). 

Draught  of  water  forward  ^ 

Draught  of  water  aft  >  to  bottom  of  keel. 

Mean  draught  ; 

Power. 

Speed  in  knots  per  hour. 

■ .    i    ,  D§  x  T8 

Admiralty  constant  =  — 

l.M.Jr. 

Per. 

xii 


Symbols  Common  in  Naval  Architecture 


t3fl"    .  .  .  Per  inch  ;  also  tons  per  inch  of  immersion  at  L.W.L. 

□ '  .  .  .  .  Square  foot. 

□  ".   .  .   .  Square  inch. 

f Cubic  foot. 

Algebraical  Signs. 

-(-  Plus,     addition.       Positive.    ^  Semicircle. 

Compression. 

—  Minus,    subtraction. 

Nega-    CD  Quadrant. 

tive.     Tension. 

tst  Equal  to. 

co  Infinity. 

4=  Unequal  to. 

Pi  Arc. 

>  Greater  than. 

~  Difference. 

^j>  Not  greater  than. 

0   []    H   Vincula- 

<  Less  than. 

c   Constant. 

<JC  Not  less. 

d  Differential. 

X  By.     Multiplied  by 

f  Integration. 

::    Multiplied  by.    Ratio. 

Is  to.  /  Functions. 

:    So  is.  As  (ratio).  Divided  by.  9   Gravity. 

J_  Perpendicular  to. 

k  Coefficient. 

II   Parallel  to. 

n  Any  number. 

-ti-  Not  parallel. 

a   An  angle. 

V  Because. 

8   Variation. 

.'.  Therefore. 

A  Finite  difference. 

/_  Angle. 

0,  cfi  Any  angles. 

L  Right  angle. 

7T  Ratio  of  circumference  to  di- 

ameter of  circle. 

A  Triangle. 

p   Radius. 

O  Parallelogram. 

5  Sum  of  finite  quantities. 

□   Square. 

V  Square  root. 

O  Circumference. 

%/  Cube  root. 

O  Circle. 

V  nth.  root. 

THE 

NAVAL  CONSTRUCTOR 


CHAPTER   I. 

DISPLACEMENT    (D). 

The  displacement  of  any  floating  body  whether  it  be  a  ship,  a 
barrel,  a  log  of  lumber  or,  as  in  the  case  of  the  great  Philosopher 
who  first  discovered  its  law,  the  human  person,  is  simply  the 
amount  of  water  forced  or  squeezed  aside  by  the  body  immersed. 
The  Archimedian  law  on  which  it  is  based  may  be  stated  as  :  — 
All  floating  bodies  on  being  immersed  in  a  liquid  push  aside  a  volume 
of  the  liquid  equal  in  weight  to  the  weight  of  the  body  immersed. 
From  which  it  will  be  evident  that  the  depth  to  which  the  body  will 
be  immersed  in  the  fluid  will  depend  entirely  on  the  density  of  the 
same,  as  for  example  in  mercury  the  immersion  would  be  very 
little  "indeed  compared  with  salt  water,  and  slightly  less  in  salt 
water  than  in  fresh.  It  is  from  this  principle  that  we  are  enabled 
to  arrive  at  the  exact  weight  of  a  ship,  because  it  is  obvious  that 
if  we  can  determine  the  number  of  cubic  feet,  or  volume  as  it  is 
called,  in  the  immersed  body  of  a  ship,  then,  knowing  as  we  do 
that  there  are  35  cubic  feet  of  salt  water  in  one  ton,  this  volume 
divided  by  35  will  equal  the  weight  or  displacement  in  tons  of  the 
vessel.  If  the  vessel  were  of  box  form,  this  would  be  a  simple 
enough  matter,  being  merely  the  length  by  breadth  by  draught 
divided  by  35,  but  as  the  immersed  body  is  of  curvilinear  form, 
the  problem  resolves  itself  into  one  requiring  the  application  of 
one  of  a  number  of  ingenious  methods  of  calculation,  the  principal 
ones  in  use  being  (1)  The  Trapezoidal  Rule,  (2)  Simpson's  Rules, 
and  (3)  Tchibyscheffs  method. 

Simpson's  First  Rule. 

The  calculation  of  a  curvilinear  area  by  this  rule  is  usually 
defined  as  dividing  the  base  into  a  suitable  even  number  of  equal 
parts,  erecting  perpendicular  ordinates  from  the  base  to  the  curve, 
and  after  measuring  off  the  lengths  of  these  ordinates,  to  the  sum 

1 


2 


The  Naval  Constructor 


of  the  end  ones,  add  four  times  the  odd  p.nd  twice  the  even  ordi- 
nates.  The  total  .sum  multiplied  by  one  third  the  common  inter- 
val between  these  ordinates,  will  produce  the  area.  It  should, 
however,  be  stated  that  the  number  of  equal  parts  need  not  neces- 
sarily be  even,  and  as  it  is  sometimes  desirable  to  calculate  the 
area  to  an  odd  ordinate  by  taking  the  sum  of  the  first  ordinate 
and  adding  to  it  four  times  the  odd  ones,  and  twice  the  last  as  well 
as  the  even  ordinates  into  one  third  the  common  interval,  the  area 
may  be  calculated  accurately.  In  the  foregoing  definition  it 
should  be  noted  that  the  first  ordinate  is  numbered  "0,"  and  that 
the  number  of  intervals  multiplied  by  3  should  equal  the  sum  of 
the  multipliers. 


Fig.  1. 


Area  of  ABCD 


to  +  4  yx  +  2  y2  +  4  yz  +  y4). 


And  if  half  ordinates  be  inserted  between  y0  and  2/1  and  between 
yz  and  y4  we  should  then  have  :  — 

Area  =  I  ft  y0+  2  y^+  1§  yx  +  4  y2+ 1|  y3+  2^  +  1  y4). 

Should,  however,  we  desire  to  calculate  the  area  embraced  within 
the  limits  of  yz  only,  omitting  the  half  ordinate  y^,  then  :  — 

Area  =  ^  (y0+  4  yx  +  2  y2  +  2  y3). 

So  that  it  is  immaterial  what  subdivision  of  parts  we  may  use  as 
long  as  the  multiplier  is  given  the  relative  value  to  the  space  it 
represents  as  exemplified  in  the  subjoined  table.  It  will  be  obvi- 
ous that  we  may  also  give  multiplier  only  half  its  value,  as 

£2/0+  2  2/1  +  1 2/2  +  2  yz  +  \y^, 


Multipliers  for  Subdivided  Intervals         3 


and  multiply  the  sum  by  §  of  x,  which  will  be  found  the  more  con- 
venient way  to  use  the  rule,  involving  as  it  does  figuring  with 
smaller  values. 


Multipliers   for 

Subdivided 

Intervals 

. 

Ordinates, 

0 

* 

1 

2 

3 

4 

5 

5i 

Multipliers, 

J 

2 

M 

4 

2 

4 

1* 

1 

Ordinates, 

0 

1 

2 

2* 

8 

H 

4 

8f 

4 

H 

4^ 

4^ 

42 

4| 

5 

Multipliers, 

1 

4 

l\ 

2 

i 

4 

i 

J 

1 

A 

| 

3 

I 

75" 

2 
3 

1 

Ordinates, 

0 

1 

H 

2 

2* 

8 

4 

0 

<4 

a 

«i 

<4 

n 

; 

Multipliers, 

2 

1 

2 

1 

2 

H 

4 

H 

2 

3 

l 

~7, 

\ 

1 

1 

Ordinates, 

0 

1 

2 

2^ 

2H 

S 

s* 

m 

4 

5 

6 

<H 

7 

71 

Multipliers, 

1 

i 

n 

H 

f 

H 

1 

i\ 

H 

4 

M 

2 

1 

2 

1 
1 

As  proof  of  the  rule  let  us  deal  with  an  example  : 

Area  ABCD  =  |  (y0  +  4  Vl  +  y2). 

Assume  curve  DFC    is  part  of    a  common   parabola ;    area 
DKCFD  is  f  area  of  parallelogram.     Join  DC,  and  draw  parallel 

H 


Fiq.  2. 

to  GH  touching  curve.  If  DFC  be  part  of  parabola  area,  DFC 
is  f  of  parallelogram  DCHG. 

EK=\{y0  +  yx).  FK=yx-V-±^. 

Parallelograms  on  same  base  and  between  same  parallels  are  equal. 
Draw  through  G  and  H  two  lines  parallel  to  base  as  GM  and  DL, 
then  area 

DCHG  =  area  DLMG 

=  2  x  x  DG 

=  2  x  x  FK 


?hfc*$*i 


The  Naval   Constructor 

Area  DFC  =  §  of  above  =  ±g  [yx  -  ^±^)| 

'(M)     j 

X 


Area  ^4  BCiTD 


Simpson's  second  rule  for  determining  areas  bounded  by  a  par- 
abola of  the  third  order  and  the  "five  eight"  rule  applicable  to 
the  calculation  of  one  of  the  subdivided  areas  are  given  in  most 
text-books,  but  are  omitted  here  as  superfluous,  Simpson's  first 
rule  being  adaptable  to  either  of  these  cases,  so  that  for  all  ship 
calculations  where  areas,  volumes,  or  moments  are  required,  the 
first  rule,  or  as  hereafter  explained  Tchibyscheff 's  rule,  are  recom- 
mended. 

We  have  seen,  then,  how  the  area  or  surface  may  be  calculated 
by  this  rule,  and  as  the  volume  is  the  area  by  the  thickness,  it  will 
be  evident  that  if  the  areas  be  calculated  at  various  levels  or 
water  lines,  as  shown  in  the  figure,  and  these  areas  in  turn  treated 
as  a  curve  and  integrated  by  means  of  the  rule,  that  the  result  will 
be  the  volume  of  the  body. 


L.W.L. 

] 

4  W.L. 

^ 

1  \      \ 

s- 

1 9V  / 

J 

IL 

3  W.L. 
2  W.L. 
1  W.L. 
BASE 

l\\ 

\ff 

8/       J 

1 

w 

\2 

/  / 7/// 

5^0\\^    \ 

//    /Oj^/5 

Fig.  3. 

Let  the  Figs.  3  and  4  represent  the  immersed  half  longitudinal 
body  of  a  vessel  100  feet  long  by  12  feet  broad  submerged  to  5 
feet  draught  as  represented  by  L.W.L.  It  is  required  to  calculate 
the  volume  of  water  displaced  by  Simpson's  first  rule.  The  base 
line  length  between  perpendiculars  should  be  divided  into  an 
equal  number  of  intervals,  and  as  advocated  in  the  chapter  on 
Design,  it  will  be  well  to  have  a  definite  number  and  retain  same 
for  all  designs,  as  by  so  doing  it  will  facilitate  comparisons  and 
working  from  one  design  to  another.  Ten  such  intervals  with 
half-end  ordinates  is  a  very  convenient  division,   and  in  this  case 


Displacement  Sections 


will  giv^e  a  common  interval  of  10  feet.     The  draught  of  5  feet 
must  likewise  be  subdivided  into  a  certain  number  of  equal  inter- 
vals, which  in  this  case  we  will  fix  at  4,  so  that 
5  ft.  draught  =125ft> 
4 
intei'val  between  water  lines.   These  divisions  of  water  lines  must  be 
drawn  across  the  body  plan  of  ten  sections,  and  the  half  breadths 
read  off  with  a  scale  and  tabulated  as  in  table  on  following  page. 


rV\ '  >A\    I  \\S — |\\V    tA  -.    \T~-  4-V    iT" 


v 


„ — u 


L.W.L. 


ZSZ. 


Fig.  4. 

It  should  be  stated  in  connection  with  the  subdivision  of  the 
base  line  that  the  length  taken  for  displacement  is  measured  by 
some  designers  from  the  after  side  of  body  post  i.e.,  ignoring  the 
propeller  aperture  ;  and  by  others  from  the  fore  side  of  body  post 
to  the  after  side  of  stem  omitting  the  moulded  size  of  these  for- 
giugs.  Both  of  these  methods  are  inaccurate  besides  leading  to 
confusion,  as,  in  the  first  case,  the  displacement  of  the  propeller 
with  its  boss  will  equal  the  displacement  cut  out  for  aperture  not 
to  mention  the  volume  of  the  rudder,  which  is  rarely,  if  ever, 
taken  into  account.  And  in  the  second  case  the  tiny  amount  of 
displacement  added  at  the  knuckle  formed  by  the  bearding  line  of 
plating  when  the  length  is  taken  to  forward  and  after  sides  of 
stem  and  stern  post  respectively,  is  compensated  for  by  the  gud- 
geons on  stern  post.  Therefore  the  most  correct  and  also  the 
most  convenient  length  is  from  after  side  of  rudder  post  to  for- 
ward side  of  stem  at  load  water  line. 

Where  vessels  have  a  very  flat  floor  line  a  half  water  line  should 
be  taken  be- 
tween base  line 
and  first  water 
plane,  and  the 
keel  or  bottom 
half-breadth  _  «ee| 
given  a  value 
proportioned  to 
the  rise  of  floor 
line  as  in  Fig.  5. 


The  Naval  Constructor 


Required  the  half-breadth  x  at  the  keel  for  the  displacement 
sheet,  where  10  feet  is  the  actual  scaled  length  L,  6"  the  rise  of 
floor,  7"  the  distance  from  the  rise  line  to  first  water  line  at 
moulded  half-breadth  of  ship  and,  of  course,  13  inches  the  water 
line  interval,  then  :  — 

13":  7"::  10  feet  :  x. 

.-.  x  =  5.38  feet  =  bottom  breadth. 


Displacement  Table. 


Water  lines  apart 

.      1.25' 

Load 

draught .    . 

.    . 

5.00' 

Ordinates  apart    ....    10.00'              Displacement  length,  100.00' 

as  « 

Keel. 

W.L.  1. 

W.L.  2. 

W.L.  3. 

W.L.  4. 

8 

< 

§3 
to  a. 

S 

GO 

co 

■ 

3 

co* 
M 

to' 

J 

CO 

BS 

,1 

3 

■a 
1  " 

3 

J 

o 

.1 

V 

1 

s 

a 
o 

02» 

3« 

I 

u 

3« 

1 

P4 

1 

5  >-< 

1 

3* 

"5 
o 
E 
£ 

0 

| 

.04 

.01 

.04 

.01 

.04 

.01 

.04 

.01 

.04 

.01 

i 

l 

.03 

03 

.08 

.08 

.18 

.18 

.43 

.43 

1.41 

1.41 

1 

3 

.02 

.01 

.16 

.12 

.73 

.55 

1.78 

1.33 

3.10 

2.32 

2 

2 

.02 

.04 

.92 

1.84 

2.35 

4.70 

3.78 

7.56 

4.81 

9.62 

3 

1 

.02 

02 

2.13 

2.13 

4.03 

4.03 

5.16 

5.16 

5.50 

5.56 

4 

2 

.02 

.04 

3.20 

6.40 

4.98 

9.96 

5.67 

11.34 

6.96 

11.92 

5 

1 

.02 

.02 

3.54 

3.54 

5.20 

5.20 

5.80 

5.80 

6.00 

6.00 

6 

2 

.02 

.04 

3.00 

6.00 

4.66 

9.32 

5.34 

10.68 

5.58 

11.16 

7 

1 

.02 

.02 

2.00 

2.00 

3.58 

3.58 

4.42 

4.42 

4.87 

4.87 

8 

2 

.02 

.04 

1.25 

2.50 

2.28 

4.56 

3.04 

6.08 

3.57 

7.14 

9 

f 

.02 

.01 

.48 

.36 

1.00 

.75 

1.50 

1.12 

1.90 

1.42 

n 

1 

.02 

.02 

.18 

.18 

.50 

.50 

.74 

.74 

.97 

.97 

10 

\ 

•    • 

•    • 

•    • 

.03 

.01 

.03 

.01 

15 

15 

Sum      ,__ 

of     .30 

25.16 

43.34 

54.68 

62.41 

=  10 

Prod- 

xl.5 

Sum 
of 

Mul- 
tiple 

ucts. 

j 

2(1)              1( 

t)            2(1 

)                \ 

.15    +     50.32     +     43.34    +  109.36    +     31.20 

=  234.37 

(f  W.L.  interval)  X  (f  ordinate  interval)  x  2  (both  sides)  _ 
35  (Cub>  ft>  of  s  w  in  a  ton)  "  T  ° 

_(1.25xf)x(10xf)x2 
35 


=  .315. 


Area  of  Water  Plane 


234.37 

x.315 

Displacement  to  W.L.  4 =   73.82 

.15      +      50.32      +      43.34      +      54.68      =148.49 

x.315 

Displacement  to  W.L.  3_. =46.77    tons. 

.15      +      50.32      +  <^2US>  =   72.09 

x.315 

Displacement  to  W.L.  2 =   22.70    tons. 

.15      +      25.16  =   25.31 

X.315 
Displacement  to  W.L.  1 =     7.97    tons. 

The  displacement  to  the  load  water  line  being  73.82  tons  it  is 
useful  to  know  what  relation  that  weight  bears  to  the  vessel  if  she 
were  of  box  section,  in  other  words,  the  amount  that  has  been  cut  olff 
the  rectangular  block  formed  by  the  length,  breadth,  and  draught, 
to  fine  it  to  the  required  form,  or  the  block  coefficient  or  coeffi- 
cient of  displacement  represented  by  the  symbol  "5".  It  will 
be  evident  that  this  coefficient  may  readily  be  computed  by  mul- 
tiplying the  length  X  breadth  X  draught,  and  dividing  the  product, 
which  is  the  volume  of  the  box  in  cubic  feet,  by  35  to  get  the  tons 
displaced  by  the  rectangular  block.  The  displacement  as  calcu- 
lated, divided  by  this  result,  will  give  the  block  coefficient  "  5  ",  or, 

£^5x3=. 432  nearly. 

The  range  of  this  coefficient  for  various  types  is  given  else- 
where in  the  Table  of  Element  Coefficients. 


Area  of  Water  Plane. 


Keel. 

W.L.  1. 

W.L.  2. 

W.L.  3. 

W.L.  4. 

Sum  of  products  . 
f  common  interval, 
Half-areas  .     .     . 

Areas    of    water 
planes      .     .     . 

.30 

25.16 

<4 

43.34 

54.68 
6f 

62.41 

2.00 
2 

167.73 
2 

288.93 
2 

364.53 
2 

416.07 

2 

4.00 

335.46 

577.86 

729.06 

832.14 

The  area  of  any  of  the  water  planes  in  the  specimen  displace- 
ment table  will  simply  be  the  sum  of  the  products  of  the  particular 


The  Naval   Constructor 


water  plane  required,  multiplied  by  $  the  interval  between 
ordinates.  This  product  doubled  will  be  the  total  area  of  both 
sides. 

Tons  per  Inch  of  Immersion  (^jJ"). 

It  is  useful  to  know  the  amount  of  displacement  of  the  vessel 
for  each  inch  of  immersion  at  various  draughts,  as  from  this 
data  small  amounts  of  cargo  taken  out  or  placed  on  board  can  be 
accurately  determined  without  reference  to,  or  scaling  from,  the 
regular  displacement  curve.  It  will  be  seen  that  if  A  represents 
the  area  of  water  plane,  that  this  surface  multiplied  by  a  layer 
1  inch  in  thickness  and  divided  by  12  will  equal  the  volume  of 
water  displaced  in  cubic  feet  at  the  particular  water  plane  dealt 
with,  and  that  this  volume  divided  by  35  will  equal  the  displace- 
ment in  tons  for  one  inch,  or  in  other  words,  the  tons  per  inch 
immersion.     Or, 

^  x  To  =  To  CUDic  feet» 

and  the  weight  of  water  in  the  layer 
A       1        A 


420 


=  tons  per  inch. 


Tons  per  inch  immersion  in  salt  water, 

area  of  water  plane 
•  420  ' 

Tons  per  inch  immersion  in  fresh  water, 

area  of  water  plane  > 

(12  X  36)  =  432 

So  that  referring  to  the  table  we  have  been  working  out,  we  get :  — 


Keel. 

W.L.  l. 

W.L.  2. 

W.L.  3. 

W.L.  4. 

Area  of  water  plane 

12"  X  35  =     .     .     . 

Tons  per  inch  = 

4.00 

4*5o 
.01 

335.46 

4J0 

.79 

577.86 

420 
1.37 

741.06 

4J0 
1.76 

832.14 

420 
1.98S.W. 

It  is  often  necessary  to  estimate  the  tons  per  inch  approxi- 
mately, and  for  this  purpose  the  coefficient  of  the  load  line  or 
"a"  is  used.  The  method  of  arriving  at  this  coefficient  is  ex- 
plained in  the  chapter  on  design  when  the  displacement  is  known. 


Immersion,  from  Salt  to   Fresh  Water       9 

It  has  a  range  of  about  .6  iu  fine  vessels  to  .9  in  exceptionally 
full  ones.     In  the  above  example  it  is  found  to  be 
832.14  832.14 


Length  x  Breadth  ~  1200 
Therefore  the  tons  per  inch  is  equal  to 
L  x  Bx  .694 


.694. 


=  1. 


420 

Its  relation  to  the  other  element  coefficients  is 

8 

Immersion  Passing  from  Salt  to  Fresh  Water. 

From  what  has  been  previously  said  it  will  be  obvious  that  the 
draught  of  water,  or  immersion  of  a  vessel,  will  undergo  a  change 
in  passing  from  fresh  water  into  the  sea  or  vice  versa,  owing  to 
the  difference  in  density  of  the  two  liquids.  If  we  take  the  case 
of  the  ship  passing  from  salt  water  to  fresh,  the  immersed  Volume 
will  be  in  each  case  as  follows  :  — 

Immersed  volume  in  salt  water    =  35  J), 
Immersed  volume  in  fresh  water  =  36  D, 

where  D  is  the  displacement  in  tons,  which  in  the  example  we 
have  been  investigating  equals  73.82  tons.  Therefore  the  volume 
in  cubic  feet  which  the  vessel  has  sunk  on  entering  the  fresh 
water  is  36  D  -  35  D  =  2657  -  2584  =  73  cubic  feet.  Let  T=  tons 
per  inch  immersion  in  fresh  water  .  • .  area  of  water  plane  =  432  T 
and  the  extent  to  which  the  vessel  will  sink 

73     .    4  12  x  73  73        ,  AO  .     , 

feet  =  in^  m-. — ; —  =  ttx-^7  =  1.02  inches. 


432  T  432  T  inches     36  T 

Inversely  we  have  the  amount  that  the  vessel  emerges  in 
passing  out  of  a  river  into  the  ocean.  Thickness  of  the  layer 
which  vessel  has  risen  in  feet 

_Difference  in  volume  I) 
Area  of  the  plane 
and  in  inches, 

Difference  in  Volume  D  x  12-_  12  X  73  _  73   _       _  . 
Area  of  water  plane  ~  420  T  ~  69.3  — 

This  immersion  and  emersion  is,  of  course,  the  mean  amount  as 
the  vessel  will  also  slightly  change  her  trim  due  to  the  altered 
position  of  the  centre  of  gravity  of  water  plane,  about  which  the 
ship's  movements  are  pivotal. 


10 


The  Naval  Constructor 


Area  of  Midship  Section  (X  -4)- 

The  area  of  this,  or  any  of  the  other  sections  on  the  displace- 
ment table,  is  calculated  by  taking  the  half-breadths  of  the 
water  lines  and  integrating  them  as  explained  for  water-line  area. 
The  sum  of  the  products  thus  obtained  is  multiplied  by  f  the 
distance  of  water  lines  apart,  and  that  result  by  2  for  both  sides. 
Where  the  vessel  has  little  rise  of  floor  a  half  water  line  should  be 
introduced,  and  the  bottom  half-breadth  proportioned  to  the  rise 
line,  as  pointed  out  in  the  displacement  calculation.  In  the 
example  with  which  we  are  dealing,  however,  the  vessel  has 
considerable  rise,  so  that  this  subdivision  has  been  omitted. 


Ordinate. 

Keel. 

W.L.  1. 

W.L.  2. 

W.  L.  3. 

W.L.  4. 

"5" 

Half- 
Breadth. 

Half- 
Breadth. 

Half- 
Breadth. 

Half- 
Breadth. 

Half- 
Breadth. 

Simpson's 
Multipliers 

.02 

i 

3.54 

2 

5.20 
1 

5.80 
2 

6.00 
1 

.01     +    7.08    +    5.20    +  11.60    +  3.00 

=  26.89 

$  distance  between  water  lines x  .83 

Half  area  of  midship  section  to  L. W.L.      .     .     .    =22.31 

For  both  sides x2 

Midship  section  area =44.62 

The  coefficient  of  this  area,  or  /3,  is  a  very  important  element 
of  the  design  as  explained  elsewhere,  and  is  obtained  by  dividing 
the  midship  area  by  the  area  of  the  rectangle  formed  by  the 
molded  breadth  and  the  draught,  or 


Mid.  area 


Breadth  x  draught 


44.62 
60 


=  .743  coefficient  of  mid.  area. 


Its  relation  to  the  midship-section  cylinder  or  prismatic  co- 
efficient "p"  is  ->  and  "p"  is  equal  to  the  volume  of  dis- 
placement  divided  by  the  length  x  mid.  area,  thus  :  — 


P  = 


and  consequently, 


L  x  B  x  d  x  5 
L x  B x  dx p 


0 


=  prismatic  coefficient, 


Centre  of  Buoyancy  11 

Centre  of  Buoyancy  (C.B.). 

The  centre  of  buoyancy  of  the  displaced  water  is  simply  its 
centre  of  gravity,  and  its  location  below  the  load-water  line  is 
greater  or  less  in  accordance  with  the  form  of  the  immersed  body. 
This  distance  may  be  found  by  dividing  the  under-jvater  part  into 
a  number  of  planes  parallel  to  the  load  line,  and  multiplying  the 
volumes,  lying  between  these  water  planes,  by  their  depth  below 
load-water  line.  These  moments  divided  by  the  displacement 
volume  will  give  the  location  of  centre  of  buoyancy  below  load- 
water  plane.  So  that  by  taking  the  functions  of  the  products  at 
each  water  plane  on  the  sheet  we  have  been  working  and  multi- 
plying them  by  the  number  of  the  water  line  they  represent 
below  L.W.L.,  and  dividing  the  sum  of  those  products  by  the 
sum  of  the  functions  referred  to,  we  shall  have  the  number  of 
water-line  intervals  (or  fraction  of  an  interval),  which  the  C.B. 
is  below  load-water  line.  This  result,  multiplied  by  the  common 
interval  between  water  lines,  will  give  the  required  distance  in 
feet. 

Keel.    W.L.I.     W.L.  2.       W.L.  3.       W.L.  4. 
Functions  of 

products 


.15  -f  50.32  +  43.34  +  109.36  +  31.20  =  234.37 
4  3  2  10 


.60  4-150.96  +  86.68  +  109.36  +         0  =  347.60 
347.6  4-234.37  =       1.49 
x 

Water  lines  apart =      1.25 

Centre  of  buoyancy  below  W.L.  4 =      1.86  ft. 

The  centre  of  buoyancy  may  be  determined  from  the  displace- 
ment curve  by  calculating  the  area  enclosed  within  the  figure 
formed  by  the  vertical  line  representing  the  draught  of  5  ft., 
the  horizontal  line  equal  to  the  tons  displacement  at  this  draught 
and  the  curve  itself.  This  area  divided  by  the  length  of  the  hori- 
zontal line  referred  to,  will  give  the  depth  of  C.B.  below  L.W.L. 
In  the  present  example  we  have  :  area  =  138.6  sq.  feet,  and 
length  of  horizontal  line  (displacement  in  tons)  =  73.82,  and 

138.6      ,  «.  -, 
^  =  1-87  feet, 

distance  of  C.B.  below  L.W.L. 

A  like  result  may  also  be  obtained  by  taking  the  sum  of  the 
products  of  each  water  line,  and  dividing  them  by  the  sum  of 
Simpson's  multipliers.  The  mean  half-breadths  of  water  lines 
so  obtained  may  be  then  used  to  draw  a  mean  section  of  the 


12 


The  Naval   Constructor 


vessel  on  stout  paper,  which  on  being  cut  out  with  a  knife  and 
swung  in  two  positions,  the  points  being  intersected  afterwards, 
will  give  the  centre  of  gravity  (buoyancy)  very  accurately. 

Various  approximate   methods  are   in  vogue  for  finding  this 
centre,  some  of  which  are  fairly  accurate. 

— a )' 

(2)   Approx.  C.B.  below  L.  W.L.  =  H|  +  Z  Y 

where  A  is  the  area  of  load-water  plane. 

This  centre,  as  will  be  explained,  has  an  important  bearing  on 
the  stability  of  the  ship. 

Centre  of  Buoyancy  Longitudinally  (L.C.B.). 


Ordin- 

ATES. 

Areas. 

Multi- 
pliers. 

Func- 
tions. 

Inter- 
vals. 

Moments. 

After 
Moment. 

0 

.24 

\ 

.06 

5 

.30 

\ 

1.91 

1 

1.91 

*l 

8.59 

1 

6.17 

| 

4.63 

4 

18.52 

2 

14.18 

2 

28:36 

3 

85.08 

3 

21.40 

1 

21.40 

2 

42.80 

4 

5 

25.71 
26.89 

2 
1 

51.42 
26.89 

1 

0 

51.42 

206.71 

6 

24.14 

2 

48.28 

1 

48.28 

Forward 

7 

18.86 

1 

18.86 

2 

37.72 

8 

12.65 

2 

25.30 

3 

75.90 

9 

5.92 

\ 

4.44 

4 

17.76 

n 

2.83 

1 

2.83 

H 

12.74 

10 

.08 

\ 

.02 

5 

.10 

192.50 

Preponder-  "^ 
ating 
moment     J-=  14.21 

Function  of  disj 

)lacemen 

I   .     .  = 

234.40 

abaft,  Ordi-  | 
nate  5.      J 

14.21 
23474 
Common  Interval  =  10  ft.  x  .06 


=  .00  Interval  C.B.  abaft  5. 

0.6  ft.  C.B.  abaft  No.  5. 


The  locus  of  the  centre  of  buoyancy  in  a  fore-and-aft  direction 
is  of  course  the  centre  of  gravity  of  the  displacement,  and  is  the 


Transverse  Metacentre  13 


pivotal  point  or  fulcrum  for  the  moments  of  all  weights  placed 
forward  or  aft  of  this  position.  It  will  be  obvious,  therefore,  that 
its  location  is  of  great  value  in  determining  the  trim  of  the  vessel, 
and  the  various  alterations  thereof  due  to  rearrangements  of 
weights  on  board.  Its  position  is  calculated  by  taking  the  areas  of 
the  sections  and  putting  them  through  the  multipliers  ;  these 
functions  of  areas  are  in  turn  multiplied  by  the  number  of  inter- 
vals, (each  one  is  forward  or  aft  of  the  inid-ordinate,)  and  the 
difference  between  these  forward  and  after  moments  divided  by 
the  sum  of  the  area  functions.  The  quotient  resulting  is  the 
number  (or  fraction)  of  intervals  that  the  centre  of  buoyancy  is 
forward  or  aft  of  the  \  length  according  as  the  moment  prepon- 
derates forward  or  aft  respectively. 

This  centre  should  be  calculated  for  various  draughts,  as  of 
course  it  changes  with  different  draughts  and  alterations  of  trim, 
owing  to  the  changing  relationship  between  the  fineness  of  fore 
and  after  bodies  at  different  immersions  and  trims. 

Transverse  Metacentre  (M.C.) 

The  position  of  this  element  is,  in  conjunction  with  the  centre 
of  gravity,  the  most  vital  in  the  design  of  the  ship.  As  its  name 
implies,  it  is  the  centre  or  point  beyond  which  the  centre  of  gravity 
of  the  ship  may  not  be  raised  without  producing  unstable  equilib- 
rium in  the  upright  position,  or,  otherwise  stated,  if  the  ship  be 
inclined  transversely  to  a  small  angle  of  heel,  the  centre  of 
buoyancy  which  originally  was  on  the  centre  line  will  move  out- 
board to  a  new  position  ;  but,  as  it  acts  vertically  upward,  it  must 
somewhere  intersect  the  centre  line.  This  point  of  intersection  is 
known  as  the  metacentre.  One  of  the  factors  in  the  determination 
of  its  location  above  the  centre  of  buoyancy  has  already  been 
calculated,  viz  :  the  volume  of  displacement  V ;  the  other,  the 
moment  of  inertia  of  the  water  plane  about  the  centre  line  of  ship, 
we  shall  proceed  to  compute.  The  height  M  above  the  C.B.  or 
B.M.  is  found  by  :  — 

Moment  of  Inertia  of  Water  Plane  I  _ 

Volume  of  Displacement  '      '   V  ~ 

The  moment  of  inertia  of  the  water  plane  is  a  geometrical 
measure  of  the  resistance  of  that  plane  to  "upsetting,"  or  when 
taken  about  the  centre  line,  as  in  the  case  of  calculating  for  trans- 
verse metacentre,  to  "careening."  So  that  the  greater  the  water- 
line  breadth  the  higher  will  be  its  value ;  for  we  must  imagine  the 
water  plane  as  being  divided  into  a  great  number  of  small  areas, 
and  each  of  these  multiplied  by  the  square  of  its  distance  from  the 


14 


The  Naval  Constructor 


centre  line  of  ship,  when  the  sum  of  these  products  will  equal  the 
moment  of  inertia  of  half  the  water  plane,  about  the  middle  line 
of  vessel  as  an  axis.  As  both  sides  of  the  water  plane  are  sym- 
metrical, the  total  i"  will  be  this  result  multiplied  by  2.  Applying 
this  principle  to  W.L.  4  in  the  example  with  which  we  are  con- 
cerned, we  get  the  following  tabular  arrangement :  — 

Moment  of  Inertia  of  "Water  Plane  (I). 


Ordi- 

Half- 

Cubes  op 

Simpson's 

Breadths 

Half- 

Mul- 

Products. 

of  W.L.  4. 

Breadths. 

tipliers. 

0 

.04 

i 

\ 

1.41 

2.74 

2.74 

1 

3.10 

29.79 

3 

22.34 

2 

4.81 

111.28 

2 

222.56 

3 

6.56 

171.88 

1 

171.88 

4 

6.96 

211.71 

2 

423.42 

5 

6.00 

216.00 

1 

216.00 

6 

6.58 

173.74 

2 

347.48 

7 

4.87 

115.50 

1 

115.50 

8 

3.57 

45.50 

2 

91.00 

9 

1.90 

6.86 

3 

i 

5.14 

»i 

.97 

. 

10 

.03 

¥ 

1,618.06 
f  C.I (US 

10,787.07 

| 

Moment  of  Inertia =  7,191.38 

Volume  of  Displacement,  V =  2,583.70 

_  _  _        I       7191.38      _  nn  .t 
B-M-=F=^583T  =  2-77ft- 

The  calculation  for  Moment  of  Inertia  and  Transverse  Meta- 
centre  above  C.B.  may  be  more  easily  remembered  if  we  treat  the 
cubes  of  water  line  half-breadths  as  the  ordinates  of  a  curve  two- 
thirds  the  area  of  which  will  equal  I,  and  this,  in  turn,  divided  by 
Twill  give  B.M. 

However,  when  we  know  a,  or  the  coefficient  of  water  line,  we 
may  arrive  very  accurately  at  the  moment  of  inertia  of  the  water 


Longitudinal   Metacentre  15 

plane,  and  consequently  at  the  B.M.  without  the  labor  of  the 
foregoing  calculation  by  multiplying  the  Length  by  the  Breadth3  by 
a  coefficient,  which  coefficient  will  be  determined  by  a  and 
selected  from  the  table  given  on  page  48.  By  referring  to  this 
table,  we  find  for  a  (value  .694)  that  the  coefficient  "i"  (inertia 
coefficient)  is  equal  to  .0414,  whence  we  get  I  =  L  x  J33  X  i  —  100 
X  123x  .0414=7154  moment  of  inertia,  which  is  sufficiently  close 
for  all  purposes,  and  :  — 

By  transposing  and  taking  the  calculated  I,  we  find 
7191 


100  X  123 


= .0416. 


Longitudinal  Metacentre  (L.M.C.) 

From  the  definition  given  for  the  transverse  metacentre  it  will 
be  seen  that  if  the  ship  be  inclined  longitudinally,  instead  of,  as  in 
the  former  case,  transversely,  through  a  small  angle  that  the  point 
in  which  the  vertical  through  the  altered  C.B.  intersects  the 
original  one  will  also  give  a  metacentre  known  as  the  longitudinal, 
or  L.M.C.  Its  principal  use  and  value  are  in  the  determination  of 
the  moment  to  alter  trim  and  the  pitching  qualities  of  the  vessel, 
or  longitudinal  stability.  It  will  be  obvious  that  the  moment  of 
inertia  of  the  water  plane  must  be  taken  through  an  axis  at  right 
angles  to  the  previous  case,  viz.,  at  right  angles  to  the  centre  line 
through  the  centre  of  gravity  of  water  plane,  which  will  be  where 
the  original  and  new  water  planes  cross  one  another  in  a  longitu- 
dinal view. 

t  ™  r,     v        ^  t>       A  of  Water  Plane  about  its  C.G. 

L.M.C.  above  C.B.  = ^rr-. -— — = • 

Volume  of  Displacement 

Therefore,  to  calculate  the  M  Ji,  we  must  figure  the  moment  of 
inertia  with,  say,  ordinate  5  (or  any  other  one)  as  an  axis  when 
the  moment  about  a  parallel  axis  through  the  centre  of  gravity 
plus  the  product  of  the  area  of  water  plane  multiplied  by  the 
square  of  the  distance  between  the  two  axes  will  equal  the  moment 
about  ordinate  5. 

The  moment  of  inertia  about  the  midship  ordinate  we  shall  call 
I,  and  the  distance  of  the  centre  of  gravity  from  this  station  =  x. 
The  moment  of  inertia  about  the  centre  of  gravity  of  plane  =  Ix. 
We  then  have  I = I\  +  Ax2,  or  Ix  =  I  —  Ax2.  A  clearer  conception 
of  this  will  be  obtained  from  the  tabulated  arrangement. 


16 


The  Naval  Constructor 


Longitudinal  Metacentre. 
(Common  Interval  10  Feet.) 


00 

X 

5      H 

Pro- 

Pro- 

a 8  . 

Products 

Ordi- 

NATES. 

ducts 

fok 

Area. 

W 

« 
3 

ducts 
for  Mo- 
ments. 

*a 

Pm 

Moments 

OF 

Inertia. 

0 

.04 

1 

I 

.01 

5 

.05 

5 

.25 

| 

1.41 

1.41 

4i 

6.34 

4h 

28.53 

1 

8.10 

3 

2.32 

4 

9.28 

4 

37.12 

2 

4.81 

2 

9.62 

3 

28.86 

3 

80.58 

3 

5.5G 

1 

5.50 

2   * 

11.12 

2 

22.24 

4 

5 
6 

696 
6.00 
5.58 

2 
1 

2 

11.92 

6.00 

11.16 

1 
0 
1 

11.92 

1 
0 
1 

11.92 
11.16 

67.57 

11.16 

7 

4.87 

1 

4.87 

2 

9.74 

2 

19.48 

8 

3.57 

2 

7.14 

3 

21.42 

3 

64.26 

9 

1.90 

f 

1.42 

4 

5.68 

4 

22.72 

9i- 

.97 

.97 

4* 

4.36 

4* 

19.62 

10 

.03 

i 

.01 

5 

.05 

5 

.25 

62.41 

52.41 

324.13 

Area  of  water  plane  =  62.41  X  (f  X  10)  x  2. 
=  832.14  square  feet. 

Distance  of  centre  of  flotation  abaft  ordinate  5 


(67.57-52.41)  10 
62.41 


=  2.42  feet. 


Moment  of  inertia  of  water  plane  about  ordinate  5 

=  324.13  x  (I  x  10)  x  102  x  2  =  432,172  =  I. 

Moment  of  inertia  of  water  plane  about  axis  through  its  centre 
of  flotation. 

=  432,172  -  (832.14  X  2.422)  =  427,304  =  Jv 

Longitudinal  metacentre  above  C.B. 

T  ~  loWT  =  165  feet  =  Lonsitudinal  B- M- 


Moment  to  Change  Trim  17 

An  excellent  approximate  formula  for  the  longitudinal  B.M.  is 
given  by  J.  A.  Normand  in  the  1882  transactions  of  the  I.N. A. 
Taking  the  symbols  we  have  been  using  :  — 

L.B.M.=.0735^i.       -^ 

Applying  this  formula  to  the  vessel  with  which  we  are  dealing, 
we  find : 

-•M.  =  .0735f^|^=10.12fee, 

which  is  a  very  close  approximation  ^°  the  calculated  result  of 
165  feet. 

We  may  also  use  the  apipruximate  formula  which  we  applied  in 
the  case  of  the  transverse  B.M.  altered  to  suit  the  new  axis  with  a 
modified  coefficient,  as  :  — 

L.B.M.  =L*xBx  h. 
Moment  to  Change  Trim  (Mi). 

As  the  centre  of  gravity  of  the  displacement  (or  centre  of  buoy- 
oncy),  either  in  the  vertical  or  the  longitudinal  direction  may  be 
an  entirely  different  locus  from  the  ship's  centre  of  gravity,  it  is 
obvious  that  unless  the  moment  of  the  weights  of  the  ship  and 
engines,  with  all  equipment  weights,  balances  about  the  centre  of 
buoyancy  we  shall  have  a  preponderating  moment  deflecting  the 
head  or  stern,  as  the  moment  is  forward  or  aft  of  the  C.B.,  re- 
spectively, until  the  vessel  shall  have  reached  a  trim  in  which  the 
pivotal  point  or  C.B.  is  in  the  same  vertical  line  as  the  completed 
ship's  centre  of  gravity.  To  determine  the  moment  necessary  to 
produce  a  change  of  trim  (M i)  in  a  given  ship,  it  is  necessary  to  know 
the  vertical  position  of  the  centre  of  gravity  of  the  vessel  and  the 
height  of  the  longitudinal  metacentre  (L.M.C.).  The  former  may 
be  calculated  in  detail  or  preferably  proportioned  from  a  similar 
type  ship  whose  centre  of  gravity  has  been  found  by  experiment ; 
although  great  accuracy  in  the  location  of  this  centre  in  calculat- 
ing the  moment  is  not  as  important  as  in  the  case  of  G.M.  for 
initial  stability,  as  small  variations  in  its  position  can  only  affect 
the  final  result  infinitesimally.  To  investigate  the  moment  affect- 
ing the  trim,  let  us  move  a  weight  P  already  on  board  of  the  100- 
foot  steamer  whose  calculations  are  being  figured. 

D  =  Weight  of  ship  including  weight  P  =  73.82  tons. 
BM  =  165  feet.  P  =  5  Tons.  4 

GM  =  160  feet.  I  =  50  feet  (distance  moved). 

L  —  100  feet  (length  of  vessel). 


18 


The  Naval  Constructor 


In  the  figure  we  have  the  centre  of  gravity  G  to  Gu  and  the 
centre  of  buoyancy  from  B  to  Bt,  due  to  the  shifting  of  the  weight 
P  forward  for  a  distance  represented  by  I,  giving  a  moment 

Dx  GGl  =  Pxl,     and     GGX  =  —^1' 


Fig.  6. 

The  new  water  line  is  at  W\L\  and  BxGx  are  in  the  same  verti- 
cal and  at  right  angles  to  it,  and  the  point  of  intersection  of  the 
original  and  new  water  line  at  uO"  equal  to  the  centre  of  gravity 
(flotation)  of  water  plane,  therefore  the  triangles  GMGX,  WOWi, 
and  LOLi,  are  of  equal  angle,  so  that 

GGj  _  WWj  _  LLx  _  WWX  +  LLX 
GM  ~  WO  ~  L0~    WO  +  LO  ' 

But  WWx  +  LLi  is  the  change  of  trim,  and  WO  +  LO  is  the  length 
of  the  vessel  =  X,  then 


change  of  trim 
L~ ~ 
but  we  have  seen  that 


WWX  +  LLX  . 


GG1  = 


~     WO+LO 
GM  X  change  of  trim      P  x  I 


Then 


Change  of  trim  = 


P  x  Ix  L 
Dx  GM 


J) 


feet. 


Substituting  the  values,  we  get :  — 
P  xlx  L      5  X  50'  x  100' 


D  x  GM 


73.82  X  100 


=  2. 116  feet  =  24^  inches. 


Calling  this  change  of , trim  24  inches,  and  assuming  that  the  point 
of  intersection  u  O  "  is  at  the  centre  of  the  length,  we  should  have 


Moment  to  Alter  Trim  One  Inch        19 

the  stem  immersed  12  inches  and  the  stern  raised  12  inches  from 
the  original  water  line,  the  sum  of  these  figures  equalling  the 
total  change. 

Moment  to  Alter  Trim  One  Inch  {M"). 

From  the  foregoing  it  will  be  seen  that  the  total  change  of  trim 
being  known  for  a  given  moment,  inversely  we  may  get  the 
amount  necessary  to  alter  the  trim  for  one  inch  only,  this  being  a 
convenient  unit  with  which  to  calculate  changes  of  trim  when  a 
complexity  of  varying  conditions  are  being  dealt  with.  As  we 
have  seen  Pxl  =  M%  the  moment  to  change  trim,  and 


therefore, 


Change  of  trim  =  D  x  GM  feet  ; 


•     ,       D  x  GM      __ 

TX2  foot  or  one  inch  =  =  M ". 


12  x  L 
Substituting  values  we  have  :  — 

In  designing  preliminary  arrangements  of  vessels,  it  is  necessary 
that  we  should  know  fairly  accurately  the  moment  which  it  will 
take  to  alter  the  trim  one  inch  (M")  to  enable  us  to  arrange  the 
principal  weights  in  the  ship,  and  the  varying  effects  on  the  trim 
consequent  on  their  alteration  in  position  or  removal.  For  this 
purpose  a  close  approximation  to  this  moment  (M")  is  desirable 
and  may  be  calculated  from  Normand's  formula  as  follows  : 

If"  =  ^.0001725,    or    HX8M. 
Jo  x> 

Where  .A2  =  the  square  of  the  water  plane  area,  and  B  —  the  great- 
est breadth  of  water  plane.  Applying  this  approximate  formula 
to  the  foregoing  example,  we  have :  — 

QQO    142 

Jf"=       '       x  .0001725  =  9.95  foot-tons, 
12 

as  against  9.84  foot-tons  found  by  actual  calculations,  a  difference 
too  insignificant  to  affect  noticeably  the  change  in  trim. 

This  moment  is  useful  to  have  for  various  draughts,  and  con- 
sequently should  be  calculated  for  light  and  load  conditions,  and 
for  one  or  two  intermediate  spots  and  a  curve  of  M"  run  on  the 
usual  sheet  of  "  Curves  of  Elements." 


20 


The  Naval  Constructor 


Alteration  in  Trim  through  Shipping   a   Small 
Weight. 

If  it  be  required  to  place  a  weight  on  board  but  to  retain  the 
same  trim,  i.e.,  to  float  at  a  draught  parallel  to  the  original  one, 
the  weight  added  must  be  placed  vertically  above  the  centre  of 
gravity  of  the  water  plane.  Should,  however,  the  weight  be  re- 
quired in  a  definite  position,  then  the  altered  trim  will  be  as 
under: — 


Fig.  7. 

Instead  of  dealing  with  the  weight  at  P  let  us  assume  firstly 
that  it  is  placed  on  board  immediately  over  the  C.G.  of  water 
plane,  when  we  shall  find  the  parallel  immersion  to  be  a  layer 

P 
equal  to  the  distance  between  WL  and  W\Li  whose  depth  is  -^ 

V 
Let  the  weight  be  now  moved  to  its  definite  position  at  a  distance 
I  forward  of  C.G.,  then 

Change  of  trim  =  ^j^-  =  V. 

GM  of  course  will  be  the  amended  height  due  to  altered  con- 
dition after  the  addition  of  P.     Then  :  — 


Draught  forward 
Draught  aft 


C_  __P 

2       Wtr 


Of  course  we  assume  that  the  alteration  is  of  like  amount  for- 
ward as  aft.  This  is  only  partly  correct,  but  where  small  weights 
are  dealt  with  is  sufficiently  so  for  most  purposes.  Generally  the 
ship  is  fuller  aft  on  and  near  the  load  line  than  forward,  and  prob- 
ably a  water  plane  midway  between  base  and  L.W.L.  would  have 
its  centre  of  flotation  at  the  half  length,  so  that  a  curve  drawn 
through  the  centres  of  gravity  of  the  water  planes  would  incline 
aft,  and  as  we  have  assumed  the  weight  as  being  placed  on  board 
over  the  C.G.  of  the  original  water  plane,  it  is  obvious  that  the 


TchibyschefFs  Rule  21 

new  line  will  have  its  centre  of  flotation  somewhat  further  aft, 
and  consequently  the  tangent  of  the  angle  W1OW2  will  be  less 
than  that  of  L\OL%.  With  large  weights  and  differences  in  the 
two  draughts,  the  disparity  would  become  sufficiently  great  to 
require  reckoning,  in  which  event  the  assumed  parallel  line  in  the 
preceding  case  would  give  the  water  line  from  which  to  determine 
the  centre  of  flotation.  Thereafter  on  finding  the  change  of  trim, 
which  we  shall  call  10  inches,  the  amount  of  immersion  of  stem 
and  emersion  of  stern  post  would  be  in  proportion  to  the  distance 
from  0  to  stem  and  O  to  post  relatively  to  the  length  of  water  line. 
If  we  call  "  O  "  to  stem  60  feet  and  "  0  "  to  post  40  feet,  the  water 
line  length  being  100  feet,  we  have  :  — 

Immersion  forward  TW  x  10"  =  6  inches  )  Total  change 
Emersion  aft  T4o0^  X  10   =  4  inches  \      10  inches. 


TCHIBYSCHEFF'S   RULE. 

In  the  preceding  pages  we  have  treated  with  the  common  appli- 
cation of  Simpson's  first  rule  to  ship  calculations.  Another 
method,  equally,  if  not  more  simple,  which  is  slowly  gaining 
favor  with  naval  architects  is  that  devised  by  the  Russian  Tchi- 
byscheff.  This  rule  has  the  great  advantage  of  employing  fewer 
figures  in  its  application  ;  more  especially  is  this  the  case  in  deal- 
ing with  stability  calculations,  and  its  usefulness  in  this  respect 
is  seen  in  the  tabular  arrangement  given  here.  It  has  the  addi- 
tional advantage  of  employing  a  much  less  number  of  ordinates 
to  obtain  a  slightly  more  accurate  result  and  the  use  of  a  more 
simple  arithmetical  operation  in  its  working  out,  viz.  addition. 
As  the  ordinates,  however,  are  not  equidistant,  it  has  the  dis- 
advantage of  being  inconvenient  when  used  in  conjunction  with 
designing,  and  for  this  reason  its  use  is  advocated  for  the  finished 
displacement  sheet  and  calculations  for  G.Z. 

The  rule  is  based  on  a  similar  assumption  to  Simpson's,  but  the 
ordinates  are  spaced  so  that  addition  mostly  is  employed  to  find 
the  area.  The  number  of  ordinates  which  it  is  proposed  to  use 
having  been  selected,  the  subjoined  Table  gives  the  fractions  of 
the  half  length  of  base  at  which  they  must  be  spaced,  starting 
always  from  the  half  length.  The  ordinates  are  then  measured 
off  and  summed,  the  addition  being  divided  by  the  number  of  the 
ordinates,  giving  a  mean  ordinate,  which  multiplied  by  the  length 
of  base  produces  the  area  :  — 

Sum  of  ordinates     _  ,  , 

s -x — -r. — — -  x  Length  of  base  =  Area. 

No.    of  ordinates  & 


22  The  Naval  Constructor 

Tchibyscheff's  Ordinate  Table. 


Number 

Distance  of  Ordinates  from  Middle 

of  OR- 

of Base,  ^  ,  in 

DINATES. 

Fractions  of  Half  the  Base  Lenoth. 

2 

.5773 

3 

X,  -7071 

4 

.1876,      .7947 

5 

X,    .3745,      .8325 

6 

.2666,      .4225,      T8662 

7 

X,  -3239,     .5297,     .8839 

9 

3£,   .1679,     .5288,    .6010,     .9116 

10 

.0838,     -3127,     .5000,     .6873,     .9162 

The  employment  of  this  rule  to  find  the  volume  of  displace- 
ment and  the  other  elements  usually  tabulated  on  the  displace 
ment  sheet  is  shown  on  the  attached  Tables.  The  number  oi 
stations  used  is  ten,  as  in  the  case  of  Simpson's  rule,  but  for 
clearness  the,  after  body  five  are  indicated  by  Roman  numerals, 
and  the  fore  body  ones  in  Arabic.  The  displacement  length  is 
600  feet,  therefore  by  taking  the  fractions  given  in  the  preceding 
table  for  ten  ordinates  and  multiplying  them  by  300,  we  shall 
obtain  the  distance  of  the  displacement  sections  apart.  These 
distances  from  the  half-length  and  the  sections  are  here  given  as 
used  for  the  Table,  but  it  will  be  observed  that  the  water  lines  are 
spaced  to  suit  Simpson's  first  rule  for  the  vertical  sections  as  no 
advantage  would  be  gained  by  the  use  of  Tchibyscheff  in  this 
direction,  owing  to  the  fewer  number  of  water  lines  generally  neces- 
sary. The  various  operations  in  the  Table  will  be  clearly  under- 
stood from  the  headlines  of  the  respective  columns. 

As  already  pointed  out,  the  great  value  of  this  rule  is  in  the  cal- 
culations to  obtain  cross  curves  of  stability,  specimen  tables  of 
which  are  also  given.  The  fewness  of  the  section's  necessary,  and 
the  fact  that  the  integrator  saves  the  calculator  the  tedium  of  add- 
ing up,  tells  greatly  in  favor  of  the  adoption  of  this  rule  for  these 
calculations  both  as  a  time  saver  and  an  eliminator  of  the  chances 
of  error. 


T.  S.  S,   "Lucania' 


23 


T.  S.  S.  "LUCANIA" 

BODY  SECTIONS  FOR  DISPLACEMENT  ETC.  BY     TCHIBYSCHEFF'S  RULE 
(for  calculation  see  table) 
ORDINATES  FROM  AMIOSHIPS:- 

BEFORE       ABAFT 

1-  —  & I  --  ■    25.14 

2,_.&._.U__  m     93.90 
3--.A— 111--  =  150.00 
4.__&.__VI__  =  206.10 
27.4.  { 


WATER-LINES  3.833'  APART 


24 


The  Naval  Constructor 


Displacement  Sheet  by 


Stations 

Water  Lines. 

1 

1 

2 

3 

4 

1 

1 

i 

2 

1 

2 

I 

.60 
.15 

29.35 
29.35 

31.20 

23.40 

32.30 
64.60 

32.50 
32.50 

32.50 
65.00 

1 

.60 
.15 

29.35 
29.35 

31.20 

23.40 

32.25 
64.50 

32.50 

32.50 

32.50 
65.00 

II 

.60 
.15 

26.25 
26.25 

28.84 
21.63 

31.00 

62.00 

31.30 
31.30 

31.40 
62.80 

2 

.60 
.15 

25.00 
25.00 

27.35 
20.51 

29.25 
58.50 

30.00 
30.00 

30.20 
60.40 

III 

.60 
.15 

16.90 
16.90 

20.85 
15.64 

24.60 
49.20 

26.55 

26.55 

27.85 
55.70 

3 

.60 
.15 

17.50 

17.50 

19.85 
14.89 

22.15 
44.30 

23.35 
23.35 

24.15 
48.30 

IV 

.60 
.15 

7.80 

7.80 

11.10 
8.33 

14.80 
29.60 

17.50 
17.50 

19.40 
38.80 

4 

.60 
.15 

7.00 
7.00 

11.15 
8.36 

13.20 

26.40 

14.45 
14.45 

15.35 
30.70 

V 

.60 
.15 

1.00 
1.00 

1.50 
1.13 

2.55 
5.10 

3.55 
3.55 

4.65 
9.30- 

5 

.00 
.00 

.00 
.00 

.15 
.11 

2.20 
4.40 

3.10 
3.10 

3.65 
7.30 

Sum  of 
Ordinates 

5.40 

160.15 

183.19 

204.30 

214.80 

221.65 

Functions 

1.35 

160.15 

137.38 

408.60 

214.80 

443.30 

Levers 

7.00 

6.50 

6 

5 

4 

3 

Moments 

9.45 

1,040.98 

824.28 

2,043.00 

859.20 

1,329.90 

Multipliers  for  Areas 

Areas  of 
Water 
Lines 

648.00 

19,218.00 

21,983.00  24,516.00 

25,776.00 

26,598.00 

Divisor  for  Tons 

Tons  per 
Inch 

r= 

D  = 

1.543 1        45.76        52.36|      58.371  |        61.37  |        63.29 

■rv    ,              .  .        ,.    ,       2X600X2X  3.833 
Displacement  m  cubic  feet ^  ^  ,  A  . x 

o  X  10  * 

_.    .              L  .    .                    1 2  x  600  x  2  x  3.833 
Displacement  in  tons     .     .  1 3  x  10  x  35 —  x 

10: 


A  =  Distance  of  Ordinates. 
number  of  stations.  t  3  =.  Simpsons'  multiplier. 


Displacement  Tables 


25 


Tchibyscheff s  Rule. 


Vertical  Sections. 

5 

6 

7 

Func- 
tions. 

Differ- 
ences. 

Levers. 

Mo- 
ments. 

1 

2 

* 

32.50 
32  50 

32.40 
64.80 

32.35 
16.18 

328.48 

.13 

.0838 

.109 

32.50 

32.50 

32.40 
64.80 

32.30 
16.15 

328.35 

31.45 
31.45 

31.50 
63.00 

31.45 
15.73 

314.31 

13.60 

.313 

4.259 

30.25 
30.25 

30.35 

60.70 

30.40 
15.20 

300.71 

28.55 
28.55 

29.10 
58.20 

29.25 

14.63 

265.52 

29.48 

.500 

14.740 

24.65 

24.65 

25.10 

50.20 

25.40 
12.70 

236.04 

21.00 

21.00 

22.45 

44.90 

23.70 
11.85 

179.93 

34.24 

.687 

23.523 

16.10 

16  10 

16.90 
33.80 

17.45 
8.73 

145.69 

5.75 
5.75 

6.90 
13.80 

8.25 
4.13 

43.91 

13.50 

.916 

12.367 

4.10 

4.10 

4.50 
9.00 

4.80 
2.40 

30.41 

226.85 

231.60 

235.35 

=  2i 

2,173.31 

Distance 

54.998 

226.85 

463.20 

117.68 

Water  Lines  =  3.833' 

2 

1 

0 

453.70 

463.20 

0 

7,023.71 

of  Water  I 

jines :  *T°B0-  X 

2. 

Centre  of  Buoyancy. 

7,023.71  x  3.833      ,    _     (  below 

2,173.31        ~12d9  J  W.L.7 

54.998  X  600     „  rn/    ,    -.  -, 

=  7.59  abaft  3£ 

2,173.31X2                          * 

27,222.00 

27,792.00 

28,242.00 

per  Inch : 

420. 

64.814 

66.171 

67.243 

2,173.31  = 

:  666,445.2 

5 

2,173.31  = 

:  19,041.29 

X(3x0i+10x02— 03)  =  Moments. 


S1x-6To7°-X2  =  Area  of  Water 
Lines. 


The  Naval   Constructor 


Center  of  Buoyancy  and 


Water 

Links. 


Keel 
W.L.£ 
W.L.  1 

W.L.  1 
W.L.  2 
W.L.  3 

W.L.  3 
W.L.  4 
W.L.  5 

W.L.5 
W.L.  6 

W.L.  7 


/. 


5.40 
160.15 
183.19 

183.19 
204.80 
214.80 

214.80 
221.65 
226.85 

226.85 
231.60 
235.35 


Prod- 
is i.s. 


1.35 

160.15 

45.80 


207.31 

91.60 

408.60 

107.40 


814.90 
107.40 
443.30 
113.43 


1,479.03 
113.43 
463.20 
117.68 


!,  173.34 


Mo- 
ments. 


80.07 
45.80 


125.88 

91.60 

817.20 

322.20 


1,356.87 
322.20 

1,773.20 
567.15 


4,019.46 
567.15 

2,779.20 
823.76 


8,189.5/ 


Formula. 


3.833  x 


3.833  x 


3.833  x 


3.833  x 


125.87 
207.31 

1356.87 
814.90 

4019.46 
1479.07 

8189.57 
2173.38 


C.B. 

\  iw.\  i: 
Ki:i.i,. 


2.328 


10.420 


14.450 


Displacement  in 
Keel    to   W.L.  I,8  x  600  X  ^X  3.833  y     ^ 

W.L.  Ito  W.L.  2:  2X7*f33  x  2,336.50  = 
Keel  to  W.L.  3  :  2  X  6°°  *  2QX  3"833  x  814.90  = 
W.L.  !  t0  w.L.  4  ,  3X600X2X3833  ^  ^  „  = 

o  X   J  U 

Keel  to  W.L.  6  ,  2X600X2^X3.83.3  x  y^  = 
W.L.  4  to  W.L.  6:      «00  *  *  *  3-833    x  1,880.65= 

o  X   1U 

Tr    1    .      lirT    ,     2x600x2    X3.833     ft  „„,,  ,, 

Keel   to   W.L.  7  : x  2,173.34  = 

»j  x  10 


A2 
X  (SxO^SxOjj—  0,)  =  Area  by  f  rule.     —  x^xOj  +  IOxO.,— 03  =  Moments. 


Displacement  Tables 
Displacement,  by  Tchibyscheffs  Rule. 


27 


183.19 
204.30 
214.80 


183.19 
204.30 
214.80 
221.65 


221.65 
226.85 
231.60 


Prod- 
ucts. 


915.95 
1634.40 
-214.80 


2335.55 

183.25 
612.90 
644.40 
221.65 


1662.14 

221.65 
907.40 
231.60 


1360.65 


549.57 
2043.00 
-214.80 


Mo- 
ments. 


2377.77 

183.19 
1225.80 
1933.20 


4228.79 

886.60 
4537.20 
1389.60 


6813.40 


Formula. 


3.833  x 


2377.77 
2335.55 


C.B.  of  W.L.-W.L.2: 

5.783X89521  63+2.328x63574.52 


89521.63+63574.62 

3.833  x4228-79 


1662.14 

9.76X286577.44+2.328X63574.52 


280577.44+63574.1 


3.833  x 


6813.40 
1360.65 


19.2X208614.86+8.4X350151.96. 


208614.86  +  350151.96 


C.B. 
ABOVE 

Keel. 


1.95 
3.833 


5.783 
4.33 

9.76 
8.40 

19.20 
12.45 


Cubic  Feet 
63,574.521 

89,521.63 


286.577.44 


208,614.86 


=  V. 

Cubic  Feet.  C.B.  Above  Keel. 

63,574.52  =  Keel  to  W.L.  1.  2.328 


153,096.15  =  Keel  to  W.L.  2.  4.33 

249,912.80  =  Keel  to  W.L.  3.  6.383 

350,151.96  =  Keel  to  W.L.  4.  8.40 

453,558.21  =  Keel  to  W.L.  5.  10.420 

558,766.82  =  Keel  to  W.L.  6.  12.45 

666,445.24  =  Keel  to  W.L.  7.  14.45 


Lever  =s 


A2      (3  X  Oj  +  10  X  02-  03)_  A      (3  X  0,  +  10  X  02  -03) 
24      (5X0!+  8  X02  — 03)-2X(5x01+  8  X02-0S)' 


28 


The  Naval  Constructor 


Longitudinal  Metacenters  and  Centers 


Stations. 


W.L.  7  .  . 
A  respective 
2  .  .  .  . 
Lever  respec- 
tive to  Lever2 

Moments 
Moments  for 
I    .    .    .    . 


W.L.  6  .  . 
A  respective 
2  .  .  .  . 
Lever  respec 
tive  to  Lever2 

Moments 
Moments  for 
I    .    .    . 


.084 


32.30 

64.65 

.007 

.453 


W.L.5  .  . 
A  respective 
2  .  .  .  . 
Lever  respec- 
tive to  Lever2 

Moments 
Moments  for 
I    .    .    .    . 


W.L.  4  .  . 
A  respective 
2  .  .  .  . 
Lever  respec- 
tive to  Lever* 


Moments 
Moments  for 
I    .    .    .    . 


32.40 


.084 


32.50 


.084 


32.50 


Mi 


32.40 

64.80 

.007 

.454 


32.50 


.007 


32.50 


31.45 
1.05 
.313 
.329 


31.50 

1.15 

.313 

.340 


31.45 
1.20 
.313 
.376 


31.40 
.20 
.313 
.876 


30.40 
61.85 


6.061 


III 
A 


30.35 
61.85 


6.061 


30.25 
61.70 


6.047 


61.60 


6.037 


29.25 

3.85 

.50 

1.925 


29.10 

4.00 

.50 

2.00 


28.55 

3.90 

.50 

1.95 


25.40 
54.65 


13.600 


27.85 

3.70 

.50 

1.85C 


25.10 
54.20 


13.55 


23.70 

6.25 

.687 

4.294 


24.65 

53.20 

.25 

13.30 

24.15 
52.00 


14.00 


22.45 
5.55 


3.813 


17.45 
41.15 

.472 

19.423 


21.00 
4.90 


3.366 


19.40 

4.05 

.687 

2.782 


16.90 

39.35 

.472 

18.573 


V 
A 

8.25 

3.45 

.916 

3.160 


16.10 
37.10 

472 

17.510 


15.35 
34.75 

472 

16.400 


6.90 

2.40 

.916 

2.198 


4.80 
13.05 


10.962 


4.50 

11.40 

.840 

9.576 


5.75 

1.65 

.916 

1.511 


4.<;r> 
LOO 
.916 
.916 


.840 


8  :>,o 
.840 


6.972 


A  =  Difference.  2  =  Sum. 

23  =  Sum  of  Moments  (Sums  x  lever2)  for  I. 


Displacement  Tables 


29 


of  Flotation,  by  Tchibyscheff  s  Rule. 


2  OF 

Moments. 

Center 

aft3£ 

^     L      1 

r     a 
o  £ 

«  2 
g  h 

ta  o 

/ 

(AXIS  =  \L 

BETWEEN 

P.P.) 

Deduction 
Area  W.L. 

X<*2. 

V 

h 
V 

h 

22 

23 

-(f); 

28,242  X12.092 
4,128,000 

666,445 

542,772,000 

Lon- 
gitu- 
dinal 
B.M. 
in  Ft. 

812.93 

10 

2X2, 
=10,800,000  23 

546,900,000 

9.708 

50.559 

9-708X2S-5 

12.09 

27,792xl0.8132 
3,249,440 

558,767 
517,461,760 

926.07 

8.351 

48.214 

8-351x2"So 

10.813 

520,711,200 

27,222x  9.525 
2,469,715 

453,558 
484,945,085 

1069.2 

7.203 

45.131 

-3X^ 

9.525 

487,414,800 

26,598x  8.0182 
1,709,932 

350,152 
167,107,268 

1334.0 

5.924 

43.409 

"***£■ 

8.018 

468,817,200 

2X=  Sum  of  Ordinates  on  Displacement  Table. 

22  =  Sum  of  Moments  (differences  x  lever)  for  Centers  of  Flotation. 


30 


The  Naval  Constructor 


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Explanation  of  Table  31 


EXPLANATION   OF    TABLE,    GIVING    EFFECT    OF 

FORM    OF    WATER    LINE    ON    POSITION 

OF  LONGITUDINAL   METACENTER. 

Longitudinal   and  Lateral    Stability   Compared.  —  The 

first  four  lines  are  exactly  the  same  as  those  in  the  other  table  ; 
and  the  last  eight  lines  differ  only  in  having  length  and  breadth 
interchanged,  so  as  to  give  pitching  instead  of  rolling. 

On  comparing  them  with  the  following  table,  it  will  be  noticed 
that,  in  the  algebraic  factor,  the  length  and  breadth  always  inter- 
change ;  and  that  the  numerical  factor  remains  unchanged  for 
forms  (1),  (3),  and  (A),  namely,  the  square  or  rectangle,  the 
circle  or  ellipse,  and  the  wedge.  Of  the  nine  forms  selected,  these 
are  obviously  the  only  ones  in  which  breadth  and  length  are 
absolutely  interchangeable. 

With  respect  to  the  comparison  of  the  different  forms,  one  with 
another,  if  we  disregard  the  wave-bow  No.  (8),  the  variation  of 
stability  follows  much  the  same  sequence  for  longitudinal  as  for 
lateral  stability,  but  with  a  somewhat  less  absolute  value.  This 
result  might  be  expected  ci  priori,  because  the  extreme  breadth 
ordinate  cuts  the  outline  at  right  angles  in  all  but  the  wedge 
form  (9)  ;  while  the  extreme  length  ordinate  meets  the  outline 
more  sharply.  In  forms  (2)  and  (4)  this  difference  is  only  of 
the  second  order  ;  but,  as  the  figures  show,  it  is  quite  sufficient  to 
be  of  practical  importance  even  in  these. 

Differ  Chiefly  in  Wave-Bow.  —  The  wave-bow  form  (8) 
falls  altogether  out  of  its  sequence,  and  its  stability  is  less  than 
the  wedge  form  (9)  as  regards  pitching.  This  is  due  to  the 
sudden  falling  off  of  the  extreme  ordinate  length,  which  meets 
the  curve  tangentially,  instead  of  normally,  as  the  extreme 
breadth  ordinate. 

Fine   Bow   Affects   Pitch   More    than  Rolling.  —  If  we 

consider  rolling  on  any  given  axis,  it  is  easily  seen  from  geometri- 
cal considerations,  and  also  from  the  algebraic  form  of  the  inte- 
gral, that  the  instantaneous  stability  depends,  firstly,  on  the  length 
of  the  transverse  axis,  and,  secondly,  on  the  slowness  of  the  rate 
of  diminution  of  that  axis,  as  we  pass  along  that  axis  of  motion. 
Hence  sharp  bows  have  less  stability  for  pitching  than  bluff  bows, 
while  their  lateral  stability  for  rolling  is  not  so  very  different. 

Caution  in  Use  of  Table.  —  In  the  table  of  lateral  stability, 
the  element  of  length  only  appears  as  a  simple  factor  ;  therefore, 
as  regards  lateral  stability,  we  may  compound  the  moments  by 


32  The  Naval  Constructor 


simple  addition  for  a  vessel  built  up  in  different  lengths  for  the 
different  forms.  Thus,  the  values  in  lines  1  to  8  of  column  (2)  are 
simply  the  means  of  the  corresponding  values  in  columns  (1)  and  (3). 
We  cannot  apply  this  process  to  the  longitudinal  stability  because 
here  the  length  element  enters  as  a  cubic  factor.  If  we  were  so  to 
compound  the  moments  of  length,  what  we  should  really  do  would 
be  equivalent  to  screwing  together  two  longitudinal  halves  of 
different  vessels ;  in  the  case  before  mentioned,  screwing  half  a 
box  to  half  a  tub  ;  not  introducing  a  flat  midship  length  between 
two  semicircular  ends. 


Effect  of  Form  of  Water  Line  33 

Explanation  of  Table  Giving  Effect  of  Form  of  "Water 
Line  on  Position  of  Metacenter. 

Explanation  of  Table.  — By  the  preceding  table  we  can  at 
once  make  an  approximate  estimate  of  the  value  of  any  proposed 
form  of  water  line,  by  selecting  that  form  in  the  table  to  which 
it  comes  nearest.  From  this  table  we  gather  that  the  more 
nearly  the  water  line  approaches  to  a  right  parallelogram,  the 
more  it  will  contribute  to  the  stability  of  a  ship.  No.  9,  on  the 
contrary,  the  straight  line  wedge  form,  is  the  least  stable  of  these 
water  lines,  and  from  the  comparison  of  the  successive  groups  of 
lines  on  the  table  we  shall  see  exactly  how  this  comes  about. 

Areas  on  Water  Lines.  —  The  first  and  second  lines  in  the 
table  give  the  measures  simply  of  the  areas  of  those  water  lines. 
From  lines  3  and  4  we  see  that,  Fig.  1  being  taken  as  the  stand- 
ard of  comparison,  Fig.  2  only  contains  89  per  cent  of  the 
rectangular  area,  and  this  diminution  is  effected  merely  by  round- 
ing off  the  rectangular  corners,  the  length  and  breadth  remaining 
the  same  in  both.  In  Fig.  3,  when  the  curvature  of  the  ends 
extends  quite  to  the  middle  of  the  water  line,  its  area  is  reduced 
to  69  per  cent.  In  Fig.  6,  by  forming  the  water  line  of  parabolic 
arcs,  a  favorite  form  of  some  builders,  the  area  is  reduced  to  two- 
thirds  of  the  rectangle.  Figs.  7  and  8  are  the  lines  used  for 
a  wave  stern  and  a  wave  bow ;  from  which  it  appears  at  once 
how  much  more  powerful  the  stern  contributed  to  the  stability  of 
a  ship  than  the  bow  ;  the  stern  line  being  62  per  cent,  and  the 
bow  line  only  50  per  cent. 

Metacentric  Moments.  —  Lines  5  and  6  are  the  actual 
measure  of  the  stability  (by  its  moments)  for  small  inclinations. 
For  example  :  in  the  rectangle,  the  moment  is  one-twelfth  part  of 
the  product  of  the  length  by  the  cube  of  the  breadth,  or  .08  of 
that  product ;  and  as  we  pass  along  line  6  we  find  it  gradually 
diminish,  until,  in  the  wedge  form,  it  is  only  .02,  showing  that  a 
sharp  wedge  form  has  only  one-fourth  part  of  the  power  to  carry 
top  weight  that  the  rectangular  form  has,  although  its  power  of 
buoyancy,  or  power  to  carry  absolute  load,  is  one-half.  This  is 
set  out  more  fully  in  lines  7  and  8  ;  so  that  by  carefully  comparing 
together  line  4  and  line  8,  the  relative  values  of  all  those  figures 
for  carrying  absolute  weight  and  for  carrying  top  weight  may  be 
clearly  seen. 

Metacentric  Intervals.  —  Lines  9  and  10  measure  the 
powers  of  ships,  formed  on  these  water  lines  only  to  carry  top 
weight  without  upsetting. 


34 


The  Naval  Constructor 


Effect  of  Form  of  Water  Line  on 

From  J.  Scott  Russell, 
Length  of  vessel  =  L.*  Breadth  on  water  line 


1  Area  of  plane  of  flotation  . 

2  The  same,  expressed  decimally 

3  Ratio  to  same  in  rectangular  | 

form 


4  The  same,  expressed  decimally 
bjixsdyl 

6  The  same,  expressed  decimally 

7  Ratio  to  same  in  rectangular 

form 

8  The  same,  expressed  decimally 

9  Height  of  longitudinal  meta- 

center  ahove  center  of  dis- 
placement % 

10  The  same,  expressed  decimally* 

11  Ratio  to  same  in  rectangular  ) 

form  % ] 

12  The  same,  expressed  decimally  % 


«  o 


LB 
LB 


L*B 
LSB 


dr. 

& 

dr. 


(1) 


EBB 


i 

.00000 

1 


.00000 


o.os:«:5 


(-*> 


(SB 


4+w 


0.89270 

4  +  ff 
8 

0.89270 

16  +5tt 
512 


0.06194 

48+lSn- 
128 

0.74340 

16  +  5ir 


16(16  +  4tt) 


3(16  + 5tQ 
4(16  +  4tt) 


(3) 

.2 


SB) 


0.78540 

in 
0.78540 

0.04909 

0.58905 

A» 

0.06250 

It 
0.75000 


*  The  length  L  appears  simply  as  a  factor.  The  numerical  factor  in  the 
table,  therefore,  remains  unchanged  if  the  proportion  of  L  to  B  be  altered, 
as  in  passing  from  the  square  to  the  rectangle,  or  from  the,  circle  to  the 
ellipse. 

t  That  is  to  say,  a  trochoid  twice  the  length  of  a  cycloid  of  the  same  width. 


Effect  of  Form  of  Water  Line 


35 


Position  of  Longitudinal  Metacenter. 

Nav.  Arch.,  1865. 

amidships  =  B.  Draught  of  water  r=  dr. 


Numerical  Factor  for 

(4) 

(5) 

(6) 

(7)t 

(8) 

(9) 

Parabola 

(Axis 
Athwart- 

ships). 

Trochoid 
1  :  2 

(a  Wave 
Stern). 

Curve  of 
Sines  (a 

Wave  En- 
trance). 

6 
be 

1 

<s> 

<E> 

<3r> 

<£> 

<£> 

<£> 

3 

4 

TT  —  2 

4(V2  - 1) 

2 
3 

5 

8 

i 

2 

2 

0.75000 

0.68901 

0.6667 

0.62500 

0.50000 

0.50000 

3 

TT  —  2 

2 

5 

1 

1 

4 

-KV2-1) 

3 

8 

2 

2 

0.75000 

0.68901 

0.66667 

0.62500 

0.50000 

0.50000 

12tt2  _  35 
192  tt2 

3tt  — 8 

1 
30 

80ir2  —  373 
1536  TT2 

»r2  —  6 
24  jt2 

1 

48 

96  V2— 1 

0.04403 

0.03583 

0.03333 

0.02748 

0.01634 

0.02083 

12ir2  —  35 

16  TT2 

3tt  —  8 
8V2-1 

2 
5 

80ir2  —  373 

128  TT2 

ir2—  6 

1 
4 

2tt2 

0.52836 

0.42996 

0.40000 

0.32974 

0.19604 

0.25000 

12*r2  —  35 

144  TT2 

3tt  — 8 

24  (tt  —  2) 

1 
20 

80tt2  —  373 
960  TT2 

TT2—   6 

1 
24 

12  TT2 

0.05871 

0.05200 

0.05000 

0.04397 

0.03267 

0.04167 

12jt2  —  35 

12  TT2 

3tt  — 8 
2  (»  —  2) 

3 
5 

80tt2  —  373 

80  TT2 

TT2—    6 

1 
2 

TT2 

0.70448 

0.62403 

0.60000 

0.52759 

0.39207 

0.50000 

%  The  entries  in  these  lines  assume  that  the  vessel  is  flat-bottomed,  with 
vertical  sides.  The  other  entries  hold  good  whatever  may  be  the  shape  of 
the  vessel  under  water.  In  general,  the  height  of  the  metacenter  may  be 
found  by  dividing  the  entry  in  lines  5  or  6  by  the  displacement. 


36 


The  Naval  Constructor 


Effect  of  Form  of  Water  Line 

From  J.  Scott  Russell, 
Length  of  vessel  =  L.*  Breadth  on  water  line 


1  Area  of  plane  of  flotation  %    . 

2  The    same,    expressed    deci- 

mally t 


3  Ratio  to  same  in  rectangular  ) 

form J 

4  The  same,  expressed  decimally 
bJlyMxt 

6  The  same,  expressed  decimallyj 

7  Ratio  to  same  in  rectangular  | 

form j 

8  The  same,  expressed  decimally 

9  Height  of  metacenter  above ) 

center  of  displacement  §     . ) 

10  The    same,    expressed    deci-) 

mally  § J 

11  Ratio  to  same  in  rectangular  \ 

forms ) 

12  The  same,  expressed  decimallyf 


g 

«H 


LB 
LB 


LB* 
LB* 


(1) 

%£ 

-60 
©  q 


GOB 


1.00000 

1 

1.00000 

12 

0.08338 

1 

1.00000 

1 

12 


1.00000 


(2) 


©  c  oe   . 


1+5 
8 

0.89270 

i±2T 
8 

0.89270 

16-f  3tt 
384 

0.06621 

16  +  37T 

32 
0.79452 

16  +  37T 


12(16  +  4tt) 
0.07417 

16  +  37T 
16  +  47T 

0.89003 


(3) 
fig 

IK 


*« 

0.78540 
*» 

0.78540 
A» 

0.04909 

A* 

0.58905 

0.06250 

It 
0.75000 


*  The  length  Z  appears  simply  as  a  factor.  The  numerical  factor  in  the 
table,  therefore,  remains  unchanged,  if  the  proportion  of  L  to  B  be  altered, 
as  in  passing  from  the  square  to  the  rectangle,  or  from  the  circle  to  the 
ellipse. 

t  That  is  to  say,  a  trochoid  twice  the  length  of  the  cycloid  of  the  same 
width. 


Effect  of  Form  of  Water  Line 


37 


on  Position  of  Metacenter. 

Nav.  Arch.,  1865. 
amidships  =  B.  Draught  of  water  =  dr. 


Numerical  Factor  for 

(4) 

<5>. 

(6) 

(7)t 

(8) 

(9) 

W  H  O 

Parabola 
(Axis 

Athwart- 
ships). 

2    o  . 

Curve  of 
Sines  (a 

"Wave  En- 
trance). 

£ 

be 

1 

► 

® 

«£> 

O 

© 

<s> 

<3> 

3 
4 

it  — 2 

2 
3 

5 

8 

1 

2 

i 

2 

4(V2-1) 

0.75000 

0.68901 

0.6667 

0.6250 

0.50000 

0.50000 

3 
4 

ir  — 2 

2 
3 

5 

8 

1 
2 

1 
2 

4(V2-1) 

0.75000 

0.68901 

0.6667 

0.62500 

0.50000 

0.50000 

35 

1      9  77  —  28 

4 

55 

5 

1 

768 

24    20V2— 28 

105 

1536 

192 

48 

0.04557 

0.04021 

0.03810 

0.03581 

0.02608 

0.02083 

35 

1      9tt  — 28    . 

16 

55 

5 

1 

64 

2    20V2— 28 

35 

128 

16 

4 

0.54688 

0.48252 

0.45714 

0.42969 

0.31250 

0.25000 

35 

2 

11 

5 

1 

576 

35 

192 

96 

24 

0.06076 

0.05836 

0.05714 

• 

0.05729 

0.05208 

0.04167 

35 

24 

11 

5 

1 

48 

35 

16 

8 

2 

0.72917 

0.70031 

0.68571 

0.68750 

0.62500 

0.50000 

t  These  are  all  areas  or  moments,  and  therefore,  for  compound  forms,  it 
is  only  necessary  to  add  them,  or  take  a  mean  of  them,  as  may  suit  the  par- 
ticular case. 

§  The  entries  in  these  lines  assume  that  the  vessel  is  flat-bottomed,  with 
vertical  sides.  The  other  entries  hold  good,  whatever  may  be  the  shape  of 
the  vessel  under  water.  In  general,  the  height  of  the  metacenter  may  be 
found  by  dividing  the  entry  in  lines  5  or  6  by  the  displacement. 


38  The  Naval  Constructor 


Modulus  of  Fineness.  —  Lines  11  and  12  enable  us  to  com- 
pare the  different  forms;  and  by  running  our  eye  along  line  12 
we  are  enabled  to  trace  the  effect  of  the  successive  changes  in  the 
form  of  water  line,  in  bringing  down  the  metacenter,  and  re- 
ducing the  stability  of  the  ship,  thus  giving  what  has  been  some- 
times called  the  modulus  of  fineness  of  water  line. 

STABILITY    CALCULATION,  USING    THE 

INTEGRATOR   AND    APPLYING 

TCHIBYSCHEFF'S   RULE. 

The  following  tables  will  show  the  application  of  the  above  rule 
to  the  calculation  of  the  stability  levers  GZ  from  the  body  plan 
reproduced,  noting  that  the  integrator  used  was  metrically 
divided,  and  the  original  drawing  was  to  a  scale  of  j  to  the  foot  or 
g>y  full  size  with  ten  Tchibyscheff  ordinates.  The  center  of 
gravity  was  assumed  at  24  feet  above  base.  The  coefficients  are 
therefore  as  follows,  the  length  of  vessel  being  600  feet :  — 


600     962  x  3.2812 

TO  *    100X35    =1701-5- 


For  displacements  (tons), 

For  levers  (feet), 

.06  x  96  X  3.281  =      18.9. 
and, 

Displacement  in  tons  = 

1701.5  x  sum  of  differences  of  area  readings. 
T  .     ,  18.9  X  sum  of  differences  of  moment  readings 

Sum  of  differences  of  area  readings 
or, 

Displacements  (D)  =  1701.5  x  I  )  I  respective  to  II  taken  up 
Levers  (GZ)  =      18.9  x  II  \  *£«  corresponding  water 

The  angles  calculated  were  15°,  30°,  45°,  60°,  75°,  and  90°,  and 
the  results  as  tabulated  used  to  plot  off  the  Stability  Cross  Curves 
shown  from  which  the  Stability  Curves  at  various  displacements 
were  taken,  the  correction  being  calculated  for  the  new  locii  of 
the  center  of  gravity  where  G  is  the  assumed  position  below  S  then 
GZ  =  SZ  +  SG  sin  0,  and  when  above  S  then  GZ—SZ  —  SG  sin  0. 
So  that  taking  the  ordinates  from  the  cross  curves  at  the  displace- 
ment dealt  with  SG  being  now  known,  we  can  determine  the  exact 
values  of  GZ  for  any  angle. 


Stability   Calculations  39 


Fig.  9. 


40 


The  Naval  Constructor 


Calculation   of  GZ   Levers   for  Stability  Cross   Curves, 
Using  the  Integrator  and  Tchibyscheff s  Rule. 


J  o 

W  <j  © 

«©2 
a  fi  w 

-  fa  y 

/ 

ftz> 

§4« 

2  •<  © 
3f 

<a©« 

S23 

fa  M      I 

o  'n  » 

II 

&  £ 

H   W 
GZ 

4555 

4511 

5 

7666 
7666 

3111 

3.111 

5,290 

5097 
5097 

+.586 

+.586 

3.560 

4 

9668 
9668 

2002 

5.113 

8,700 

4931 
5169 

-.166 

+.420 

1.550 

o 

3 

1779 

2111 

7.224 

12,280 

4974 

-.195 

+.225 

.590 

T-l 

1779 

5211 

2 

3896 
3896 

2117 

9.341 

15,900 

5141 

5378 

-.070 

+  155 

.314 

L.W.L. 

6115 
6115 

2219 

11.560 
11.570 

19,700 

5423 
5661 

+.045 

+  200 

.327 

L.W.L. 

7685 

5863 

+  202 

Check 

0625 

5060 

5 

3766 
3766 

3141 

3.141 

5,350 

5820 
6079 

+.760 

+.760 

4.570 

4 

5578 
5578 

1812 

4.953 

8,440 

6122 
6380 

+.043 

+.803 

3.070 

o 

3 

7681 

2103 

7.056 

12,000 

6317 

-.063 

+.740 

1.980 

8 

7681 

6575 

2 

9980 
9980 

2299 

9.355 

15,920 

6525 
6784 

-.050 

+.690 

1.395 

L.W.L. 

2411 
2411 

2431 

11.786 

20,050 

6963 
7221 

+.179 

+.869 

1.386 

L.W.L. 

4201 

11.790 

8091 

+.870 

Check 

8309 

9862 

5 

1620 
1620 

3.311 

3.311 

5,640 

0549 
0549 

+.687 

+.687 

3.930 

4 

3412 
3412 

1792 

5.103 

8,680 

0820 
1056 

+.271 

+.958 

3.550 

o 

3 

5519 

2107 

7.210 

12,250 

1411 

+.355 

+1.313 

2.950 

«# 

5519 

1647 

2 

7874 
7874 

2355 

9.565 

16,300 

1999 
2235 

+.352 

+1.665 

3.260 

L.W.L. 

0365 
0365 

2491 

12.056 
12.058 

20,400 

2463 
2699 

+.228 

+1.893 

2.970 

L.W.L. 

2423 

1.896 

Check 

Calculation  of  GZ 


41 


Calculation   of   GZ   Levers  for   Stability   Cross    Curves, 
Using  the  Integrator  and  Tchibyscheffs  Rule. 


h!  o 

P  R 

si 

3  3« 

i  t.  & 

»to% 

ft  ^  w 

Sum  of 
Differ- 
ences. 

g  w 

m  0  to 

i  '—  to 

M  5  «< 

CO   3 

^ 

wpq 

/ 

H2> 

Af 

.  Sp5 

a 

GZ 

6097 

4869 

5 

9808 
9808 

3711 

3.711 

6,315 

5547 
5547 

+.678 

+.678 

3.46 

4 

1684 
1684 

1876 

5.587 

9,520 

6051 
6285 

+.504 

+1.182 

4.00 

O 

3 

3746 

2062 

7.649 

13,000 

6637 

+.352 

+1.534 

3.80 

o 

to 

3746 

6871 

2 

5976 
5976 

2230 

9.879 

16,800 

7186 
7420 

+.315 

+1.849 

3.50 

L.W.L. 

8241 
8241 

2265 

12.144 

I 

20,550 

7544 

7778 

+.124 

+1.973 

3.07 

L.W.L. 

0389 

12.148 

9754 

+1.976 

Check 

0622 

1355 

5 

4832 
4832 

4210 

4.210 

7,160 

2078 
2078 

+.723 

+.723 

3.25 

4 

6676 
6676 

1844 

6.054 

10,300 

2448 
2920 

+.370 

+1.093 

3.42 

o 

3 

8599 

1923 

7.977 

13,600 

3166 

+.246 

+1.339 

3.18 

8599 

3402 

2 

0689 
0689 

2090 

10.067 

17,130 

3503 
3740 

+.101 

+1.440 

2.70 

L.W.L. 

2860 
2860 

2171 

12.238 
| 

20,800 

3890 
4137 

+.150 

+1.590 

2.46 

L.W.L. 

5090 

12.230 

5737 

+1.600 

Check 

0521 

5890 

5 

5039 
5039 

4518 

4.518 

7,690 

6332 
6332 

+.442 

+.442 

1.85 

4 

6783 
6783 

1744 

6.262 

10,560 

6438 
6674 

+.106 

+.548 

1.65 

o 

3 

8637 

1854 

8.116 

13,810 

6767 

+.093 

+.641 

1.49 

% 

8637 

7004 

2 

0685 
0685 

2048 

10.164 

17,295 

7128 
7364 

+.124 

+.765 

1.42 

L.W.L. 

2880 

2195 

12.359 

21,030 

7436 

+.072 

+.837 

1.29 

2880 

I 

7672 

L.W.L 

5242 

12.362 

.  .  . 

8511 

...  +.839 

Check 

42 


The   Naval   Constructor 


133d    8U3A3T  JO  31V09 


Cross  Curves  of  Stability 


43 


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: 

[Mil  |l  1  1  III  1  1  1  |  II  1  1  |ll  1  l|l  1  1  III  1  II  |  1  1  II  1  1  1  1  l  |  1  II  1 

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s                 *                 e                 z                  i 

44  The  Naval  Constructor 


CHAPTER   II. 

DESIGN. 

In  the  foregoing  pages  we  have  treated  with  the  various  calcula- 
tions which  confront  the  naval  architect,  but  the  relation  of  these 
to  one  another  and  to  the  particular  qualities  that  the  projected 
ship  shall  possess  belong  to  Design. 

In  designing  the  ship,  nothing  should  be  left  to  chance,  or  what 
is  the  same  thing  —  trial  and  error.  The  vessel  must  first  be  de- 
signed with  figures.  Before  a  single  line  is  run  on  paper,  the  vari- 
ous element  coefficients  should  be  carefully  selected  and  their 
functions  worked  out  in  consonance  with  the  results  desiderated 
in  the  finished  ship.  The  relation  of  these  coefficients  to  one 
another  must  be  firstly  mastered  for  all  types  of  vessels  and  con- 
ditions of  draught  and  trade,  when  with  the  aid  of  the  tables  given 
an  unerring  selection  will  be  possible  and  a  definite  result  attained. 

When  the  way  is  prepared  for  the  drawing  part  of  the  design  to 
be  taken  in  hand,  it  will  be  found  advantageous  to  have  a  definite 
routine  in  which  to  prepare  the  various  views  comprised  under 
the  general  term  "Lines."  Each  step  should  be  taken  in  its 
proper  time  and  order.  Much  time  will  thus  be  gained,  and  a 
clearer  conception  of  the  art  of  designing  obtained.  To  this  end 
we  submit  the  following  method  as  one  fulfilling  these  proposi- 
tions, dividing  the  task  broadly  into  two  parts,, viz.  :  — 

(a)  Figures  and  (b)  Lines,  the  first  embracing  the  moulded 
dimensions,  draught,  element  coefficients,  and  their  functions,  and 
the  latter,  the  sheer  draught,  half-breadth,  and  body  plans. 

The  shipowner  will  specify  the  trade  for  which  the  ship  is  in- 
tended and  the  limit  of  draught  on  the  particular  service  proposed. 
It  will  generally  be  found  economical  to  take  advantage  of  the 
maximum  draught  permissible.  When  the  dimensions  are  solved 
to  meet  the  requirements  stipulated,  the  grade  numerals  should  be 
worked  out,  for  the  Classification  Society's  Rules  in  which  it  is 
proposed  to  class  the  ship,  and  if  it  be  found  that  a  grade  can  be 
saved  either  in  plating,  framing  or  equipment  numerals,  or  the 
requirements  for  extreme  proportions  evaded  by  a  slight  alteration 
or  adjustment  of  the  dimensions,  this  of  course  should  be  done. 

As  an  example  we  shall  postulate  that  the  shipowner  requires  a 
3-deck  freighter  with  complete  shelter  deck  to  carry  10,000  tons 
dead  weight,  exclusive  of  coal  for  12  days'  steaming,  fresh  water 
and  stores,  on  a  mean  draught  of  27  feet  with  a  B.T.  Freeboard 
and  a  sea  speed  of  12  knots.  The  ship  to  be  classed  in  American 
Record  and  to  conform  to  the  U.S.  Inspection  Laws.     To  these 


Design  45 


demands  of  the  owner  the  naval  architect  should  add  the  G.M.  when 
fully  loaded  with  a  homogeneous  cargo.     Let  us  call  this  1.5  ft. 

The  first  point  to  determine  is  the  amount  of  displacement  we 
shall  require  to  provide  for  over  and  above  the  specified  dead 
weight  of  10,000  tons,  to  allow  for  weight  of  finished  ship  and 
machinery,  coal,  fresh  water,  and  stores.  At  this  stage  we  cannot 
calculate  these  items,  as  we  are  uninformed  as  to  the  dimensions 
of  the  ship,  so  that  the  remaining  method  to  solve  this  is  to  esti- 
mate a  weight  embracing  all  of  these  items  based  on  a  percentage 
of  the  dead  weight.  This  percentage  of  course  is  determined  from 
vessels  of  similar  type  and  trade  duly  worked  out  and  tabulated 
by  the  naval  architect.  We  shall  take,  then,  each  step  in  its 
proper  order  : 

(1)  Displacement  =  dead  weight  x  1.64  =  16,400  tons. 

(2)  Block  coefficient  "  5  "  =  a./S.e.  =  .79. 

(3)  Relation  coefficient  "e"  =—  =  .945.* 

a.p 
s 

(4)  Mid.  area  coefficient  "fl"  =  — =  .97. 

(5)  Prismatic  coefficient  "p"=-  =  .814. 

(6)  Area  of  L.W.L.  coefficient  "a"  =  ^=.861. 


(7)    Moment  of  inertia  coefficient  "  i "  (see  table)  =  .0638. 
i 


(8)   B.M.  coefficient  "m  "  =  ?-  =  . 08. 


(9)   Center  of  gravity  coefficient ■ '  g ' '  =  ■==  =  .  559.     (See  table. ) 

(10)  Depth  "  H  "  to  upper  deck  per  Freeboard  Tables  =  33.5  ft. 

(11)  Depth  "fli"  to  shelter  deck  =  H  +  7.5  ft.  =  41  ft. 

(12)  Center  of  gravity  above  base  =  HX  X  g  =  41  x.559  =  22.90  ft. 

(13)  Metacenter  above  base  =  C.G.  +  G.M. 

=  22.90 +  1.50  =  24.40  ft. 

(14)  Breadth  "£"  to  give  M.C.  of  24.4  ft.  = 

(15)  Length  -£»  =  ^x^x§  =  460  ft. 

(16)  B.M.  = y =y=  10.23  ft. 

(17)  Center  of  buoyancy  above  base 

*  May  be  taken  constant  .9,  as  per  -table. 


4G  The  Naval  Constructor 

(18)  Bilge  diagonal  coefficient  (see  diagram)  =  .82. 

(19)  Dimensions  as  determined  =  400  x  58'  0"  x  33'  0". 

(20)  Displacement  "  D  " 

460'  X  58.5'  X  27'       _.      lfl  .„  . 

= ^ X  .79  =  16,400  tons. 

oo 

(21)  Calculated  weights : 

Hull  complete      ....     4,670  tons 

Machinery 730     "    (4,000  I. H. P.) 

Coal 750    "    (for  12  days) 

Fresh  water 200    " 

Stores 50    " 

6,400     " 

Dead  weight 10,000    " 

Displacement  =  16,400  tons 

Should  it  be  found,  however,  that  the  weights  calculated  for  the 
dimensions  as  worked  out  are  lighter  than  anticipated  when  we 
started  with  the  64  per  cent  of  the  dead  weight,  the  length  should 
be  reduced  accordingly.  On  the  other  hand,  if  the  weights  be 
excessive,  the  length  must  be  increased.  The  length  is  the  only 
dimension  that  should  be  adjusted,  as  it  is  the  one  factor  which 
has  no  vital  relationship  to  the  element  coefficients,  as  it  will  have 
been  noticed  that  the  primary  quality  aimed  at  was  the  G.M.  as  a 
measure  of  the  ship's  initial  stability  ;  and  as  the  center  of  gravity 
varies  with  the  depth,  so  the  metacentric  height  is  dependent  on 
the  breadth  and  draught. 

For  the  preliminary  design  it  will  be  sufficiently  close  to  esti- 
mate the  machinery  weights  on  the  I.H.P.  required,  and  for 
ordinary  merchant  practice  the  power  may  be  calculated  fairly 
accurately  by  the  Admiralty  constant  with  the  formula  :  — 

T.H.P.  =  -P>*y»  * 
C 
We  then  have  for  the  present  example,  with  constant  =  267,  speed 
12  knots,  and  displacement  16,400,  an  indicated  horse-power  =4000. 
By  referring  to  the  table  given  elsewhere,  it  will  be  found  that  for 
twin  screw  freight  steamers  with  this  speed  that  the  I.H.P.  per 
ton  of  engine  boilers  and  water  equals  about  5.5,  so  that  we  get 
for  a  total  machinery  weight 

^  =  730  tons. 
5.5 

The  displacement  and  coefficients  should,  in  all  cases  of  steel 

steamers,  be  calculated  to  the  moulded  line  of  frames,  the  excess 

water  displaced  by  the  shell  plating,  amounting  to  about  1%,  being 

retained  in  hand  as  a  margin  against  contingencies.     In  this  case 

its  value  is  164  tons,  representing  3  inches  of  draught. 

*  See  Table  of  Constants,  and  chapter  on  Kesistance. 


Relation  of  Coefficients  to  One  Another    41 


Relation  of  the  Coefficients  to  One  Another. 


Relation  coefficient, 


.9,  constant  = 


Block  coefficient,  5  =  a./S.e. 

Area  of  water  line  coefficient, 

p  S 

a=        or         . 

e  p.e 

/?         *? 
Mid.  area  coefficient,     #  =  -,  or  — 
'     r      p        a.e 

Prismatic  coefficient,    p  =  —  • 

Bilge  diagonal  coefficient, 


i,  =  X2t0|§(P=-6t0-82>- 


Type  of  Vessel. 

€ 

6 

■ 

P 

P 

b 

Steam  pinnaces,  30  ft.  to      ( 
60  ft ) 

.9 

.36 

.666 

.600 

.600 

.652 

.9 

.36 

.666 

.616 

.600 

.652 

r 

.9 

.38 

.666 

.633 

.600 

.652 

.9 

.39 

.666 

.649 

.600 

.652 

Steam  yachts,  100  ft.  to 

.9 

.40 

.666 

.666 

.600 

.652 

300  ft. ,  also  destroyers  - 

.9 

.41 

.670 

.680 

.603 

.653 

and  torpedo  craft .     . 

.9 

.42 

.671 

.695 

.604 

.653 

.9 

.43 

.671 

.712 

.604 

.653 

k 

.9 

.45 

.675 

.740 

.608 

.654 

.9 

.46 

.674 

.758 

.607 

.654 

.9 

.47 

.674 

.774 

.607 

.654 

.9 

.48 

.675 

.790 

.608 

.655 

Small    river    propeller     J 

.9 

.49 

.676 

.804 

.609 

.656 

steamers,  50  ft.  to  150 

.9 

.50 

.677 

.820 

.610 

.657 

ft.  ......     . 

.9 

.51 

.679 

.834 

.611 

.659 

.9 

.52 

.680 

.849 

.612 

.661 

.9 

.53 

.683 

.860 

.615 

.663 

.9 

.54 

.688 

.870 

.620 

.665 

L 

.9 

.55 

.694 

.880 

.625 

.670 

Sound  and  river  steamer, 

.9 

.56 

.700 

.890 

.630 

.676 

150  ft.  to  400  ft.    .     . 

.9 

.57 

.703 

.900 

.633 

.679 

.9 

.58 

.707 

.910 

.637 

.683 

.9 

.59 

.712 

.920 

.641 

.687 

*• 

.9 

.60 

.716 

.930 

.645 

.692 

48 


The  Naval  Constructor 


Type  of  Vessel. 

e 

6 

a 

0 

P 

b 

.9 

.58 

.677 

.950 

.610 

.667 

High     speed      channel 
steamers,    200    ft.    to 

300  ft 

r  "S 

.9 
.9 
.9 

.59 
.60 
.61 

.689 
.697 
.707 

.953 
.956 
.959 

.620 
.627 
.636 

.665 
.673 
.681 

.9 

.62 

.716 

.962 

.644 

.690 

.9 

.63 

.725 

.965 

.652 

.698 

Ocean  liners,  400  ft.  to  \ 
750  ft 

.9 
.9 

.64 
.65 

.734 
.743 

.968 
.971 

.661 
.669 

.706 
.714 

.9 

.66 

.755 

.975 

.680 

.722 

. 

» 

.9 

.70 

.820 

.950 

.737 

.768 

.9 

.71 

.828 

.952 

.745 

.770 

Full-rigged  ships,  250  ft.  ' 

.9 

.72 

.838 

.954 

.754 

.777 

to  350  ft 

.9 

.73 

.847 

.957 

.762 

.785 

I 

.9 

.74 

.857 

.959 

.771 

.792 

.9 

.75 

.866 

.962 

.779 

.800 

.9 

.76 

.874 

.965 

.787 

.807 

.9 

.77 

.884 

.967 

.796 

.814 

Intermediate  liners  and 
freighters,  300   ft.  to 
700  ft 

.9 
.9 
.9 

.78 
.79 
.80 

.894 
.903 
.913 

.969 
.971 
.973 

.805 
.813 

.822 

.819 
.825 
.830 

.9 

.81 

.922 

.976 

.830 

.836 

' 

.9 

.82 

.933 

.978 

.840 

.843 

-   .9 

.83 

.941 

.980 

.847 

.850 

Coefficients  of   Centers  of  Gravity  for  Various  Vessels. 

Value 

OF"0." 

Small  steamers,  as  harbor  tenders,  revenue 

steamers,  etc .     .65  to  .70 

Torpedo  boats 67 

Torpedo  boat  destroyers 55  to  .60 

Auxiliary  steam  yachts 65 

Full-power  steam  yachts 70 

Full-rigged  sailing  ships 69  to.  71 

Shelter-deck  intermediate  liners     ....     .60  to  .65 

Swift  ocean  liners 56  to  .58 

Shelter-deck  freighters 66  to  .58 

Three-deck  freighters,  with   poop,  bridge, 
and  forecastle 54  to  .56 


Inertia  Coefficients 


49 


Moment  of  Inertia  of  Water  Line  Coefficients. 

L  x  B*  x  i  =  I. 


Water  Line 

Inertia 

Water  Line 

Inertia 

Coefficient, 

Coefficient, 

Coefficient, 

Coefficient, 

"a." 

"  i." 

"a." 

"*." 

.50 

.02250 

.75 

.04841 

.51 

.02316 

.76 

.04966 

.52 

.02383 

.77 

.05100 

.53 

.02466 

.78 

.05233 

.54 

.02540 

.79 

.05383 

.55 

.02633 

.80 

.05500 

.56 

.02710 

.81 

.05650 

.57 

.02800 

.82 

.05783 

.58 

.02910 

.83 

.05930 

.59 

.03000 

.84 

.06075 

.60 

.03100 

.85 

.06200 

.61 

.03200 

.86 

.06341 

.62 

.03300 

.87 

.06500 

.63 

.03400 

.88 

.06625 

.64 

.03500 

.89 

.06766 

.65 

.03600 

.90 

.06900 

.66. 

.03733 

.91 

.07050 

.67 

.03844 

.92 

.07200 

.68 

.03955 

.93 

.07341 

•  .69 

.04100 

.94 

.07500 

.70 

.04200 

.95 

.07600 

.71 

.04325 

.96 

.07833 

.72 

.04500 

.97 

.07900 

.73 

.04600 

.98 

.08050 

.74 

.04700 

All  the  elements  insuring  the  qualities  that  embody  a  well- 
shaped  boat  of  the  particular  type  contemplated  and  at  the  same 
time  a  stable  ship  having  been  thus  determined,  the  lines  may  be 
commenced  with  the  certainty  that  no  unnecessary  alterations  will 
be  required. 

The  freeboard  will  be  calculated  from  the  legal  tables  given  and 
explained  herein,  but  in  any  case  the  limiting  draught  consistent 
with  the  block  coefficient  determined  on  as  the  maximum  avail- 
able for  the  required  speed  should  be  taken  advantage  of. 

After  carefully  drawing  the  center  and  other  construction  lines, 
and  marking  off  the  ten  or  twenty  ordinates  that  it  is  proposed  to 


50  The  Naval  Constructor 


use,  it  will  be  well  to  have  a  definite  routine  or  method  in  which 
to  draw  down  the  various  views  comprising  what  are  embraced 
under  the  general  term  "  lines." 
To  this  end  the  following  will  prove  a  good  sequence : 

1.  The  "  dead  fiat"  section  on  body  view. 

2.  Rail  sheer  line. 

3.  Contour  of  stem  and  stern  in  profile. 

4.  Kail  half-breadth. 

5.  Load  water  line  half-breadth. 

C.  Bilge  diagonal.  • 

7.  Transfer  L.W.L.  and  B.D.  ^-breadths  to  body  plan. 

8.  Draw  freehand  the  sections  to  foregoing. 

9.  Trial  displacement  by  planimeter. 

10.    Sheer  heights  from  profile  to  body  plan. 

Taking  this  routine  in  order  :  — 

1st.  The  dead  flat  or  midship  section  should  present  no  difficul- 
ties, as  the  area  of  this  section  is  pre-determined  from  the  co- 
efficient /S.  This  being  so,  the  height  of  rise  of  floor  construction 
line  is  assigned  by  giving  the  easiest  bilge  consistent  with  the 
area  of  section  demanded.  In  no  case  should  the  bilge  be 
"squarer"  than  the  demands  of  this  area  require,  as  in  full 
vessels  sufficient  difficulty  is  encountered  in  setting  the  bilge  strake 
plates  and  bending  the  frames  without  adding  further  to  it. 

2d.  In  most  vessels,  except  yachts  and  launches,  .it  will  be 
found  advisable  to  make  the  lowest  part  of  sheer  at  the  half-length 
amidships,  as  otherwise  correction  would  have  to  be  made  for 
freeboard  and  the  classification  societies'  numerals.  It  is -best, 
then,  after  fixing  the  height  of  bulwark  or  sheer  strake  above 
upper  deck  to  underside  of  moulding,  to  run  a  pencil  line  parallel 
to  L.W.L.  from  A. P.  to  F.P.,  at  which  points  and  above  this  line 
the  sheer  forward  and  aft  should  be  set  up.  The  amount  of  sheer 
will  of  course  depend  on  the  type  of  vessel,  i.e.  whether  intended 
for  sea  or  river.  In  the  latter  case  it  is  evident  the  same  amount 
of  "  spring  "  would  not  be  required  as  for  over-sea  voyages.  The 
standard  sheer  prescribed  by  the  British  freeboard  tables  will  be, 
however,  a  good  guide,  and  where  this  is  deemed  insufficient  or 
where  special  cases  suggest  a  departure  from  these,  as  in  passenger 
steamers  and  first  class  ocean  liners,  a  handy  rule  and  one  that  gives 
a  very  symmetrical  sheer  is  to  take  one-fifth  of  the  vessel's  length 
in  feet,  calling  the  quotient  inches  which  will  equal  the  amount 
of  sheer  forward.     One-third  of  this  will  be  the  sheer  aft,  as  :  — 

_ =  Sheer  forward  in  inches, 

5 

,                Sheer  forward  .    _,,  ^  .     .     . 

and, =  Sheer  aft  in  inches. 


Inertia  Coefficients  51 


The  amount  of  sheer  having  been  decided  upon  with  the  lowest 
part,  say,  at  the  half-length,  the  quickest  and  simplest  way  to  run 
the  sheer  line,  insuring  a  fair  curve,  will  be  to  divide  the  half- 
length  before  and  abaft  the  lowest  sheer,  into  four  equal  parts, 
and  at  each  of  these  points  set  up  the  perpendicular  heights 
obtained,  as  under,  postulating  in  this  case  that  the  sheer  at  F.P. 
is  equal  to  82  inches,  and  the  sheer  at  A. P.  30  inches,  giving  a 
mean  sheer  of  56  inches,  as  per  freeboard  tables. 

82"  x  1.000   =  82"  sheer  at  4th  station  =  P.P. 
82"  X    .562   =  46"  sheer  at  3rd  station  forward  of  lowest 
82"  X    .250   =  20i"  sheer  at  2d  station  forward  of    " 
82"  X    .0625  =    51"  sheer  at  1st  station  forward  of     «« 

and  for  the  sheer  aft :  — 

30"  X  1.000   =  30"  sheer  at  4th  station  =  A. P. 
30"  X    .562   =  16|"  sheer  at  3d  station  abaft  lowest 
30"  X    .250   =   7£"  sheer  at  2d  station  abaft      " 
30"  X    .0625  =    If"  sheer  at  1st  station  abaft     " 

By  pinning  the  spline  to  these  spots  and  adjusting  the  free  ends 
to  the  eye,  an  absolutely  fair  sheer  line  may  be  run  in,  bearing  in 
mind,  however,  that  in  ships  with  a  very  full  rail  line  forward, 
compensation  must  be  given  on  the  sheer  to  adjust  the  great  dis- 
parity in  the  length,  of  the  half-breadth  rail  line  and  the  same  line 
projected  on  sheer  plan;  as,  if  this  be  not  done,  the  rail  line  on  model, 
and  of  course  on  the  actual  ship,  will  appear  as  "rounding  down." 

3d.  The  contour  line  of  the  stem  will  be  very  much  a  matter 
of  individual  taste,  although  above  water  line  it  is  usual  to  make 
it  straight  unless  in  special  cases.  By  "straight"  is  meant 
"apparently"  so,  as  it  is  customary  to  give  about  f-inch  round 
on  face  of  stem  from  where  it  leaves  the  top  of  the  forefoot  curve 
to  stem  head,  an  absolutely  straight  line  adjoining  a  curve  appear- 
ing as  slightly  hollow.  Also,  it  is  not  advisable  to  make  the  stem 
plumb,  as  the  illusion  in  that  case  is  to  make  it  appear  as  leaning 
aft.  A  rake  forward  of  about  twice  the  moulding  of  the  stem 
head  is  common.  In  outlining  the  stern  and  counter  the  same 
remarks  as  to  taste  apply,  care  being  taken  that  the  counter  line 
where  it  meets  the  rudder  post  is  carried  by  an  imaginary  curve 
to  harmoniously  meet  the  arch  of  body  post.  The  counter  line, 
from  knuckle  moulding  to  stern  post,  should  be  perfectly  straight 
—  not  hollow.  A  hollow  to  this  line  gives  the  appearance  of  an 
overweighted  overhang,  and  a  broken  sheer,  besides  making  the 
plating  more  difficult  to  set. 


52  The  Naval  Constructor 

Dimensions  of  Figureheads  and  Lacing  Pieces. 


Fig.  12. 


A 

Length  of 

B 
Size 

c 

Depth  of 

D 
Length  of 

Figure 

Outside  of 

Stem. 

Vessel, 
B.S. 

op  LacijTg 
Piece. 

Figure- 
head. 

Feet. 

Inches. 

Inches. 

Feet.  Inches. 

450 

121 

30^ 

9         6 

400 

12 

28| 

9         0 

350 

1U 

26| 

8         0 

300 

10^ 

25 

8        0 

250 

n 

231 

7         6 

200 

9 

211 

7         0 

150 

81 

19| 

0        6 

100 

n 

18 

6        0 

Note.  —  Angle  o 

f  lacing  piece, 

45°. 

The  length  of  overhang  of  course  cannot  be  arbitrarily  fixed, 
but  a  very  fair  proportion  for  ordinary  freighters  is  ■£$  to  -fa  of  the 
length.  The  height  of  deck  or  rail  at  taffrail,  or  " cock-up,"  will 
be  dependent  on  the  camber  of  deck  at  transom  frame  (No.  0). 
The  midship  camber  proportioned  to  the  half-breadth  at  this 
frame  should  be  set  up  and  the  deck  line  carried  through  this 
spot  in  a  fair  curve  to  taffrail.  The  height  so  obtained  should  be 
then  transferred  to  body  plan,  and  the  deck  (or  rail  line)  between 
No.  0  section  and  taffrail  drawn  in  as  a  round  of  beam  curve,  from 


Figureheads 


53 


which  may  be  obtained  the  intermediate  spots  for  deck  at  side  (or 
rail)  on  sheer  plan. 

4th.  The  rail  half-breadth  will  depend  on  the  particular  type 
of  ship  being  designed.  In  freighters  it  will  be  parallel  to  the 
center  line  for  probably  half  the  length  amidships,  whereas  in 
yachts  and  other  fine  vessels  it  will  "round  "  all  the  way.  It  is 
convenient  to  have  rail  half-breadths  at  hand  for  various  types  of 
vessels  for,  say,  ten  ordinates  with  half-end  ordinates  or  which- 
ever number  is  adopted  as  the  standard.  These  should  be  tabu- 
lated with  the  half-breadth  amidships  as  unity,  when,  with  the  aid 
of  a  slide  rule,  the  half-breadths  for  the  design  may  be  very  rapidly 
proportioned.  It  will  be  found  convenient  to  have  these  for 
liners,  freighters,  sound  and  river  steamers,  yachts,  etc.,  from 
good  examples  of  their  respective  classes.  The  contour  of  rail  line 
around  taffrail  will  require  careful  fairing  into  the  A. P.  ordinate 
spot,  and  also  at  center  line,  where  in  no  case  should  it  be  per- 
fectly straight,  the  effect  of  such  being  a  hollow.  Neither,  on  tne 
other  hand,  should  it  come  to  a  "peak"  or  point,  but  carefully 
drawn  as  an  arc  of  a  circle.  The  knuckle  mouldings,  whether 
they  be  one  or  more,  may  with  advantage  be  delineated  by  tracing 
the  rail  line  just  drawn  and  transferring  it  forward  to  its  exact 
location.  By  so  doing  it  will  be  seen  that  the  stern  between 
knuckle  and  rail  lines  will  develop  with  a  pleasing  gradation  from 
"  0  "  frame  to  the  upper  counter  line. 

Table  of  Rail  Half-Breadths  for  Various  Types. 


Ordi- 
nates. 
"0"=A.P. 

Ocean 
Liner. 

H 

w  . 

<  a 
go 

Sail- 
ing 
Ships. 

03 

Oce- 
anic. 

0 

.630 

.444 

.756 

.756 

.603 

.603 

.655 

* 

.714 

.757 

.812 

.829 

.730 

.691 

.790 

1 

.786 

.889 

.854 

.872 

.810 

.772 

.845 

2 

.882 

.990 

.918 

.934 

.910 

.875 

.912 

3 

.946 

1.000 

.951 

.977 

.967 

.955 

.965 

4 

.985 

1.000 

.988 

.994 

.979 

.995 

.987 

5  = 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

0 

.989 

1.000 

.991 

.994 

.979 

.978 

.971 

7 

.934 

1.000 

.965 

.965 

.960 

.930 

.944 

8 

.820 

.985 

.891 

.877 

.910 

.803 

.884 

9 

.594 

.856 

.727 

.619 

.740 

.532 

.666 

9J 

.358 

.572 

.576 

.366 

.515 

.298 

.404 

10 

Stem 

Stem 

.355 

Stem 

Stem 

Stem 

Stem 

54 


The  Naval  Constructor 


6th.  The  load  water  line,  as  already  stated,  must  circumscribe 
the  area  calculated  with  the  aid  of  the  coefficient  o.  The  method 
of  obtaining  a  has  been  previously  explained.  To  obtain  the  form 
of  this  water  line,  and  at  the  same  time  insure  the  accuracy  of  the 
required  enclosed  area,  it  will  be  found  advantageous  to  prepare  a 
diagram  similar  to  the  one  opposite,  or  this  one  may  be  used  with 
the  aid  of  proportional  compasses.  Opposite  the  value  of  a  for 
the  design  in  hand  half-breadths  for  ten  ordinates  may  be  read  off 
and  transferred  to  the  half-breadth  plan.  Should,  however,  the 
line  delineated  after  the  spline  has  been  fixed  not  meet  with  the 
designer's  individual  taste,  or  where  greater  fullness  or  fineness  is 
required  for  special  cases,  forward  or  aft,  it  will  be  a  very  simple 
matter  to  modify  the  line,  at  the  same  time  observing  that  what- 
ever area  be  cut  off  at  any  one  point  be  compensated  for  elsewhere 
on  the  water  line,  as  the  offsets  taken  from  the  diagram  will  en- 
close exactly  the  area  required.  Of  course  the  designer  may  make 
his  own  diagram  for  the  number  of  ordinates  he  prefers  to  design 
with.  In  any  case  the  run  of  the  line  for  a  few  feet  forward  of  the 
post  will  require  special  adjusting  when  the  oxter  is  being  faired. 

In  addition  to  the  diagram,  the  following  table  is  given  of  actual 
load  water  lines  of  several  types  with  the  coefficients  of  area  of 
same  (a). 

Load  Line  Half-Breadths  Standardized. 


Ordi- 
nates. 

Fast 

OCEAN 

Liner. 

H 

w 

H 

K 
O 

s 

S3 
ft 

S.S. 
Yacht. 

H 
1 

Sail- 
ing 
JShip. 

H 
02 

Oce- 
anic. 

"0"=A.P. 

a  =.726. 

a  =.857. 

a  =.683. 

a  =.717. 

a  =.797. 

a  =.656. 

a  =.771. 

0 

Post 

Post 

Post 

Post 

Post 

Post 

Post 

} 

.289 

.448 

.148 

.382 

.407 

.275 

.333 

1 

.531 

.770 

.479 

.642 

.678 

.483 

.631 

2 

.828 

.980 

.818 

.884 

.898 

.750 

.892 

8 

.945 

1.000 

.948 

.977 

.965 

.900 

.977 

4 

.988 

1.000 

.999 

1.000 

.992 

.980 

.995 

5  = 

1.000 

1.000 

1.000 

.987 

1.000 

1.000 

1.000 

G 

.976 

1.000 

.928 

.932 

.989 

.900 

.980 

7 

.881 

1.000 

.793 

.791 

.955 

.760 

.942 

8 

.670 

.985 

.578 

.578 

.830 

.550 

.775 

9 

.357 

.781 

.328 

.308 

.537 

.303 

.440 

H 

.180 

.464 

.150 

.154 

.282 

.182 

.228 

10 

Stem 

Stem 

Stem 

Stem 

Stem 

Stem 

Stem 

L.W.L.   Half-Breadths 


55 


6th.  The  construction  line  for  the  bilge  diagonal  is  variously 
drawn  from  rise  line  or  base  line  ;  but  the  latter  is  the  more  use- 
ful, being  adaptable  to  extremes  of  types  and  unaffected  by  rise 
of  floor  line  ;  i.e.,  the  line  should  be  drawn  diagonally  across  the 


.65 


DIAGRAM  OF  BILGE  DIAGONAL  OFFSETS 

FOR  VARIOUS  VALUES  OF  **b" 
(TEN  ORDINATES) 


$ 

\ 

10 

*- 

jL 

_s 

-' 

o7 

s- 

/ 

9 

& 

/ 

2 

/ 

y^ 

/ 

7' 

/ 

/ 

/ 

/ 

8, 

/ 

y 

/ 

Yi 

(•' 

/ 

/ 

91 

y 

y 

1 

/ 

/ 

/ 

f 

/ 

/ 

i. 

/ 

9/ 

** 

/ 

/ 

y 

>- 

— " 

)'■• 

<- 

C. 

L  C 

F 

5H 

P 

.7  .75  .8 

VALUES  OF"bT'(COEFF.OFB.D,) 
Fig.  13. 


.85 


body  plan  from  the  intersection  of  the  base  with  the  half  moulded 
breadth  line  to  center  line  at  load  water  line  height.  It  is  evi- 
dent that  the  area  enclosed  by  this  line  must  bear  a  close  relation- 


56 


The  Naval   Constructor 


ship  to  the  prismatic  coefficient  which  varies  with  p  and  is  equal 

to  -— -  to  -^  where  p  ranges  from  .60  to  .82,  respectively. 

.His      .yy 

By  determining  the  value  of  the  bilge  diagonal  coefficient  "  0," 
and  referring  to  the  diagram  opposite,  the  offsets  for  a  line  enclos- 
ing an  equivalent  area  may  be  taken  off  and  run  as  a  half -breadth 
line. 

DIAGRAM    OF   L.  W.  L.    HALF-BREADTHS 

FOR   VARIOUS   VALUES   OF   "oc" 

(TEN   ORDINATES) 


ioV 

5 

OR 

1' 

5 

6 

3 

7^ 

4 

r 

•     8'~ 

/ 

/ 

o 

*> 

y 

s 

s 

/ 

E     7  - 
o 

? 

/ 

o 

J 

V 

£     e'- 

/ 

/' 

A 

j 

i- 

9 

y 

/ 

<     5  - 

/ 

/ 

■ 

s 

s 

/ 

' 

_j 

1 

H 

/ 

X 

L 

s 

s 

-j     3   ,, 

i 

j 

C.  1 

.0 

:  s 

HI 

P 

values  0f"a"  (coeff.  of  l.w.l.) 
Fig.  14. 

7th.  The  load  water  line  and  bilge  diagonal  half-breadths  hav- 
ing been  preliminarily  faired,  may  be  lifted  off  on  a  slip  of  pa- 
per and  transferred  to  body  plan  construction  lines,  when  there 
should  be  no  difficulty  in  drawing  in  freehand  the  sections,  having 
the  "dead  flat"  section  as  one  extreme  guiding  curve  and  the 
transom  frame  as  the  other. 

8th.    After  the  preceding  sections  have  been  carefully  outlined 


Body   Plan  of  "Oceanic" 


57 


BODY  PLAN  OF  "OCEANIC 


LENGTH  B.P.  6&5f-3l*,  B.MLD.  68'-2",  D.MLD.  4a'-l" 
SECTIONS  68.537' APT. 


STATION  No.j 


STATION  No, 
STATION  No.  2 
STATION  NO.  3 
STATION  Noi 
STATION  No.  5 


STATION  No.  9^ 

STATION  No. 
ft/H,         l~~~~~~^     STATIPN 


iTION  No.  8 
STATION  No.  7 


ELEMENT  COEFFICIENTS 


AREA  OF  MID.    SECT. 

0 

= 

393 

BLOCK  CO-EFF. 

J 

= 

666 

PRISMATIC  CO-EFF.  . 

P 

= 

742 

AREA  OF  L.W.I 

_a 

■ 

771 

BILGE  DIAGONAL  -_ 

_b 

= 

723 

RELATION  CO-EFF. 

_£ 

= 

Ml 

Fig.  15. 

to  eye  with  the  guide  spots  mentioned,  the  planimeter  should  be 
used  to  take  a  trial  displacement,  on  the  result  of  which  will  de- 
pend how  near  the  designer's  judgment  has  determined  the  true 
section  line.  In  any  case  he  cannot  have  got  far  away,  and  a  very 
slight  alteration  (if  any)  is  all  that  will  be  required. 

9th.    The  sheer  heights   may  now  be  taken  from   profile  and 
spotted  on  body  plan,  level  lines  being  struck  across  at  these 


58 


The  Naval   Constructor 


heights  on  which  to  set  off  the  rail  half-breadths  previously  run  in 
plan,  as  described  in  paragraph  4.  This  will  enable  the  completed 
body  plan  to  be  drawn  in  approximately,  from  which  spots  may 
be  obtained  to  fair  up. 

Having  got  thus  far,  the  final  work  of  fairing  will  be  a  compara- 
tively easy  matter.  A  buttock  line  half-way  out  on  the  counter 
will  prove  a  very  useful  line  for  this  purpose,  thereafter  taking 
buttock  and  water  line  alternately  until  the  whole  body  is  faired. 
Where  great  fairness  is  required,  a  complete  set  of  diagonal  lines 
should  be  run  ;  but  ordinarily  this  is  unnecessary,  unless  in  small 
craft  where  the  sections  are  intended  directly  for  the  floor  with- 
out further  fairing. 

The  following  will  prove  a  suitable  method  for  designing  and 
fairing  the  bossed  plating  enclosing  after-end  of  shafting.  Hav- 
ing determined  the  outside  diameter  of  the  boss  of  spectacle  frame, 
lay  off  the  distance  to  outer  edge  of  boss  barrel  at  forward  end  of 
same  on  the  half-breadth  plan,  as  at  A.  Then  take  another  spot 
at  the  fore  end  of  the  stern  tube  equal  to  the  siding  of  the  vessel's 
bulkhead  frame  plus  one  inch  clear  of  the  stuffing  box  flange  on 
the  stern  tube  bulkhead  at  "C."  Through  these  two  spots  con- 
tinue a  straight  line  until  it  intersects  the  water  plane  at  the  shaft 
center  level  "D."     The  angular  space  formed  by  the  junction  of 


Bhd 


Fig.  16. 


the  water  plane  mentioned  and  the  projected  line  should  then  be 
carefully  faired  into  the  eye  with  a  spline,  when  the  resulting  line 
will  give  you  half-breadths  at  the  shaft  center  height.  These  half- 
breadths  being  transferred  to  the  body  plan,  radii  should  be  struck 
through  them  giving  the  contour  of  the  bossing,  which  may  be 
continued  freehand  into  the  frame  sections  above  and  below  the 
boss,  observing  that  the  general  tone  harmonizes  with  the  outline 
of  spectacle  frame  previously  drawn  in,  in  accordance  with  the 
form  advocated  under  that  heading. 

Having  outlined  the  form  of  bossing  on  body  plan,  three  diago- 
nal lines  should  be  struck,  the  lower  one  intersecting  the  arcs 
forming  oxter  under  spectacle  frame,  the  middle  one  through  the 


Bossing 


59 


center  of  shaft,  as  shown  to  diagonal  1J,  and  the  other  making  a 
like  intersection  with  the  curves  of  the"  slope,  as  shown  on  the 
diagram.    These  diagonals  may  now  be  lifted  off  and  run  in  the 


DIAGRAM 

SHOWING 
METHOD  OF  DESIGNING  BOSSING. 


Fig.  17. 


usual  way  on  half-breadth,  faired  up,  and  retransf erred  to  body 
plan,  thus  permitting  of  same  being  more  accurately  delineated, 
as  it  will  be  remembered  these  were  originally  drawn  freehand. 


60 


The  Naval   Constructor 


Elements  of 


Piston 
Speed. 

Class  of  Steam i:k. 

to 

k  M      • 

O  W  w 

-  3  '■ 

Ft.  per 
Miu. 

Type  of 
Propeller. 

Type  of 
Engine. 

400 

500 
600 

700 
700 

Paddle. 
River  paddle  steamer    .... 

River  paddle  steamer    .... 
River  paddle  steamer    .    :    .    . 

River  paddle  steamer    .... 

(  Sea   paddle  steamer,  heavier  ) 
}     paddle  wheels  required  .    .    J 

13-15 

15-17 
18-22 

18-22 
18-22 

( Side  wheels 
(   feathering 

it            M 

Inclined 
it 

530 
530 
600 
600 

Cargo. 
Ordinary  freight,  300  to  450  .    . 
Ordinary  freight,  300  to  450  .     . 
Ordinary  freight,  300  to  450  .     . 
Ordinary  freight,  300  to  450  .    . 

8-11 
11-13 
11-13 
11-13 

Single  screw 
Twin  screw 

Inverted 

t« 

700 
750 

Cargo  and  Passenger. 
Intermediate  steamships,  450-600 
|  Very  large  intermediate,  cargo  I 
(  and  passenger,  600  and  over  .    J 

13-16 
14-16 

Single  screw 
Twin  screw 

Inverted 

800 
800 
950 
950 
950 

Ocean  Liners. 
Passengers  and  mail     .... 
Passengers  and  mail     .... 
Passengers  and  mail     .... 
Passengers  and  mail     .... 
Passengers  and  mail     .... 

16-19 
16-19 
19-23 
19-23 
19-23  • 

Single  screw 
Twin  screw 

Inverted 

it 

800-910 

Fast  channel  &  sound  steamers 

19-23 

Twin  screw 

Inverted 

950 
950 
950 

Battleships  &  cruisers,  1st  class 
Battleships  &  cruisers,  1st  class 
Battleships  &  cruisers,  1st  class 

23 
23 
23 

Twin  screw 

M             U 

it             «( 

Inverted 

tt 

1,200 

|  Torpedo-boat    destroyers   and  ) 
I      scouts ) 

30 

Twin  screw 

Inverted 

5,700 
6,000 
6,200 
7,000 
10,000 

8,000 

Turbine-driven   Vessels. 
\  Turbine  river  steamer  and  tur- ) 
(     bine  steam  yachts  .    .    .    »    1 
\  Turbine-driven  Atlantic  liner,  i 
(     passenger  and  mail     .    .    .    \ 
i  Turbine-driven  pass,  and  mail ) 
|     channel  and  sound  steamers  J 
j  Turbine-driven    torpedo  -  boat ) 
I     destroyer  and  scout    .    .    .    J 
I  Turbine-driven   torpedo  -  boat  1 
|     destroyer  and  scout    ...    I 
(Small  44-ton  displacement  ex-) 
j     perimental  vessel,  low  coalj 
(     radius      ) 

16-22 

22 
25 
30 
3G 

32 

\  Multiple 
{     6crew 

Hor. 
Conip. 

tt      ti 

Hor. 
Triple 

*  By  permission  of 


Elements  of  Engines 

Marine  Engines.* 


61 


Machinery  Particulars. 

_  ji 

o  a>  £ 

M  O 

Number  of 
Cylinders 
in  Each 
Engine. 

Cylinder 
Ratios. 

Type 

ot 

Boilers. 

Boiler 
Press. 
Lbs. 

Boiler 
Draft. 

2-Comp. 
Side  by  side 

M         (> 

3-Triple 
Side  by  side 

1  to  3.5 

I  :  2.16  :  4.82 

II  II           h 

Cyl. 

Loco. 
Cyl. 

100 

110 
120 

160 

Nat. 
Forced 

it 

6.50 

7.22 
11.00 

10.00 
9.00 

3-Triple 

11           M 

4-Quad. 

1  :  2.65  :  7.1 
1  :  2.1  :  4.5  :  9.14 

Cyl. 

175 
200 

214 

Nat. 
Forced 

4.85 
6.00 
5.85 
5.45 

3-Triple 
4-Quad. 

1  :  2.65  :  7.1 
1;  2.07: '4.24:  8.82 

Cyl. 

200 
214 

Nat. 

Assist. 

5.12 
4.37 

3  or  4-Triple 

4-Triple 
6-Quad. 
6-8  Quad. 

1 :  2.65  :  6.38 

1  :  2.07  :  6.37 
1  :  2.08  :  4.16  :  8.71 

M             M             II 

Cyl. 

180 

M 

H 

220 

Nat. 

Forced 

Nat. 

Forced 

7.00 
6.00 
6.16 
5.95 
6.25 

4-Triple 

1 :  2.28  :  5.84 

Cyl. 

180 

Forced 

8.00- 
9.70 

4-Triple 

1  :  2.26  :  7.00 

Cyl. 
W.  Tube 

175 
250 

Nat. 

Forced 

Nat. 

8.50 
10.00 
12.00 

4-Triple 

1  :  2.36  :  5.50 

Yarrow 
W.  Tube 

250 

Forced 

41.00 

P? 
T 

irson's  ) 
urbine  ) 

No  Expansions. 
125 
135 
125 

150 

Cyl. 
W.  Tube 

150 
180 
170 

150 

Forced 

Super- 
heated 
steam 

12.00 
16.00 
20.00 
55.00 
70.00 
100.00 

J.  Calder,  B.Sc. 


62  The  Naval  Constructor 


Level  lines  as  shown  at  Z2>  h,  h,  etc.,  are  now  drawn  from  the 
point  of  intersection  of  frame  with  diagonals  1  and  2,  and  the 
half-breadths  taken  off  at  these  levels  and  finally  faired-up  on 
half-breadth,  when  it  will  be  found  that  the  resulting  horizontal 
ribband  line,  besides  acting  as  a  check  on  the  fairness  of  the  di- 
agonals, will  show  the  "  wind  "  of  the  shell  plating  wrapping  into 
oxter  and  body  post  and  insuring  a  natural  **  snye  "  without  any 
chance  of  "  gather  "  or  unfairness. 

The  oxter  underneath  the  ship's  counter  may  be  faired  in  a 
similar  manner. 


Engine  Room   Lengths 

Engine  Room  Lengths. 


63 


£  fc  * 
3 


8' 6" 
10  6 
12  9 

12  3 

13  6 

14  0 
16  0 

16  6 

17  0 

18  0 
18  4 
20  0 
20  0 
20  0 

20  0 

21  0 

21  0 

22  0 
22  0 
22  0 
22  0 


Size  of 
Engines. 


10"&20", 

10" 

22&40 

27 
17&26  , 

20 
15&30  , 


21 
11,  17,  17 

11 

10,  16,  26 

21 

23&46 

36 

13£,  22£,  36 

24 

19,  30,  50 

30 

18,  28,  45 

30 

21J,  31,  34,  34 


24 

18£,27,  42 

18 

21,  34,  59 
36 

17.26J,  40 

24 
24,  40,  63 

42 

22,  36,  57 
36 

19,  32,  52 

36 
23^,  38,  62 

36 
24,  38,  62 


36 


Z  fc  Sn 


22' 0' 

23  0 

24  0 
24  0 
26  0 
26  0 
26  0 
26  0 
26  0 

26  6 

27  0 
27  6 
27  6 

27  6 

28  0 
28  0 
28  0 
28  0 
28  2 
28  3 


Size  of 
Engines. 


19", 

31" 

54" 

27 

42" 
40, 

65 

ttfc 

36 

28,  39,  57  r 

30 

36 
45, 

70 

28 

54 
46. 

75 

22 

48 
36, 

59 

25 

42 
41*. 

68 

42 
23£,  39, 

65 

22, 

42 
35, 

59 

30, 

62 
50, 

80 

28, 

54 
46, 

75 

25, 

48 
42£, 

72  T 

31, 

48 
52, 

83 

25, 

54 

72 

28, 

48 
46, 

76 

29, 

48 
45, 

74 

32, 

48 
52, 

81 

30, 

54 
50, 

80 

54 
19,  28i,  41,  60  n 

42 

19£,28f,30f,30f, 
18 


32' 07' 
34  0 

34  0 

35  0 

35  0 

36  0 

39  7 

40  0 
40  0 
42  0 
45  0 

47  6 

48  0 
48  0 

0 

59  0 

60  0 
62  6 
74  0 
77  6 


Size  of 
Engines. 


24J",  34£",  49£", 

-()" 

36" 

32|,  59,  92 

42 

24,  34,  48,  68 

T. 

42 
32£,  59,  92 

54 
40,  66,  106 

72 
32,  52,  60,  60 

42 

29,  46,  72 

48 

31,  43,  60,  86 

T. 

54 

33£,  51,  78 

48 

34f,  53,  63,  63 

T. 

'J' 

48 
30,  43,  63,  89 

T. 
6 

60 

32,  45£,  66,  66,  6 

54 
35,  50,  70,  100 

T. 

77 

28J,  28J,  55,  77,  77 

60 

43,  69,  79 

60 

40£,  55,  77,  77,  77 

60 
40£,  55,  77,  77,  77 

54 
35|,  50£,  73J,  105 

69 
49£,  73,  95,  95,  95 

60 
37,  37,  79,  98,  98^ 

69 

Twin  sets  noted  with  "  T.' 


64  The  Naval  Constructor 

CHAPTER  III. 

THE  PREPARATION  OP  SPECEflCATlONS. 

Too  much  care  cannot  be  expended  in  the  drafting  of  the  hull 
specification.  Clearness  and  conciseness  should  be  aimed  at 
consistent  with  an  embodiment  of  all  details  of  hull,  fittings,  and 
outfits  supposed  to  be  supplied,  and  all  repetition  or  ambiguity  of 
phraseology  carefully  avoided.  Hampering  restrictions  should 
be  left  out.  Know  your  requirements  and  state  them  distinctly. 
As  in  all  other  ship  construction  work,  it  will  pay  to  have  a 
definite  routine  or  system  in  which  to  draft  the  specification.  Of 
course,  it  is  obviously  impossible  to  have  a  standard  specification 
which  shall  apply  to  all  ships,  as  vessels  are  so  diverse  in  their 
types,  design,  construction,  and  equipment  as  to  make  this  an 
impossibility.  But  by  keeping  a  routine  list  of  headings  of 
paragraphs  before  one,  and  taking  these  in  rotation  when  drafting 
the  clauses,  the  liability  to  omit  important  requirements  is  reduced 
to  a  minimum,  besides  the  saving  in  time  and  distraction  of 
thoughts  through  having  to  recollect  what  comes  next.  For  this 
purpose  the  following  headings  have  been  selected  which  will 
apply  to  ordinary  vessels;  Of  course,  for  special  types  these  will 
require  modifications  and  additions  which  will  suggest  themselves. 

Specification  Headings. 

Title  giving  type  of  vessel.  character    of    erections, 

1.  Dimensions,         moulded  number  of  masts.    Num- 

length,  breadth  and  ber  of  passengers,  de- 
depth,  depth  of  hold,  load  scription  of  housing  of 
draft  and  deadweight.  passengers,  officers,   and 

2.  Classification.    The  Govern-  crew.     Nature    of  cargo 

ment  laws  to  which  the  and  handling  appliances, 

vessel  and  her  equipment  Location  of   machinery, 

are  to  conform,  also  full  and  any  special  features 

particulars   of  the  class  of  the  vessel, 

she    is    to    take  at  the  4.    Material  of  hull  and  rivets. 

Classification  Society  5.  Keel,  and  centre  girder  in 
concerned.  double  bottom  ships. 

3.  General  Description.      Type  6.    Bilge    or  side  fenders   and 

of       stem      and     stern,  mouldings,  docking  keels, 

number  of  decks,  laid  or      7.    Stem, 
otherwise,      length    and      8.    Stern  frame. 


Specification   Headings 


65 


9.    Shaft  brackets. 

10.  Kudder    and    stock    (also 

trunk  and  bearing). 

11.  Shell  plating. 

12.  Inner    bottom,     including 

plating,  side  girders, 
floors  and  margin  plate. 

13.  Scantling      in    machinery 

space. 

14.  Peak  tanks. 

15.  Deep  tanks. 

16.  E.  W.  storage  tanks. 

17.  Steel  decks  and  flats. 

18.  Transverse  bulkheads. 

19.  Longitudinal  bulkheads. 

20.  Bunkers,  oil  or  coal. 

21.  Engine  and  boiler  casings. 

22.  Shaft  tunnels. 

23.  Oil  trunks,  expansion. 

24.  Centre  keelson   J  £j£S2S 

25.  Side  keelsons      }  j^med 

26.  Hold     and     'tween    deck 

stringers. 

27.  Panting  arrangements. 

28.  Frames  and  reverse  frames, 

in  double  bottom,  up 
sides  and  at  ends. 

29.  Floors,  .     throughout      in 

single-bottomed  ships,  at 
ends  and  tail  brackets  in 
double  bottom  ships,  also 
reference  to  No.  12. 

30.  Web  frames. 

31.  Deck     beams     and     knee 

brackets. 

32.  Stanchions  to  beams. 

33.  Strong  beams  in  E.  and  B. 

space. 

34.  Hatchways  and  coamings, 

in  oil  or  cargo  spaces, 
covers,  fore  and  afters, 
bearers,  etc. 

35.  Cargo  and  coal  ports. 

36.  Grain    trimming    hatches. 

37.  Chain  lockers. 


38.  Machinery      Foundations; 

main,  auxiliary  and  deck 
machinery,  also  boiler 
saddles  and  shaft  and 
thrust   bearing    seats. 

39.  Sheet  steel  bulkheads. 

40.  Steel     deck    houses,   other 

than  erections. 

41.  Bridges,  navigating  or  dock- 

ing. 

42.  Steel  masts. 

43.  Steel  kingposts. 

44.  Steel  derricks,  spars,  etc. 

45.  Wood      masts,     kingposts 

and  spars. 

46.  Wood  decks. 

47.  Wood  deck  houses. 

48.  Ceiling  and  sparring. 

49.  Boat  stowage. 

50.  Anchor  stowage. 

51.  Watertight  doors  and  scut- 

tles. 
General    description    of  joiner 
work,  including  entrances  and . 
stairways  : 

52.  In  passengers'  quarters. 

53.  In  officers'  quarters. 

54.  In  crew's  quarters. 

55.  Pantry  accommodations. 

56.  Galley  accommodations. 

57.  Ice  room. 

58.  Sidelights  and  decklights; 

also  borrowed  lights. 

59.  Cattle  fittings. 

60.  Hawse  pipes. 

61.  Bollards  and  fairleads. 

62.  Hold  ladders. 

63.  Ladders    to    erections  and 

bridges. 

64.  Davits,  boat  and  anchor,  also 

provision  or  coaling  davits. 

65.  Bails,    bulwarks,   also  rail 

and  awning  stanchions. 

66.  Standing  and  running  rig- 

ging, including  cargo 
boom  handling  gear. 


66 


The  Naval  Constructor 


67. 

Sails,  covers,  and  awnings. 

97. 

Trim  and  stability. 

68. 

Cement  and  tiling. 

98. 

Plans  to  be  furnished  own- 

69. 

Paint  work. 

ers. 

70. 

Heating  system. 

Capacity      and      dead- 

71. 

Lighting  system. 

weight. 

72. 

Ventilating. 

General  arrangement. 

72a.  Refrigerating  system. 

Cabin  booking  plans. 

73. 

Deck  Machinery,  including 

Piping  plans. 

windlass,   winches   and 

Stability     curves     and 

capstan,  also  steam  and 

information. 

exhaust  piping. 

99. 

Docking. 

74. 

Fresh  and  salt  water  ser- 

100. 

Trial  trips. 

vice. 

101. 

Inspection     fees     ("class, 

75. 

Fire,  pumping  and  drain- 

etc). 

ing  system. 

102. 

General  clause  relating  to 

75a 

;.  Cargo  oil  system. 

material,  workmanship, 

76. 

Scuppers,  from  all  exposed 

inspection    by    owners, 

houses,  etc.,  and  from 

alterations,  extras,  etc. 

sanitary  quarters. 

77. 

Engine  room  and  docking 

Flags. 

telegraphs. 

National  colors. 

77a 

.  Steering  gear. 

House  flags,  and  burgee  with 

78. 

Anchors,  chains,   and  line 

name. 

outfit. 

International  signal  code. 

79. 

Boats  and  outfits. 

80. 

Flags,  etc. 

Boat  Outfit. 

81. 

Hose,  fire  and  wash  deck, 

Ash  oars,  thole  pins  or  rowlocks. 

also  fire  buckets. 

Rudder  (lanyard). 

82. 

Oil  tanks,  for  lamps,  etc. 

Tiller  (lanyard). 

83. 

Steaming  lights. 

Painter,  5  fathom  line. 

84. 

Lamps  and  lanterns,  also 

Cable,  20  fathom  line. 

rockets,  etc. 

Boat  hook. 

85. 

Navigating  instruments. 

Water  breakers. 

86. 

Boatswain's  stores. 

Bread  tank. 

87. 

Carpenter's  stores. 

Plugs  for  bung  hole ;   2,   with 

88. 

Cargo  handling  gear,  slings, 

chaiil. 

hooks,  etc. 

One  anchor. 

89. 

Cook's  or  galley  outfit. 

One  sea  anchor. 

90. 

Cabin  outfit. 

One  bailer. 

91. 

Cutlery  outfit. 

One  mast  yard  and  sail. 

92. 

Crockery  and  glass. 

One  compass  4"  card  in  case. 

93. 

Table  linen. 

Four 

oil    lanterns   to   burn   8 

94. 

Bed  linen  and  bedding. 

hours. 

95. 

Spare  glasses  for  side-lights 

Four 

oil  distributers,  1  gallon 

in  passenger  ships. 

each. 

96. 

Galvanizing. 

Twelve  boat  hatchets. 

Specification   Headings 


67 


Boatswain's  Stores. 

Watch  tackles. 

Relieving  tackles. 

Luff  tackles. 

Spare  blocks,  double  and.  single, 

assorted. 
Spare  sheaves,  for  boat  falls. 
Snatch  blocks. 
Cargo  gins. 
Deck  scrubbers. 
Wood  fenders,  with  lanyards. 
Cork  fenders,  with  lanyards. 
Marline  spikes. 
Crowbars. 
Chain  hooks. 
Chain  slings. 
Hair  crate  hooks. 
Screw  shackles. 
Pairs  of  grip-hooks. 
Pairs  of  case-hooks. 
Coir  brooms  and  handles. 
Mops. 

Ballast  shovels. 
Scrapers,  triangular. 
Scrapers,  steel  file. 
Set     of     funnel    blocks     and 

boards. 
Boatswain's  chairs,  one  to  each 

mast. 
Pilot  ladder. 
Five-inch   portable  fire   engine 

pump  with  hose. 
Bath  bricks. 
Hand  spikes. 
Paint  scrubbers. 
Pairs  of  handcuffs. 
Branding  iron. 
Paint  brushes,  assorted. 
Paint  pots,  one-half  gallon. 
Squeegees,  large. 
Scraping  box,  tin. 
Sewing  palms. 
Needles. 
Beam  clamps. 
Whitewash  brushes. 


Carpenter's  stores. 

"  Propeller  "  notice  boards. 

"  Smoking  "  notice  boards. 

' '  No  admittance ' '  notice  boards. 

Pump  hook,  jointed. 

Chain  punches. 

Pitch  pot,  3  gals,  and  ladle. 

Tar  bucket. 

Grindstone    and    trough,     18" 

diam. 
Shifting  spanner,  large. 
Ring  spanners,    to  fit    bunker 

plates,  etc. 
Keys  for  cargo  ports. 
"     "   sidelights. 
"     "   coal  ports. 
"     "   mushroom  ventilators. 
Rim  spanner  for  sidelights. 
Spanners  for  deep  tank  hatch 

bolts. 
Rail  straightener,  3'  6"  long. 
Rod  sounding  rods. 
Flexible  sounding  rods,   2'  0" 

long. 
Caulking  tools. 
Caulking  mallet. 
Spare  hatch  wedges. 
Capstan  bars  and  rack, 
Monkey  wrench. 
Wheel-house  axes,  large. 
Tools    in    chest,    with    ship's 
name     on ;     chest     and 
tools. 
One  26"  hand  saw. 
One  crosscut. 
One  auger  \\". 
One  purger  \\". 
One  adze. 
One  hammer. 
Two  top  mawls. 
Two  screwdrivers. 
One  jack  plane. 
One  hand  plane. 
Three  chisels,  assorted. 
Three  gimlets,  assorted. 


68 


The  Naval  Constructor 


J  oil. 


Steaming  Lights. 
Two  masthead  ^^    ^ 
Starboard  J  for  electric. 

do.  do.  galvanized  iron,  for  oil. 

Two  riding  lights 

One  overtaking  light 

Three  ruby  lights 

Three  black  balls. 

Spare  glasses  for  lamps,  2  for 
each. 

Carriers  and  halliards  for  mast- 
head and  riding  lights. 

Lamps  and  lanterns. 

"Exit"  lamps  in   passengers' 

quarters. 
Dark  lanterns  (3  for  large  ships). 
Cargo    lanterns    (12   for    large 

ships). 
White    lanterns    (2    for    large 

ships). 
Hurricane  lights   (5    for  large 

ships)      with      3      spare 

glasses. 
Lamps  for  saloon  and  officers' 

rooms  in  small  ships. 
Lamp  scissors. 
Oil  funnels. 
Lamp  wicks. 

Rockets,  signal  cannon,  to  be 
supplied  as  required  by 
U.  S.  laws,  together  with 
owner's  night  signals, etc. 

Navigating  Instruments. 

Standard  compass  and  stand. 

Ten  inch  spirit  compasses  in 
navigating  positions. 

One  spare  card. 

Boat's  compasses,  4"  card. 

Sounding  machine,  or  deep  sea 
lead  (28  lbs.),  line  and 
reel.     130  fathoms. 


Hand  lead   (16  lbs.),    line,  and 

reel,  30  fathoms. 
Pelorus. 
Clocks. 

Aneroid  barometers. 
Telescope. 
Binoculars,  marine. 
Log  slates. 
Parallel  ruler. 
Pair  dividers. 
Chart  weights. 
Foghorn. 

Tarpaulins. 

Usually  3  to  each  weather  deck 
hatch  ;  1  to  others. 

One  rubber  sheet  to  hatches  on 
which  cattle  are  carried. 

Covers  to  all  sails  and  instru- 
ments, wheels,  etc.,  in 
exposed  positions  ; 
weather  cloths  to  shelter 
passenger  decks  in  large 
passenger  ships. 

Bakery  Outfit. 
Two  biscuit  tubes. 
One  biscuit  forcer. 
One  apple  corer. 
One  bread  rasp. 
One  galvanized  bucket. 
One  buckwheat  jug. 
Six  cake  hoops. 
One  hundred  and  twenty  corn 

bread  tins. 
One  dough  knife. 
One  scraper. 
One  sugar  dredger. 
One  flour  dredger. 
Two  flour  scoops. 
One  tin  opener. 
One  casserole  mould. 
Eighteen  (quart)  jelly  moulds. 
Six  pudding  moulds  with  lids. 
Seventy-two  muffin  rings. 
One  bread  grater. 


Specification  Headings 


69 


One  nutmeg  grater. 

One  barm  can. 

One  palette  knife. 

Two  sets  cutlet  paste  cutters. 

Six  paste  brushes. 

Two  rolling  pins. 

to  14 

One  flour  sieve. 

One  spice  box  complete. 

Twelve  bread  tins. 

Two  French  roll  tins. 

Twenty-four  open  tart  tins. 

One    hundred     and  forty-four 

patty  tins. 
Six  rice  pudding  tins. 
Six  roll  tins. 
Eighteen  sandwich  bread  tins, 

with  lids. 
Twenty-four        sponge       cake 

frames. 
One  water  can. 
Two  egg  whisks. 
One  set  icing  pipes. 
One  icing  bag. 

One  enameled  whisking  bowl. 
One  patent  egg  whisk. 
One  egg  basket. 
One  suet  machine. 
One  bread  knife. 
Twelve  large  bread  sheets. 
One  bread    prover,   galvanized 

iron,  6'  0"  x  2'  5"  x  V  5" 

with  copper  steam  pipe. 

Galley  Outfit, 
Braising    pans,     copper,    with 

wire  nets. 
Water  cans. 
Butcher's  choppers. 
Cook's  saws. 
Tin  colanders. 
Chopping  block. 
Dippers,  tin. 
Aluminum     stew    pans,     with 

handles  and  lid. 


Sauce  pans  (enameled  iron),  1 
qt.,  3  pt.,  and  2  qt. 

Oval  fish  kettle  and  lid. 

Potato  masher. 

Dog  baskets,  wicker,  tin  lined. 

Sieves,  hair  mesh. 

Sieves,  wire  mesh. 

Sauce  ladles,  small. 

Tin  opener. 

Beef  press. 

Pea  soup  masher,  tammy  sieve. 

Copper  stew  pans,  6"-16"  diam., 
with  long  handles,  and 
lids  with  long  handles. 

Stock  bucket. 

Stock  pot. 

Omelette  pans,  copper. 

Prying  pans,  round. 

Prying  pans,  oval. 

Tormentors. 

Pokers. 

Shovels. 

Rakes. 

Gridirons,  double. 

Gridirons,  large. 

Sets  of  skewers,  assorted  sizes. 

Egg  basket. 

Glaze  pot,  copper  and  brush. 

Pour-inch  basket  ladle,  wire. 

Frying  baskets,  round,  wire. 

Cook's  forks. 

Salt  box. 

Plour  box. 

Wire  gravy  strainer. 

Grill  tins. 

Two  gallon  copper  kettle. 

Jelly  bag. 

Knives,  French. 

Knives,  butcher's. 

Knives,  mincing. 

Knives,  oyster. 

Knives,  palette. 

Knives,  potato. 

Bill  of  fare  frame. 

Pie  pans,  12"  x  8",  enameled. 

Pie  pans,  8"  x  6". 


70 


The  Naval  Constructor 


Steak  tongs. 

Store  tins. 

Stove  top  hooks. 

Porridge  whisks,  strong  wire. 

Cutlet  bat. 

Vegetable  cutters. 

Vegetable  scoops. 

Brawn  moulds. 

Tongue  press. 

Pepper  dredgers. 

Hot  pot  tins. 

Plate  carriers. 

Bread  grater. 

Flour  dredge. 

Iron  ladles. 

Larding  needles. 

Trussing  needles. 

Potato  masher. 

Egg  slicer. 

Fish  slicer. 

Spoons,  iron. 

Spoons,  wood. 

Steel. 

Ship's  Galley  Outfit. 
Mess    kids,    large,-  small    and 

oval. 
Square  steamers. 
One    square    coffee    boiler   (28 

gal.)  B.  T. 
Oval  boilers  (15  gal.)  B.  T. 
Roast  tins. 

Saucepans,  iron  enameled. 
One    round    steam    boiler    (50 

gal.)  cast  iron  with  large 

brass  tap. 
Range. 
Colanders. 
Shovel. 
Poker. 

Buckets,  galvanized  irov. 
Rake. 

Tormentor. 
Large  ladle. 
Square  duff  tins. 
Chopping  block. 


Pantry  Outfit. 

Pair  butter  spades. 

Meat  choppers. 

Poultry  choppers. 

One  clock. 

Dish  covers,  B.  M. 

Egg  slicers. 

Ice  pricker. 

Jugs  (enameled),  1  gallon. 

Two  bread  knives. 

Two  carving  knives. 

Two  French  knives. 

Two  ham  knives. 

Pairs  knives  and  forks  for  poul 
try. 

Plate  covers,  tin. 

Iron  spoons,  18"  long. 

Lemon  squeezer. 

Tin  openers. 

Slop  receivers,  20  gallons. 

Soup  ladles. 

Soup  tureens,  B.  T. 

Steel. 

Waiter's  Carpathian. 

Wire  whisks  12"-18". 

Milk  cans  with  lid  and  spout, 
2  gallons. 

Steam  carving  table  6'  0"  x  2' 

6",  with  tin  top,  3  large, 

2    medium   and  2  small 

wells. 

Steam  egg  boiler. 

Steam  bain-marie,  4  stew  pans, 

brass  frame. 
One  coffee   boiler,    10  gallons, 

E.P. 
One  hot  water  boiler,    15  gal- 
lons E.  P. 
Whisking  bowl. 
Water  cooler. 

Electroplate  and  Cutlery. 

Asparagus  tongs. 
Butter  coolers. 
Cheese  scoops. 


Specification  Headings 


71 


Tea  pots,  3  pints. 
Tea  pots,  1|  pints. 
Coffee  pots,  2  pints. 
Coffee  pots,  1  pint. 
Entree  dishes,  10"  oval. 
Entree  dish  covers,  with  mov- 
able handles. 
Vegetable  dishes. 
Vegetable     dish    covers,    with 

movable  handles. 
Ice  tongs. 
Sauce  frames   (Worcestershire, 

etc.). 
Prs.  fish  carvers. 
Fish  forks. 
Fruit  forks. 
Dessert  forks. 
Pickle  forks. 
Butter  knives. 
Fish  knives. 
Dessert  spoons. 
Soup  spoons. 
Sauce  ladles. 
Soup  ladles. 
Finger  bowls. 
Ice  pails. 

Napkin  rings,  numbered. 
Prs.  nut  crackers. 
Toast  racks,  large. 
Toast  racks,  small. 
Fruit  knives. 
Mustard  spoons. 
Salt  spoons. 
Tea  spoons. 
Egg  spoons. 
Table  spoons. 
Sugar  bowls,  large. 

"      bowls,  small. 

"      tongs,  small. 

"      tongs,  large. 
Sardine  tongs. 
Cream  jugs,  large. 
Cream  jugs,  small. 
Fine  sugar  sifters,  gilt  bowls. 
Fine  sugar  bowls. 
Syrup  jugs,  hinged  lids. 


Hot  water  jugs,  1  pint. 
Tureen  and  covers  for  soup,  6 

quarts. 
Tureen  and  covers  for  sauce. 
Fruit    dishes,    gilt,    large    12" 

long. 
Fruit  dishes,  gilt,  small,  9\" long. 
Wine  corks. 
Waiters,  8",  10",  12". 
Wine  funnel. 

Glass. 
Celery  glasses. 
Tumblers. 
Soda  glasses. 
Champagne  glasses. 
Claret  glasses. 
Liqueur  glasses. 
Port  and  Sherry  glasses. 
Cocktail  glasses. 
Bedroom  tumblers. 
Pickle  jars. 
Glass  dishes,  small  oval. 

"        "       large  oval. 

"         "       large  round. 

"         "       small  round. 

"         "       ground    glass    for 
ice  cream. 
Water  decanters,  saloon. 
Water  decanters,  bedroom. 
Salt  casters. 

Pepper  casters,  E.  P.  tops. 
Red  pepper  casters,  E.  P.  tops. 
Salad  bowls. 

China. 

Dessert  plates. 

Tea  cups,  afternoon. 

Tea  saucers,  afternoon. 

Earthenware. 

Breakfast  cups  and  saucers. 
Tea  cups  and  saucers. 
After-dinner    coffee   cups    and 
saucers. 


72                  The  Naval 

Constructor 

Egg  cups,  d.  e. 

Towels,  bath. 

Dinner  plates. 

Dusters. 

Soup  plates. 

Covers  for  saloon  chairs  and 

Cheese  plates. 

settees. 

Slop  basins. 

Jardinieres,  large. 

General  Stores. 

Jardinieres,  small. 

Chambers,  bedroom. 

Spring  balance. 

Milk  jugs. 

Scales  and  weights. 

Linen. 

Handy  billy. 
Brooms. 

Two  prs.  sheets  to  each  berth. 

Brushes,  banister. 

One  pr.  blankets  to  each  berth. 

Dustpans  and  brushes. 

One  bed-spread  to  each  berth. 

Shoe  brushes. 

Two    pillow    cases     to     each 

Buckets. 

pillow. 

Mops. 

Two  pillows  to  each  berth. 

Cuspidores  and  linings. 

One  mattress,  over  spring  mat- 

Dinner bell. 

tress. 

Cork  screws. 

One  mattress  cover. 

Knife  board. 

Three  sets  tablecloths. 

Table  gong. 

Napkins. 

Deck  chairs. 

Table  covers,  baize,  red,  etc. 

Wicker  chairs. 

Glass  cloths. 

Blotting  pads. 

Towels,  pantry. 

Bibles,  etc. 

"       passenger,  four  to  each. 

Chess  men,  etc. 

44       officers,  four  to  each. 

Library  books. 

"       lavatories. 

Printing  press. 

Freeboard  73 

CHAPTER   IV. 
FREEBOARD. 

In  the  following  tables  the  word  Freeboard  denotes  the 
height  of  the  side  of  a  ship  above  the  waterline  at  the  middle 
of  her  length,  measured  from  the  top  of  the  deck  at  the  side,  or, 
in  cases  where  a  waterway  is  fitted,  from  the  curved  line  of  the 
top  of  the  deck  continued  through  to  the  side.  The  freeboards 
and  the  corresponding  percentages  of  reserve  buoyancy  neces- 
sary for  flush-deck  steamers  not  having  spar  or  awning  decks 
and  for  flush-deck  sailing  vessels  are  given  in  Tables  A  and  D 
for  vessels  of  these  classes  and  of  various  dimensions  and  pro- 
portions. The  freeboards  necessary  for  spar-  and  awning-deck 
steamers  are  given  in  Tables  B  and  C.  The  latter  are  deter- 
mined by  considerations  of  structural  strength,  and  they  de- 
note the  limitations  to  depth  of  loading  which  are  thereby 
imposed  upon  first-class  vessels  of  these  types.  The  free- 
boards and  percentages  of  reserve  buoyancy  thus  obtained  be- 
ing in  excess  of  what  would  otherwise  be  required,  the  amount 
of  such  percentages  are  not  given  in  Tables  B  and  C. 

The  exact  freeboard  required  for  a  given  ship  of  standard 
proportions  belonging  to  either  of  the  classes  comprised  in 
Tables  A  and  D  may  be  calculated  by  constructing  a  displace- 
ment scale  to  the  height  of  the  deck  to  which  the  freeboard  is 
measured,  so  as  to  give  the  whole  external  volume  up  to  the 
upper  surface  of  that  deck.  The  percentage  of  the  total  volume 
which  is  given  in  the  tables  as  the  reserve  buoyancy  for  a  vessel 
of  given  type  and  dimensions  will  be  the  amount  of  volume 
that  must  be  left  out  of  the  water.  If  a  waterline  be  drawn  up 
upon  the  displacement  scale  aforesaid  to  cut  off  the  given  per- 
centage of  total  volume,  the  height  of  side  above  this  line  will 
be  the  freeboard  required. 

In  order  to  simplify  and  reduce  the  work  that  would  be  in- 
volved by  the  above  mode  of  determining  the  waterline  and  the 
consequent  freeboard  that  correspond  to  a  given  percentage 
of  reserve  buoyancy,  an  approximate  method  is  adopted  in  the 
following  tables,  which  enables  the  freeboard  of  a  vessel  to  be 
calculated  with  a  sufficient  degree  of  accuracy  for  all  ordinary 
working  purposes.  The  use  of  this  method  not"  only  saves  the 
time  and  labor  that  would  be  involved  by  making  a  complete 
displacement  scale  for  the  whole  external  volume  of  the  ship, 
but,  what  is  much  more  important,  it  makes  the  tables  easily 
and  directly   applicable  in   cases  where  such   a  displacement 


74  The  Naval  Constructor 


scale  for  a  vessel  is  not  at  hand,  or  where  the  data  requisite  for 
constructing  one  are  not  procurable. 

In  this  approximate  method  the  form  of  the  ship  is  taken 
into  account  by  means  of  proportionate  quantities,  which  are 
termed  coefficients  of  fineness,  instead  of  by  the  exact  volumes 
that  a  displacement  scale  would  give.  It  is  found  that  the 
whole  internal  volume  of  a  ship  as  measured  for  register  tonnage 
divided  by  the  product  of  the  length,  breadth,  and  depth,  meas- 
ured as  described  in  the  following  clauses,  1,  2,  and  3,  gives  a 
fractional  quantity  of  coefficient  which  bears  a  nearly  constant 
relation  to  the  quantity  that  would  be  obtained  by  dividing  the 
whole  external  volume  below  the  upper  surface  of  the  deck  by 
the  product  of  the  length,  breadth,  and  depth.  This  fractional 
quantity  is  called  the  "coefficient  of  fineness"  for  freeboard 
purposes,  and  it  serves  the  same  practical  object,  when  com- 
bined with  the  dimensions  of  the  ship  in  the  manner  explained 
in  the  tables,  as  the  volume  itself  would  do. 

In  applying  such  an  approximate  method  as  the  above,  it  is 
necessary  to  connect  the  coefficients  of  fineness  given  in  the 
tables  with  a  standard  sheer  and  round  of  beam.  The  standard 
scales  for  sheer  and  round  of  beam  that  have  been  adapted  for 
this  purpose  are  given  in  Clauses  18  and  19  hereafter.  De- 
scriptions are  also  there  given  of  the  corrections  that  should  be 
made  for  deviations  from  these  standard  amounts. 

The  freeboards  given  in  the  tables  are  for  flush-deck  vessels 
in  all  cases.  Such  reductions  in  freeboard  as  may  be  allowed 
for  deck  erections  of  various  kinds  and  sizes  in  steamers  not 
having  spar  or  awning  decks  and  in  sailing  vessels  are  de- 
scribed in  paragraphs  11,  12,  13,  14,  15,  16,  and  17. 

No  reduction  of  freeboard  should  be  allowed  on  account  of 
deck  erections  in  spar-deck  and  awning-deck  steamers,  except 
in  spar-deck  vessels  in  which  an  allowance  may  be  made  for  a 
long  bridge  house,  see  pp.  21  and  22. 

Tables  A  and  D  give  the  minimum  freeboards  for  first-class 
iron  and  steel  vessels,  the  strength  of  which  is  at  least  equal  to 
the  requirements  of  the  100a  class  in  Lloyd's  Register  for  three- 
deck  and  smaller  vessels.  The  freeboard  of  all  other  iron  and 
steel  vessels,  classed  or  unclassed,  should  be  regulated  by  the 
same  standard,  the  increase  of  freeboard  required  in  each  case 
being  determined  by  the  limit  at  which  the  stress  per  square 
inch  upon  the  material  of  the  hull  amidships  shall  not  exceed 
that  of  the  standard  class,  of  the  same  proportions,  form,  and 
moulded  depth,  when  loaded  to  the  freeboards  required  by 
Tables  A  and  D.  Tables  B  and  C  give  the  freeboards  for  ves- 
sels built  in  accordance  with,  or  equal  to,  the  requirements  of 
Lloyd's  Register  for  the  spar-  and  awning-deck  classes,  and  are 


Freeboard  75 


subject  to  the  conditions  just  stated  for  any  modifications  of 
strength  in  excess  of  diminution  of  the  requirements  of  their 
respective  classes. 

1.  Length.  —  The  length  of  the  vessel  is  measured  on  the 
load  line  from  the  fore  side  of  the  stem  to  the  aft  side  of  the 
sternpost  in  sailing  vessels,  and  to  the  aft  side  of  the  aft  post  in 
steamers. 

2.  Breadth.  —  The  breadth  used  in  obtaining  the  coefficient 
of  fineness  is  the  extreme  breadth  measured  to  the  outside  of 
plank  or  plating  as  given  on  the  certificate  of  the  Ship's  Regis- 
try. 

3.  Depth  of  Hold.  —  The  depth  used  in  obtaining  the 
coefficient  of  fineness  is  the  depth  of  hold  as  given  on  the  Certif- 
icate of  the  Ship's  Registry.  This  dimension  is  subject  to 
modification  in  determining  the  coefficient  of  fineness  as  ex- 
plained in  Clause  4. 

4.  Coefficient  of  Fineness.  —  The  coefficient  of  fineness 
in  one-,  two-,  and  three-deck  and  spar-deck  vessels  is  found  by 
dividing  100  times  the  gross  registered  tonnage  of  the  vessel 
below  the  upper  deck  by  the  product  of  the  length,  breadth, 
and  depth  of  hold.  In  awning-deck  vessels  the  registered  depth 
and  tonnage  are  taken  below  the  main  deck. 

(a)  It  is  of  importance  in  the  application  of  the  rules  and 
tables  of  freeboard  that  the  coefficient  of  fineness  deduced  from 
the  under-deck  tonnage  and  the  principal  dimensions  to  be  a 
correct  index  to  the  vessel's  relative  fullness  of  form,  and  that  a 
change  in  any  of  those  elements  which  affect  the  coefficient, 
determined  in  accordance  with  the  rule  set  forth,  should  be 
considered,  and  the  necessary  correction,  having  regard  to 
the  special  circumstances  of  the  case,  introduced.  Among  the 
cases  that  have  from  time  to  time  come  under  notice  are 
the  following: 

(b)  Vessel  Having  a  Cellular  Bottom  Throughout,  or  Floors  of 
Greater  Depth  than  those  Usually  Fitted.  —  In  such  a  case  the  co- 
efficient as  determined  from  the  under-deck  tonnage  is  in  most 
instances  slightly  greater  than  it  would  be  if  the  vessel  were 
framed  on  the  ordinary  transverse  system  with  floors  of  the 
usual  depth.  No  general  rule  can  be  given  for  guidance,  but  it 
is  not  difficult,  if  the  depth  and  slope  of  the  top  of  the  cellular 
bottom  or  floor  be  compared  on  the  midship  section  with  the 
depth  and  slope  of  an  ordinary  floor,  to  determine  very  closely 
the  amount  of  the  correction  necessary. 

(c)  Vessel  Constructed  with  Floors  of  the  Ordinary  Kind,  but 
with  a  Cellular  Bottom  for  a  -part  of  the  Length  Amidships  Under 


76  The   Naval   Constructor 


the  Engines  and  Boilers.  —  In  such  case  the  registered  under- 
deck  tonnage  is  smaller  than  it  would  be  if  the  vessel  were 
framed  with  ordinary  floors  throughout,  the  difference  being 
the  tonnage  of  the  space  between  the  bottom  of  the  cellular 
bottom  in  the  part  amidships  and  the  level  of  the  ordinary 
floor.  The  depth  of  hold  is  also  measured  by  the  customs 
officials  to  the  top  of  the  cellular  bottom,  and  this  depth  is  in- 
serted in  the  register.  Under  such  circumstances,  in  order  to 
arrive  at  the  coefficient  of  fineness  the  vessel  would  have,  if 
built  on  the  ordinary  system  throughout  and  for  which  the 
tables  are  framed,  the  tonnage  of  the  volume  between  the  top 
of  the  cellular  bottom  and  the  level  of  the  ordinary  floor  should 
be  calculated  and  added  to  the  registered  under-deck  tonnage. 
The  tonnage  so  corrected  used  in  conjunction  with  the  depth  of 
hold  to  the  top  of  the  ordinary  floor,  gives  the  coefficient  to  be 
used  in  the  tables. 

(d)  Vessel  Constructed  with  a  Cellular  Bottom  Throughout  the 
the  Fore  and  After  Holds,  but  wiih  Floors  of  the  Ordinary  Kind 
Fitted  for  a  Part  of  the  Length  Amidships  Under  the  Engines  and 
Boilers.  —  In  such  a  case  the  tonnage  of  the  space  between  the 
top  of  the  ordinary  floors  in  the  part  amidships  and  the  top  of 
the  cellular  bottom,  if  made  continuous,  should  be  estimated 
and  deducted  from  the  registered  under-deck  tonnage  and  the 
remainder  employed  in  conjunction  with  the  depth  of  hold  to 
the  top  of  the  cellular  bottom  in  determining  the  coefficient  of 
fineness. 

(e)  Other  cases  may  in  practice  arise  in  which  the  registered 
under-deck  tonnage,  or  the  registered  depth  of  hold,  or  registered 
breadth  require  modification  before  being  used  in  the  determi- 
nation of  the  coefficient  of  fineness,  but  little  difficulty  will  be 
experienced  in  making  the  necessary  correction  if  it  be  re- 
membered that  the  coefficient  sought  is  the  coefficient  the  vessel 
would  have  if  framed  on  the  ordinary  transverse  system. 

5.  Moulded  Depth.  —  The  moulded  depth  of  an  iron  or 
steel  vessel,  as  given  in  the  tables,  is  the  perpendicular  depth 
taken  from  the  top  of  the  upper  deck  beam  at  side,  at  the  middle 
of  the  length  of  the  vessel,  to  the  top  of  the  keel  and  the  bottom 
of  the  frame  at  the  middle  fine,  except  in  spar-  and  awning- 
deck  vessels,  in  which  the  depth  is  measured  from  the  top  of 
the  main-deck  beams.  In  wooden  and  composite  vessels  the 
moulded  depth  is  taken  to  be  the  perpendicular  depth  from  the 
top  of  the  upper-deck  beam  at  the  side  of  the  vessel  amidships 
to  the  lower  edge  of  the  rabbet  at  the  keel. 

(a)  The  form  at  the  lower  part  of  the  midship  transverse  sec- 
tion of  many  wooden  and  composite  vessels  being  of  a  hollow 


Freeboard  77 


character,  as  in  cases  where  thick  garboard  strakes  are  fitted, 
the  moulded  depth  in  such  instances  should  be  measured  from 
the  point  where  the  line  of  the  flat  of  the  bottom  continued 
cuts  the  keel. 

6.  Freeboard.  —  The  moulded  depth,  taken  as  above  de- 
scribed, is  that  used  in  the  tables  for  ascertaining  the  amount 
of  reserve  buoyancy  and  corresponding  freeboard  in  vessels 
having  a  wood  deck,  and  the  freeboard  is  measured  from  the 
top  of  the  wood  deck  at  side,  at  the  middle  of  the  length  of  the 
vessel. 

(a)  On  the  same  principle,  in  flush-deck  vessels,  other  than 
spar  or  awning  decked,  and  in  vessels  fitted  with  short  poop  and 
forecastle,  having  an  iron  upper  deck,  not  covered  with  wood, 
the  usual  thickness  of  a  wood  deck  should  be  deducted  from  the 
moulded  depth  of  the  vessel  measured  as  above,  and  the  amount 
of  reserve  buoyancy  and  corresponding  freeboard  taken  from 
the  column  in  the  tables  corresponding  with  this  diminished 
moulded  depth :  Example.  —  In  a  steamer  fitted  with  an  iron 
upper  deck,  not  covered  with  wood,  and  having  a  moulded 
depth  of  19  ft.  10  ins.,  four  inches,  or  the  usual  thickness  of  a 
wood  deck,  must  be  deducted  from  this,  leaving  a  depth  of  19  ft. 
6  ins.  The  freeboard  of  such  a  vessel  with  a  coefficient  of  fine- 
ness of  0.76,  taken  from  the  column  under  19  ft.  6  ins.,  is  3  ft.  8£ 
ins.,  which  should  be  measured  from  the  top  of  the  iron  upper 
deck. 

(6)  In  spar-deck  vessels  having  iron  spar  decks  and  in  awning- 
deck  vessels  having  iron  main  decks,  the  freeboard  required  by 
the  tables  should  be  measured  as  if  those  decks  were  wood 
covered.  Also  in  vessels  where  r7o,  or  more,  of  the  main  deck 
is  covered  by  substantial  erections,  the  freeboard  found  from 
the  tables  should  be  measured  amidships  from  a  wood  deck, 
whether  the  deck  be  of  wood  or  iron.  In  applying  this  principle 
to  vessels  having  shorter  lengths  of  substantial  enclosed  erec- 
tions the  reduction  in  freeboard,  in  consideration  of  its  being 
measured  from  the  iron  deck,  is  to  be  regulated  in  proportion  to 
the  length  of  the  deck  covered  by  such  erections.  Thus  in  a 
vessel  having  erections  covering  t6q  of  the  length,  the  reduction 
is  r%  of  3h  inches,  or  2  inches. 

7.  For  vessels  which  trim  very  much  by  the  stern,  through 
the  engines  being  fitted  aft,  the  freeboard,  as  ascertained  from 
the  tables,  if  set  off  amidships  would  not  cut  off  the  amount  of 
surplus  buoyancy  deemed  necessary,  and  in  such  cases  the 
suitable  freeboard  amidships  could  only  be  determined  after 
full  information  is  obtained  regarding  the  vessel's  trim. 


78  The  Naval  Constructor 

8.  The  following  example  will  illustrate  the  general  applica- 
tion of  the  tables: 

In  a  steamer  of  the  following  dimensions,  viz.,  length,  204  ft.; 
breadth  extreme,  29  ft.;  depth  of  hold,  16.0  ft.;  registered 
tonnage  under  deck,  628  tons;  and  moulded  depth,  17.0  ft.;  the 
under  deck  capacity  in  cubic  feet  is  68,200;  by  dividing  this  by 
94,656,  that  is,  the  product  of  the  length,  breadth,  and  depth  of 
hold,  the  quotient  is  0.72,  or  the  coefficient  of  fineness. 

If  we  now  refer  to  Table  A  at  17.0  ft.  moulded  depth  and 
trace  the  line  opposite  the  coefficient  0.72  to  the  column  cor- 
responding with  this  depth,  it  is  found  that  the  winter  freeboard 
given  for  a  first-class  steam  vessel  without  erections,  whose 
length  is  twelve  times  the  moulded  depth,  is  2  ft.  11  ins.,  cor- 
responding with  a  reserve  buoyancy  of  25  per  cent  of  the  total 
bulk. 

9.  Vessels  of  Extreme  Proportions.  —  For  vessels  whose 
length  is  greater  or  less  than  that  of  the  vessel  of  the  same 
moulded  depth  for  which  the  tables  are  framed,  the  freeboard 
should  be  increased  or  diminished  as  specified  in  the  footnote 
to  the  tables.  Thus,  if  the  vessel  in  the  example  clause  8  were 
224  ft.  long,  the  winter  freeboard  required  would  be  2  ft.  11  ins. 
plus  2  ins.  or  3  ft.  1  in.  For  steam  vessels  coming  under  para- 
graphs 11  and  12  with  enclosed  erections  extending  over  y6^,  or 
more,  of  the  length  of  the  vessel,  the  correction  for  length  should 
be  one-half  that  specified  in  Tables  A. 

10.  Breadth  and  Depth.  —  In  framing  the  tables  it  has 
been  assumed  that  the  relation  between  the  breadth  and  depth 
is  such  as  to  ensure  safety  at  sea  with  the  freeboard  assigned 
when  the  vessel  is  laden  with  homogeneous  cargo;  for  vessels 
of  less  relative  breadth  the  freeboard  should  be  so  increased  as 
to  provide  a  sufficient  range  of  stability,  or  other  means  adopted 
to  secure  the  same. 

1 1 .  Erections  on  Deck.  —  For  steam  vessels  with  top- 
gallant forecastles  having  long  poops,  or  raised  quarter-decks 
connected  with  bridge-houses,  covering  in  the  engine  and  boiler 
openings,  the  latter  being  entered  from  the  top,  and  having  an 
efficiently  constructed  iron  bulkhead  at  the  fore  end,  a  deduc- 
tion may  be  made  from  the  freeboard  given  in  the  tables,  ac- 
cording to  the  following  scale: 

(a)  When  the  combined  length  of  the  poop,  or  raised  quarter- 
deck, bridge-house,  and  top-gallant  forecastle  is: 

ffi  of  the  length  of  the  vessel,  deduct  90  per  cent  of  the 
difference  between  freeboards  in  Tables  A  (after  correction  for 
sheer)  and  Tables  C. 


Freeboard  79 


T9o  of  the  length  of  the  vessel,  deduct  85  per  cent  of  the  differ- 
ence between  freeboards  in  Tables  A  (after  correction  for  sheer) 
and  Tables  C. 

TVn  of  the  length  of  the  vessel,  deduct  80  per  cent  of  the 
difference  between  freeboards  in  Tables  A  (after  correction  for 
sheer)  and  Tables  C. 

T87  of  the  length  of  the  vessel,  deduct  70  per  cent  of  the  differ- 
ence between  freeboards  in  Tables  A  (after  correction  for  sheer) 
and  Tables  C. 

T7o  of  the  length  of  the  vessel,  deduct  55  per  cent  of  the  differ- 
ence between  freeboards  in  Tables  A  (after  correction  for  sheer) 
and  Tables  C. 

T6o  of  the  length  of  the  vessel,  deduct  40  per  cent  of  the  differ- 
ence between  freeboards  in  Tables  A  (after  correction  for  sheer) 
and  Tables  C. 

When  the  engine  and  boiler  openings  are  protected  only  by  a 
long  raised  quarter-deck,  a  less  reduction  in  freeboard  will  be 
allowed. 

(6)  For  intermediate  lengths  of  erections  the  amount  of  the 
reduction  in  freeboard  should  be  ascertained  by  interpolation. 

(c)  The  above  scale  of  allowance  is  prepared  for  vessels  hav- 
ing long  poops  or  raised  quarter-decks  3  ft.  high  for  vessels 
having  a  length  of  100  ft.,  4  ft.  high  at  a  length  of  250  ft.,  and 
G  ft.  high  at  a  length  of  400  ft.  and  upwards.  Intermediate 
lengths  in  proportion.  For  raised  quarter-decks  of  less  height 
the  length  allowed  is  to  be  in  proportion  to  the  standard  of 
height. 

(d)  It  is  to  be  understood  in  the  application  of  this  scale  of 
allowance  for  erections  on  deck  to  vessels  with  long  poops  or 
with  raised  quarter-decks  and  bridge-houses  combined,  that 
the  deduction  is  a  maximum  deduction,  applicable  only  to 
vessels  of  these  types  in  which  the  erections  are  of  a  most  sub- 
stantial character,  the  deck  openings  most  effectually  pro- 
tected, and  the  crew  are  either  berthed  in  the  bridge-house,  or 
the  arrangements  to  enable  them  to  get  backwards  and  for- 
wards from  their  quarters  are  of  a  satisfactory  character.  For 
other  vessels  of  the  same  class  the  amount  of  the  deduction 
should  be  fixed  only  after  a  careful  survey.  Also  such  vessels 
when  employed  in  the  Atlantic  trade  will  require  to  have 
specially  provided  greater  freeboard  than  that  given  in  the 
tables. 

(e)  A  sufficient  number  of  clearing  ports,  as  large  as  practi- 
cable and  with  shutters  properly  hung,  should  be  formed  in 
the  bulwarks  of  these  vessels,  between  the  forecastle  and  the 
bridge-house  for  the  purpose  of  speedily  clearing  this  part  of 
the  deck  of  water. 


80  The  Naval   Constructor 

12.  When  the  erections  on  a  vessel  consist  of  a  top-gallant 
forecastle,  a  short  poop  having  an  efficient  bulkhead,  and 
bridge-house  disconnected,  the  latter  in  steamers  covering  th€ 
engine  and  boiler  openings  and  being  efficiently  enclosed  with 
an  iron  bulkhead  at  each  end,  a  deduction  may  be  made  from 
the  freeboard  given  in  the  tables  according  to  the  following 
scale: 

(a)  When  the  combined  length  of  the  erection  is: 

xVir  of  the  length  of  the  vessel,  deduct  75  per  cent  of  the  dif- 
ference between  freeboards  in  Tables  A  (after  correction  foi 
sheer)  and  Tables  C. 

f$r  of  the  length  of  the  vessel,  deduct  70  per  cent  of  the 
difference  between  freeboards  in  Tables  A  (after  correction  foi 
sheer)  and  Tables  C. 

TV°(j  of  the  length  of  the  vessel,  deduct  60  per  cent  of  the 
difference  between  the  freeboards  in  Tables  A  (after  correction 
for  sheer)  and  Tables  C. 

■£$$  of  the  length  of  the  vessel,  deduct  50  per  cent  of  the 
difference  between  the  freeboards  in  Tables  A  (after  correction 
for  sheer)  and  Tables  C. 

T%%  of  the  length  of  the  vessel,  deduct  40  per  cent  of  the 
difference  between  the  freeboards  in  Tables  A  (after  correctior 
for  sheer)  and  Tables  C. 

yVu  of  the  length  of  the  vessel,  deduct  32  per  cent  of  the 
difference  between  the  freeboards  in  Tables  A  (after  correctior 
for  sheer  and  length)  and  Tables  C  (after  correction  for  length) 

13.  When  the  erections  on  a  vessel  consist  of  a  top-gallanl 
forecastle  and  bridge-house  only,  the  latter  in  steamers  cover 
ing  the  engine  and  boiler  openings  and  being  efficiently  encloser 
with  an  iron  bulkhead  at  each  end,  a  deduction  may  be  mad( 
from  the  freeboard  given  in  the  tables  according  to  the  follow- 
ing scale: 

(a)  When  the  combined  length  of  the  erections  is: 

T5^  of  the  length  of  the  vessel,  deduct  30  per  cent  of  th( 
difference  between  the  freeboards  in  Tables  A  (after  correctior 
for  sheer  and  length)  and  Tables  C  (after  correction  for  length) 

T%  of  the  length  of  the  vessel,  deduct  24  per  cent  of  the  differ 
ence  between  the  freeboards  in  Tables  A  (after  correction  foi 
sheer  and  length)  and  Tables  C  (after  correction  for  length). 

■fa  of  the  length  of  the  vessel,  deduct  10  per  cent  of  the  differ 
ence  between  the  freeboards  in  Tables  A  (after  correction  foi 
sheer  and  length)  and  Tables  C  (after  correction  for  length). 

14.  When  the  erections  on  a  steam  vessel  consist  of  a  shori 
poop  or  raised  quarter-deck  of  a  height  not  less  than  that  laic 
down   in   paragraph    11    and   top-gallant   forecastle   only,    th< 


Freeboard  81 


former  being  enclosed  at  the  fore  end  with  an  efficient  bulk- 
head, and  when  the  engine  and  boiler  openings  are  entirely 
covered  either  by  the  poop  or  raised  quarter-deck  or  by  a  strong 
iron  or  steel  deck-house  enclosing  the  machinery  casings,  a  de- 
duction may  be  made  from  the  freeboard  given  in  the  tables 
according  to  the  following  scale: 

When  the  combined  length  of  the  erection  is: 

|  of  the  length  of  the  vessel,  deduct  32  per  cent  of  the  differ- 
ence between  the  freeboards  in  Table  A  (after  correction  for 
length)  and  Table  C  (after  correction  for  length). 

f  of  the  length  of  the  vessel,  deduct  24  per  cent  of  the  dif- 
ference between  the  freeboards  in  Table  A  (after  correction  for 
length)  and  Table  C  (after  correction  for  length). 

f  of  the  length  of  the  vessel,  deduct  16  per  cent  of  the  differ- 
ence between  the  freeboards  in  Table  A  (after  correction  for 
length)  and  Table  C  (after  correction  for  length). 

£  of  the  length  of  the  vessel,  deduct  8  per  cent  of  the  differ- 
ence between  the  freeboards  in  Table  A  (after  correction  for 
length)  and  Table  C  (after  correction  for  length) . 

For  erections  which  cover  less  than  |  of  the  length  of  the 
vessel,  the  allowance  should  be  in  proportion  to  that  for  f 
covered.  When,  however,  the  engine  and  boiler  openings  are 
not  entirely  covered  by  the  poop  or  quarter-deck  or  by  a  strong 
iron  or  steel  deck-house,  the  allowance  for  erections  should  be 
xV  of  that  provided  by  the  foregoing  scale. 

15.  When  a  steam  vessel  is  fitted  with  a  top-gallant  forecastle 
only,  the  reduction  of  freeboard  is  to  be  in  accordance  with  the 
preceding  paragraph  for  a  poop  not  covering  the  engine  and 
boiler  openings  and  a  forecastle  of  the  same  combined  length. 

When  there  is  a  short  poop  only,  or  a  raised  quarter-deck  of 
a  height  not  less  than  that  laid  down  in  paragraph  11,  enclosed 
at  the  forward  end  with  an  efficient  bulkhead  and  covering  the 
engine  and  boiler  openings,  the  deduction  from  the  freeboard 
is  to  be  half  the  allowance  that  is  given  for  a  poop  or  quarter- 
deck of  the  same  character  and  a  forecastle  having  the  same 
combined  length.  When  the  poop  or  raised  quarter-deck  does 
not  cover  the  engine  and  boiler  openings  T%  of  the  foregoing 
allowance  is  to  be  given. 

16.  When  the  erections  on  a  sailing  vessel  consist  of  a  short 
poop  and  top-gallant  forecastle  only,  the  former  enclosed  at  the 
fore-end  with  an  efficient  bulkhead,  the  deduction  from  the  free- 
board given  in  the  tables  should  be  according  to  the  following 
scale: 

When  the  combined  length  of  the  erection  is: 

|  of  the  length  of  the  vessel,  deduct  10  per  cent  of  the  reserve 


82 


The  Naval   Constructor 


buoyancy,  or  12  per  cent  of  the  freeboard  required  for  the  flush- 
decked  vessel  after  correction  for  length; 

f  of  the  length  of  the  vessel,  deduct  8  per  cent  of  the  reserve 
buoyancy,  or  10  per  cent  of  the  freeboard  required  for  the  vessel 
flush-decked  after  correction  for  length; 

|  of  the  length  of  the  vessel,  deduct  6  per  cent  of  the  reserve 
buoyancy,  or  8  per  cent  of  the  freeboard  required  for  the  vessel 
flush-decked  after  correction  for  length; 

\  of  the  length  of  the  vessel,  deduct  4  per  cent  of  the  reserve  buoy- 
ancy, or  6  per  cent  of  the  freeboard  required  for  the  flush-decked 
vessel  after  correction  for  length.  In  cases  where  less  than  \  of  the 
length  of  the  vessel  is  covered  by  erections,  the  allowance  should  be 
in  proportion  to  that  given  for  erections  covering  \  of  the  length. 

17.  When  a  sailing  vessel  is  fitted  with  a  top-gallant  forecastle 
only,  the  reduction  in  reserve  buoyancy  should  be  one-half  that  pre- 
scribed by  the  previous  paragraph  for  the  case  where,  in  addition  to 
the  forecastle,  the  vessel  is  fitted  with  a  poop  of  the  same  length. 

When  there  is  a  poop  only,  the  allowance  is  to  be  half  of  that 
which  in  this  paragraph  is  given  for  a  forecastle  only  of  the 
same  length. 

18.  Sheer.  —  The  tables  are  framed  for  vessels  having  a 
mean  sheer  of  deck  measured  at  the  side,  as  shown  in  the  fol- 
lowing table: 


Length  Over  Which  Sheer 
is  Measured. 

100 

150 

200 

250    300 

350 

400 

Mean  Sheer  in  Inches  Over  the 
Length  Specified. 

Flush-deck  Vessels. — Sheer  to  be 
measured    abreast    stem    and 
sternpost 

20 
14 

14| 

25 

18 

18| 

30 
22 

23 

35 

26 

27 

40 
30 

31 

45 
34 

35§ 

50 

38 

40 

Vessels  having  short  poops  and  fore- 
castles.— Sheer  to  be  measured 
at  points  distant  £  the  length 
of  the  vessel  from  each  end 

Vessels    having    short    forecastles 
only.  —  Sheer   to   be    measured 
abreast  the  sternpost  and  at  a 
point  distant  5  the  length  from 
the  stem 

Freeboard  83 


(a)  In  flush-deck  vessels  and  in  vessels  to  which  paras.  11  and 
12  apply,  when  the  sheer  of  deck  is  greater  or  less  than  the  above 
and  is  of  a  gradual  character,  divide  the  difference  in  inches  be- 
tween it  and  the  mean  sheer  provided  for  by  4  and  the  result 
in  inches  is  the  amount  by  which  the  freeboard  amidships  should 
be  diminished  or  increased  according  as  the  sheer  is  greater  or  less. 

(b)  In  vessels  having  short  poops  and  forecastles,  and  in  those 
having  short  forecastles  only,  the  freeboard  should  be  corrected 
in  respect  of  the  excess  or  deficiency  in  reserve  buoyancy  due  to 
variations  in  sheer  from  the  standard  amount  over  the  length 
uncovered  by  substantial  erections,  as  provided  in  the  above 
table.  One-fourth  the  difference  between  the  mean  sheer  speci- 
fied and  that  measured  as  described  is  approximately  the  amount 
by  which  the  freeboard  should  be  modified  in  respect  of  sheer. 

(c)  The  divisor  4  is  to  be  used  when  the  sheer  is  of  a  gradual 
character,  and  is  not  strictly  applicable  either  to  those  cases  in 
which  the  sheer  is  suddenly  increased  at  the  bow  or  stern,  or  to 
those  in  which  it  does  not  maintain  its  normal  rate  of  increase 
to  the  ends  of  the  vessel. 

(d)  In  all  cases  the  rise  in  sheer  forward  and  aft  is  measured 
with  reference  to  the  deck  at  the  middle  of  the  length,  and 
where  the  lowest  point  of  the  sheer  is  abaft  the  middle  of  the 
length,  one-half  the  difference  between  the  sheer  amidships  and 
the  lowest  point  should  be  added  to  the  freeboard  specified  in 
the  tables  for  flush-deck  vessels  and  for  vessels  having  short 
poops  and  forecastles  only. 

(e)  Where,  as  in  some  instances,  vessels  fitted  with  long  poops 
or  raised  quarter-decks  connected  with  bridge-houses  have  the 
deck  line  rising  rapidly  from  amidships  to  the  front  of  the  bridge, 
and  from  that  point  onwards  gradually  approaching  the  normal 
sheer  line,  the  freeboard  may  be  slightly  modified  in  consider- 
ation of  the  increase  of  height  of  deck  in  the  "well," 

(J)  In  flush-deck  vessels  and  in  vessels  having  short  poops 
and  forecastles  the  excess  of  sheer  for  which  an  allowance  is 
made  shall  not  exceed  one-half  the  total  standard  mean  sheer 
for  the  size  of  the  ship. 

(g)  No  decrease  should  be  made  in  the  freeboard  of  spar-  and 
awning-deck  vessels,  in  respect  of  excess  of  sheer. 

19.  Round  of  Beam.  —  In  calculating  the  reserve  of  buoy- 
ancy an  allowance  has  been  made  of  one-quarter  of  an  inch 
for  every  foot  of  the  length  of  the  midship  beam  for  the  round 
up.  When  the  round  of  the  beam  in  flush-decked  vessels  is 
greater  than  given  by  this  rule  divide  the  difference  in  inches 
by  2  and  diminish  or  increase  the  freeboard  by  this  amount. 
For  vessels  with  erections  on  deck  the  amount  of  the  allowance 


84  The   Naval   Constructor 


should  depend  on  the  extent  of  the  main  deck  uncovered.  This 
rule  for  round  of  beam  does  not  apply  to  spar-  or  awning-deck 
vessels. 

20.  As  a  general  illustration  of  the  way  in  which  the  tables 
should  be  used  in  modifying  the  freeboard  on  account  of  erec- 
tions on  deck,  extreme  proportions  and  variations  in  sheer,  the 
following  may  be  taken  as  an  example. 

A  vessel  is  234  ft.  long,  29  ft.  broad,  and  has  a  moulded  depth 
of  17.0  ft.,  the  coefficient  of  fineness  being  .72.  Suppose  the 
vessel  to  have  a  poop  and  bridge-house  of  the  united  length  of 
121  ft.,  and  a  forecastle  20  ft.  in  length,  and  let  the  sheer  forward, 
measured  at  the  side,  be  4  ft.  6  ins.,  and  aft,  2  ft.  1  in. 

Freeboard  by  Tables  A  if  of  the  normal  Ft* In* 
length,  without  erections,  and  with  the 

normal  amount  of  sheer 2     11 

The  mean  sheer  by  rule  is  33.4  ins.  or  6  ins. 
less  than  that  in  the  vessel,  and  the  re- 
duction in  freeboard  is  6  ins.  divided  by  4  0 1J; 

Freeboard  of  vessel  without  erections  and  with 

39£  ins.  mean  sheer 2    9§ 

Freeboard  by  Tables  C  as  awning-decked. .  0 9| 

Difference  2 0_ 

The  combined  length  of  the  erections  is  \i\  or  T%  of  the 
length  of  the  vessel,  and  the  allowance  for  erections  under 
clause  1 1  will  be  therefore  &  of  24  ins.,  or  9£  ins. 

We  have  therefore:  Deduct. 

Amount  deducted  from  freeboard  for  ex-     in" 

cess  of  sheer 1| 

Amount  deducted  from  the  freeboard  for 

erections 9£ 

Amount  deducted  if  vessel  be  fitted  with 
an  uncovered  iron  main  deck  (clause  6) 

-■AX  8| _2 

13 
The  length  being  30  ft.  in  excess  of  that 
for  which  the   tables  are  framed,  the 
addition  to  the  freeboard  in  respect  of 
the  same  is  one-half  of  f$  of  1.1  in.,  or  _1| 

111 
That  is  11 J  ins.  to  be  deducted  from  2  ft.  11  ins.,  leaving  a 
winter  freeboard  of  1  ft.  11|  in. 

Corresponding  summer  freeboard,  1  ft.  9  ins. 


Freeboard 


85 


21.  Vessels  loaded  in  fresh  water  may  have  less  freeboard 
than  that  given  in  the  several  tables  according  to  the  following 
scale: 


Moulded  Depth  in  Feet. 


6  and  under  8 

8  " 

1   11 

11  " 

'   13 

13  " 

'   16 

16  " 

'   19 

19  " 

'   22 

22  " 

'   25 

25  " 

'   28 

28  " 

'   31 

31  " 

'   34 

Reduction  in  Freeboard. 


Without 
Erections 
on  Deck. 


Ins. 

H 

2 
2* 

3 

3^ 

4 

5 

5* 

6 


Awning- 
deck 
Vesseb. 


3* 

4 

4* 

8 

5* 

6 

61 


Spar- 
deck 


Ins. 


4 

H 

5 

5| 

6 

Si 

7 


Memo. — The  weight  of  a  cubic  foot  of  salt  water  is  taken,  in  the  above  table, 
to  be  64  lbs.,  and  that  of  fresh  water  62.5  lbs. 

22.  The  freeboards  assigned  by  the  following  tables  are  not 
intended  to  apply  to  vessels  when  navigating  inland  waters  or 
rivers,  and  when  a  stretch  of  such  water  has  to  be  traversed 
such  deeper  loading  will  be  permissible  as  may  be  due  to  the 
weight  of  fuel  required  for  consumption  between  the  points  of 
departure  and  the  open  sea. 

23.  The  freeboards  of  vessels  having  ports,  scuppers,  or 
other  openings  in  their  sides  is  to  be  regulated  by  the  following 
considerations.  When  the  openings  are  in  the  nature  of  water- 
tight ports  for  cargo,  coals,  etc.,  and  are  therefore  not  intended 
to  be  opened  except  in  harbor,  no  modification  of  the  free- 
board as  determined  by  the  foregoing  tables  will  be  necessary, 
provided  the  covers  of  the  openings  are  sufficiently  strong  and 
are  efficiently  secured.  In  the  case,  however,  of  vessels  having 
scuppers  through  the  sides  from  a  'tween  deck  space  below  the 
upper  deck  or  side  scuttles  or  other  openings  of  a  similar  nature, 
when  the  freeboard  as  determined  by  the  foregoing  tables  does 
not  provide  a  sufficient  height  from  the  load-line  to  the  sills  of 
the  side  scuttles,  or  to  the  deck  which  is  drained  by  the  scuppers, 
the  freeboard  is  to  be  increased;  and  the  amount  of  the  increase, 


86  The  Naval  Constructor 


if  any,  is  to  depend  on  the  nature  of  such  openings  and  on  the 
means  adopted  for  closing  them.  In  the  case  of  hinged  side- 
scuttles  of  the  usual  pattern,  when  the  glass  is  of  sufficient 
thickness  and  the  scuttles  are  efficiently  secured  by  metal  bolts 
and  nuts,  and  hinged  watertight  iron  shutters  of  deadlights  are 
provided  on  the  inside  of  the  glass,  the  loadline  as  determined 
by  the  centre  of  the  disc  or  by  the  Indian  summer  line,  if  so 
marked,  is  to  be  not  less  than  6  inches  below  the  sill  of  the 
lowest  side-scuttle. 

24.  The  freeboards  required  by  the  foregoing  tables  are  to 
be  assigned  on  the  condition  that  the  engine  and  boiler  casings 
above  the  upper  deck  are  of  sufficient  height  and  strength, 
with  suitable  means  provided  for  closing  all  openings  in  them 
in  bad  weather,  and  the  weather  deck  hatchways  are  properly 
framed  with  substantial  coamings,  and  strong  hatch  covers, 
the  latter  being  efficiently  supported  by  shifting  beams  and 
fore-and-afters   suitable   to   the   dimensions   of   the   hatchway. 

When  these  conditions  are  not  complied  with  the  freeboard 
may  require  to  be  increased,  regard  being  given,  however,  to 
the  trade  in  which  the  vessel  is  intended  to  be  employed. 

25.  In  no  case  shall  the  deepest  loadline  in  salt  water,  whether 
indicating  the  summer  or  Indian  summer  line,  be  assigned  at  a 
higher  position  than  the  intersection  of  the  top  of  the  upper 
deck  with  the  vessel's  side,  at  the  lowest  part  of  the  deck. 

In  the  case  of  shelter-decked  vessels  the  deck  next  below  the 
shelter  deck  is  to  be  regarded  as  the  upper  deck. 

Memorandum  of  Explanatory  Notes  on  the  Application 
of  the  Tables  of  Freeboard,  Drawn  Up  with  a  View 
to  Securing  Uniformity  of  Practice  on  the  Part  of 
Those  Entrusted  with  the  Assignment  of  Freeboard. 

Deck  Line.  —  In  the  case  of  vessels  with  uncovered  iron  or 
steel  decks,  a  width  of  gutter  waterway  is  to  be  assumed,  and 
the  point  so  obtained  levelled  out  to  the  vessel's  side.  In  the 
case  of  vessels  of  24  feet  beam  and  under,  the  width  of  the 
waterway  assumed  shoiHd  be  12  inches,  and  in  vessels  of  42  feet 
and  above,  21  inches.  In  vessels  of  between  24  and  42  feet, 
beam  the  width  of  the  gutter  waterway  is  to  be  taken  as  half 
an  inch  for  every  foot  in  beam. 

Where  a  wood  deck  maintains  a  uniform  thickness  to  the  sides 
of  a  vessel,  the  same  method  should  be  adopted. 

In  cases  where  an  iron  deck  is  partly  covered  with  wood,  the 
deck-line  is  to  correspond  with  the  top  of  the  deck  amidships, 


Notes  on  the  Tables  of  Freeboard         87 


whether  the  deck  at  that  part  be  of  wood  or  of  iron,  and  the 
necessary  corrections  should  be  made  in  accordance  with  para- 
graph 6,  as  also  the  correction  always  required  to  the  statutory 
deck-line. 

Bridge-house  in  Spar-decked  Ships.  —  In  a  spar-decked 
ship,  where  an  efficient  bridge-house  is  fitted  amidships,  cover- 
ing the  engine  and  boiler  openings,  if  it  extends  over  at  least 
two-fifths  of  the  vessel's  length  and  has  scantlings  not  less 
than  the  requirements  of  Lloyd's  Rules  (1885)  for  bridge- 
houses,  it  is  to  be  taken  into  consideration  in  estimating  the 
strength  of  the  vessel  for  freeboard. 

If  the  scantlings  of  the  bridge-house  are  equal  to  the  require- 
ments of  Lloyd's  Rules  (1885)  the  allowance  on  this  account 
should  not  exceed  that  given  in  the  following  table: 


Moulded  Depth  of  Vessel 
to  Main-deck. 

Allowance. 

Feet. 
16 

Inches. 
4 
3 

2 

1 

20. . . . 

24 

28 

If,  however,  the  scantlings  of  the  bridge-house  are  in  excess 
of  Lloyd's  Rules  (1885)  the  freeboard  is  to  be  determined  on 
the  basis  of  a  comparison  between  the  strength  of  the  actual 
vessel  and  the  strength  of  a  vessel  of  the  same  dimensions, 
built  to  the  three-decked  rule,  and  of  a  vessel  built  to  the  spar- 
deck  rule,  including  a  bridge-house  in  each  case. 

Tables  of  Freeboard.  —  Additional  freeboard  will  be  re- 
quired in  the  case  of  vessels  classed  90A  and  80A,  or  in  vessels 
of  equivalent  strength  thereto  in  accordance  with  the  following 
scale: 

Length  of  vessel: 


Feet. 

150 

175 

200 

225 

250 

275 

200 

90A  additions 

80A        "         

In. 
l 

2 
1 

In. 

l 

2 

1 

Ins. 

I 

2 

Ins. 

3 
4 

Ins. 

4 

If 

Ins. 
1 
2 

Ins. 

a 

2| 

Wherever  in  these  explanatory  notes  reference  is  made  to 
classes  of  vessels  of  Lloyd's  various  types,  it  is  to  be  under- 


88  The  Naval  Constructor 


stood  that  these  apply  equally  to  all  other  vessels  of  equivalent 
strength,  whether  classed  by  other  classifying  associations, 
such,  for  instance,  as  the  Bureau  Veritas  or  the  British  Cor- 
poration, or  unclassed. 

If  the  frame  spacing  be  increased  one-fourth,  the  thickness  of 
all  the  shell-plating,  excepting  garboard  and  sheer  strakes, 
should  be  increased  by  one-twentieth  of  an  inch  over  the  thick- 
ness required  in  the  standard  ship.  Other  increases  in  spacing 
should  be  dealt  with  in  the  same  proportion. 

Para.  1  —  Length.  —  The  length  of  erection  is  to  be  measured 
with  reference  to  the  length  of  the  vessel  on  the  load-line,  i.e., 
any  portion  of  the  erections  forward  of  the  fore  side  of  the  stem 
on  the  load-line,  or  abaft  the  after  side  of  the  after  post  on  the 
load-line,  is  not  to  be  measured  for  deductions. 

Para.  3  —  Depth  of  Hold.  —  The  depth  of  hold  as  used  in 
the  computation  for  ascertaining  the  coefficient  of  fineness  in 
iron  and  steel  sailing  vessels  is  to  be  measured  to  the  top  of  the 
ceiling,  and  in  steam  vessels  to  the  top  of  the  floors. 

The  cases  of  vessels  having  either  an  excess  or  a  deficiency  of 
mean  sheer,  as  compared  with  the  standard  sheer,  the  registered 
depth  to  be  used  for  ascertaining  the  coefficient  of  fineness  is  to 
be  increased  for  excess  of  sheer,  or  reduced  for  the  deficiency  of 
sheer,  by  one-third  of  the  difference  between  the  standard 
mean  sheer  and  the  vessel's  actual  mean  sheer,  after  being  re- 
duced to  the  gradual  character,  if  necessary. 

Para.  4  —  Coefficient  of  Fineness.  —  No  alteration  is  to 
be  made  in  the  freeboard  in  consequence  of  the  coefficient  of 
fineness  being  either  smaller  or  greater  than  those  given  on  the 
page  of  the  tables  from  which  the  ship's  freeboard  is  taken. 

Para.  5  —  Moulded  Depth.  —  In  cases  where  a  wood  deck 
of  extra  thickness  is  fitted,  or  where  a  wood  deck  is  doubled 
throughout,  the  moulded  depth  should  be  increased  by  the  ex- 
cess of  thickness.  The  freeboard  should  then  be  set  off  from  the 
top  of  the  deck  of  increased  thickness  at  the  side  of  the  vessel. 

Para.  6  —  Freeboard.  —  In  case  of  the  freeboard  being 
ascertained  by  an  actual  calculation  of  the  reserve  buoyancy, 
the  drawing  used  in  such  calculation  should  be  verified  by 
actual  measurements  at  the  ship,  and  such  drawing  and  calcu- 
lations forwarded  to  the  Board  of  Trade,  and,  whatever  the 
result  of  the  calculation,  the  freeboard  assigned  should  not  be 
less  than  would  be  obtained  by  taking  from  the  tables  the  free- 
board corresponding  to  the  smallest  coefficient  for  a  vessel  of 
the  same  moulded  depth,  except  in  sailing  vessels  with  large 
rise  of  floor  (see  page  26). 


Notes  on  the  Tables  of  Freeboard        89 


Freeboard  as  ascertained  by  these  tables  is  to  be  measured  to 
the  intersection  of  the  deck  with  the  side  of  the  vessel,  but  in 
granting  certificates  of  freeboard  this  must  always  be  corrected 
so  as  to  state  the  freeboard  amidships  when  measured  to  the 
deck-line,  marked  in  accordance  with  the  statute. 

Sub-paras.  (A)  and  (B).  —  For  vessels  having  iron  upper- 
decks  not  covered  with  wood,  the  allowance  is  to  be  made  under 
sub-para,  (a),  when  "the  erections  extend  over  less  than  T%  of  the 
length;  but  in  all  vessels  when  the  erections  cover  -fa  or  more 
of  the  length,  and  in  spar-  and  awning-decked  vessels  the  allow- 
ance is  to  be  made  under  sub-para  (6). 

Sub-para.  (6.)  —  (6.)  —  In  spar-decked  vessels  having  iron 
spar  decks  and  in  awning-decked  vessels  having  iron  main 
decks,  the  freeboard  by  the  tables  should  be  calculated,  as  if 
those  decks  were  wood-covered,  i.e.,  the  ordinary  thickness  of 
a  wood  deck,  less  the  thickness  of  the  stringer  plate,  should  be 
deducted  from  the  freeboard,  also  in  vessels  where  TV  or  more  of 
the  main  deck  is  covered  by  substantial  enclosed  erections,  the 
freeboard  found  from  the  tables  should  be  measured  amidships 
from  a  wood  deck,  or,  if  the  deck  is  of  iron,  it  should  be  measured 
from  the  iron  deck,  and  the  ordinary  thickness  of  a  wooded  deck 
required  for  that  size  of  ship,  less  the  thickness  of  the  stringer 
plate,  should  in  that  case"  be  deducted  from  the  freeboard.  In 
vessels  which  have  T%  of  the  deck  covered,  T%  the  thickness  of  a 
wood  deck,  less  the  thickness  of  the  stringer  plate  is  to  be  de- 
ducted from  the  freeboard.  Between  T\  and  ^  a  proportionate 
quantity;  for  example,  for  T%\  covered  allow  j\  the  thickness  of 
the  deck,  after  deducting  the  thickness  of  the  stringer  plate. 
The  remainder  of  the  paragraph  should  be  read  as  printed. 
N.B.  —  When  the  deductions  referred  to  in  this  sub-para.  (6) 
are  allowed  the  moulded  depth  is  not  to  be  reduced  as  per  sub- 
para,  (a)  para.  6. 

Para.  9.  —  In  the  case  of  vessels  coming  under  para.  12  and 
having  the  deck  erections  not  entirely  enclosed,  the  effective 
length  of  the  open  portions  is  to  be  assessed  as  described  in 
paras.  13,  14  and  15;  if  the  length  of  the  enclosed  erections 
plus  the  length  of  the  open  portions,  where  assessed  as  above, 
is  at  all  under  T%  of  the  vessel's  length,  the  entire  correction  for 
length  is  to  be  applied. 

Para.  11.  —  This  paragraph  does  not  apply  to  vessels  in 
which  the  effective  length  of  the  erections  is  less  than  T%  of  the 
length,  except  in  cases  where  the  effective  length  of  the  after 
erection  is  at  least  T%  of  the  length,  and  the  total  effective  length 
of  the  erections  is  between  T%  and  T%  of  the  length  of  the  vessel. 


90  The  Naval  Constructor 

In  such  cases  the  allowance  should  be  proportioned  between 
that  allowed  for  erections  ^  the  length  under  para.  14  and  that 
allowed  for  erections  covering  ^  of  the  length  under  para.  11, 
and  the  corrections  for  length  and  sheer  should  be  included  in 
estimating  this  allowance.  In  all  other  cases  of  vessels  with 
erections  covering  less  than  T^  of  the  length,  para.  14  is  to  be 
used. 

In  the  case  of  vessels  having  erections  which  are  partly  open 
or  are  less  than  the  standard  height  the  effective  length  of  the 
erections  is  to  be  computed  as  directed  elsewhere. 

No  allowance  is  to  be  made  for  a  monkey  forecastle  which  is 
less  in  height  than  the  main  or  top-gallant  rail,  or  4  feet,  which- 
ever is  the  least;  where  this  condition  is  satisfied,  or  the  fore- 
castle is  a  sunk  one  having  an  efficient  bulkhead  at  its  after 
end,  the  length  to  be  used  in  estimating  the  allowance  is  to  be 
obtained  by  multiplying  the  length  of  the  monkey  forecastle 
by  its  height  and  dividing  by  6  feet,  the  minimum  height  of  a 
top-gallant  forecastle.  This  rule,  as  well  as  that  relating  to  the 
heights  of  raised  quarter-decks,  applies  to  vessels  coming  under 
paras.  12,  13,  14,  and  15,  as  well  as  under  para.  11.  In  case  of 
vessels  having  no  forecastle  but  in  other  respects  coming  un- 
der this  paragraph,  the  allowance  for  erections  should  be  esti- 
mated on  the  supposition  that  there  is  a  forecastle  of  |  the 
length  of  the  vessel,  deducting  from  this  twice  the  allowance 
which  the  vessel  would  have  for  such  a  forecastle  under  para.  15. 

Sub-para.  (a). — The  difference  will  not  be  affected  by  cor- 
rection for  length,  as  the  allowance  will  be  practically  the  same 
in  both  tables. 

Sub-para.  (c). — The  engine  and  boiler  openings,  if  pro- 
tected only  by  a  raised  quarter-deck,  will  require  an  addition  in 
freeboard  varying  from  1  inch  in  vessels  of  15  feet  moulded 
depth  to  2  inches  in  vessels  of  20  feet  moulded  depth.  In  ves- 
sels having  less  than  15  feet  moulded  depth  a  proportionate 
addition  should  be  made. 

If  with  a  small  bridge-house  in  front  of,  but  not  covering  the 
openings,  an  addition  of  half  the  above  amount. 

Sub-para,  (d ) .  —  If  the  crew  are  not  berthed  in  the  bridge- 
house,  and  the  arrangements  to  enable  them  to  get  backwards 
and  forwards  from  their  quarters  are  not  satisfactory,  an  ad- 
dition should  be  made  to  the  freeboard  of  1  per  cent  of  the 
moulded  depth  of  the  ship  in  the  case  of  vessels  180  feet  or 
more  in  length  and  having  wells  70  feet  or  less  in  length.  If 
the  vessel's  length  does  not  exceed  150  feet,  or  if  the  well  is  80 
feet  or  more  in  length,  the  foregoing  addition  will  not  be  re- 
quired.    In  the  case  of  vessels  between  150  and  180  feet  in 


Notes  on  the  Tables  of  Freeboard        91 


length,  or  having  wells  between  70  and  80  feet  in  length,  the 
addition  is  to  be  found  by  interpolation. 

Planks  secured  in  position  by  lashings  are  not  to  be  regarded 
as  satisfactory  arrangements;  and  a  gangway  providing  access 
between  the  bridge-house  and  forecastle  cannot  be  considered 
satisfactory,  unless  the  following  requirements  at  least  are 
complied  with: 

The  gangway  to  be  not  less  than  18  inches  wide  and  to  be 
efficiently  supported  at  suitable  intervals.  The  ends  to  be 
strongly  bolted  to  lugs  riveted  to  the  bulkheads  of  bridge  and 
forecastle,  or  to  the  hatch  coamings,  or  to  iron  standards  bolted 
to  the  deck  or  to  be  secured  in  some  equally  efficient  manner. 

The  top  of  the  gangway  to  be  not  less  than  2  feet  6  inches 
above  the  top  of  the  deck  at  any  part.  A  life-line  or  rail  to  be 
fitted  for  the  entire  length  of  the  gangway  and  to  be  supported 
by  wrought-iron  stanchions  suitably  spaced  and  not  less  than 
2  feet  6  inches  in  height. 

If  the  hatchways  are  at  least  2  feet  6  inches  in  height  the 
gangway  may  be  fitted  between  the  hatchways  and  beyond 
them  only,  provided  that  a  continuous  platform  of  at  least  the 
required  height  is  obtained,  and  the  rail  or  life-line  is  fitted  and 
efficiently  supported  by  wrought-iron  stanchions  for  the  entire 
distance  including  the  hatchways.  The  gangway  should  be 
fitted  as  far  inboard  as  practicable. 


Sub-para.   (e). 
as  follows: 


The  minimum  freeing  port  area  is  to  be 


Length  of  Bul- 

Freeing Port  Area 

warks  in 

on  Each  Side  in 

"Well,"  in  Feet. 

Square  Feet. 

5 

4.5 

10 

6.5 

15 

7.5 

20 

8.5 

25 

9. 

30 

9.5 

35 

10. 

40 

10.5 

45 

11. 

50 

11.5 

55 

12. 

60 

12.5 

* 

65  and  above,  1  square  foot  to  each  5  feet  length  of  bulwark. 


92 


The  Naval  Constructor 


If  the  freeing  port  area  is  less  than  that  stated  above,  an 
addition  is  to  be  made  to  the  freeboard  of  1  per  cent  of  the 
moulded  depth. 

The  scale  of  allowance  for  erections  on  deck  to  vessels  with 
top-gallant  forecastles  having  long  poops  or  raised  quarter- 
decks connected  with  bridge-houses  is  not  to  be  used  without 
modification,  unless  the  strength  of  the  bulkhead  at  the  front 
of  the  poop  or  bridge-house  is  at  least  equivalent  to  the  follow- 
ing requirements: 

(a)  Poop  or  bridge  bulkheads  to  be  of  the  thickness  of  their 
side  plating  as  required  below  for  vessels  under  13  depths  to 
length,  with  coaming  plates  -h  of  an  inch  thicker,  and  to  be 
stiffened  with  bulb  angle  according  to  the  following  scale,  spaced 
30  inches  apart,  and  connected  to  the  coaming  plates  and  to 
the  deck  plating,  or  to  an  athwartship  plate  on  the  beams  both 
below  and  above,  with  a  bracket  plate  to  each  end  of  the  stiffener. 


Breadth 
op  Ship 

Size  of 
Stiffener. 

Breadth  op  Ship. 

Size  of  Stiffener. 

24 
30 
36 

42 

5X3X& 
6X3X& 
7x3x2§ 
7X3XH 

46 
50 
54 
58  and  above 

7£X3§XH 

81x3!x^f 

82  X03  Xjtf 
9  X3|XH 

Intermediate  sizes  to  be  found  by  interpolation. 

(b)  Horizontal  brackets  or  gusset  plates  of  the  same  thickness 
as  the  coamings  to  be  fitted,  connecting  the  poop  or  bridge 
bulkheads  with  the  bulwarks  on  each  side  of  the  vessel  at  about 
the  height  of  the  rail.  In  the  case  of  vessels  having  a  fore- 
castle and  raised  quarter  deck  only,  the  break  bulkhead  should 
be  the  same  thickness  as  required  for  bridge  sides  and  stiffened 
with  angles  30  inches  apart  and  of  the  size  required  for  the 
main  frames. 

In  order  to  obtain  the  allowance  for  deck  erections  provided 
by  this  paragraph,  the  openings,  if  any,  in  the  bulkhead  at  the 
front  of  the  long  poop  or  bridge  house,  must  be  provided  with 
hinged  iron  or  steel  doors,  or  with  some  equally  permanent 
means  of  closing  such  openings.  When  the  width  of  the  open- 
ings exceeds  30  inches,  special  means  are  to  be  provided  for 
maintaining  the  strength  of  the  hinged  doors. 

The  standard  of  thickness  of  the  side  plating  of  long  poops 
and  bridge-houses  is  that  required  by  Section  44  of  Lloyd's 
Rules,  as  modified  by  the  Table  of  Thicknesses  of  Side  Plating 
of  Awning-decked  Vessels,  given  in  these  tables. 


Notes  on  the  Tables  of  Freeboard 


93 


The  additional  freeboard  for  North  Atlantic  winter  is  to  be 
as  follows: 

ADDITIONAL  FREEBOARD  FOR  WINTER,   NORTH 
ATLANTIC,  FOR  WELL-DECK  VESSELS. 


Length  of 

Vessels 

Proportions  of  Length  of  Vessel  Over  Which 
Erections  Extend 

60 

tV* 

#v 

75 

i8A 

Ft. 
180 
220 
260 
300 

Ins. 
4 

3* 
8| 

3 

Ins. 

3£ 
3* 
3 
3 

Ins. 

3 
3 

2h 

2h 

Ins. 

2* 

2| 
2 

2 

Ins. 

2 
2 
2 

Para  12.  —  For  vessels  having  no  forecastle,  but  with  the 
other  deck  erections  prescribed  in  this  paragraph,  estimate 
the  allowance  for  erections  supposing  there  is  a  forecastle  \  the 
length  of  the  vessel,  and  deduct  l\  times  the  allowance  that 
would  be  made  under  para.  15  if  the  vessel  were  fitted  with 
such  a  forecastle  only. 

This  rule  also  applies  to  vessels  having  no  forecastle,  but 
with  a  bridge-house,  as  provided  for  in  para.  13. 

In  steam  vessels  coming  under  this  paragraph,  and  having 
closed  erections  extending  over  T6o  or  more  of  the  vessel's  length, 
one-half  the  length  correction  specified  in  Table  A  is  to  be  made, 
and  the  freeboard  corrected  for  sheer  only  in  estimating  the  al- 
lowance for  erections,  as  the  allowance  for  length  will  be  prac- 
tically the  same  in  both  Tables. 

For  erections  which  extend  over  less  than  T47  the  length  of  the 
ship,  the  allowance  is  to  be  in  proportion. 

For  instance,  if  T37  are  covered,  allow  f  of  25  per  cent. 

In  the  case  of  vessels  under  15  ft.  moulded  depth,  in  which 
the  combined  length  of  enclosed  erections  exceeds  T%  of  the 
vessel's  length,  or  in  which  the  combined  length  of  erections 
enclosed  and  open  is  equivalent  to  more  than  T%  the  vessel's 
length,  sub-paras,  (d)  and  (e)  of  the  preceding  paragraph  are 
to  apply;  but  the  full  addition  of  one  per  cent  of  the  moulded 
depth,  under  each  of  these  sub-paragraphs,  is  to  be  made  only 
when  the  erections  cover  T%  or  more  of  the  length;  for  lengths  of 
erections  intermediate  between  fV  and  T%,  the  required  ad- 
dition is  to  be  in  proportion;  thus,  when  T%5<j  of  the  vessel's 
length  is  covered,  the  addition  to  the  freeboard  is  to  be  5  per 
cent  of  the  moulded  depth  under  each  sub-paragraph. 


94  The  Naval  Constructor 


Paras.  12  and  13.  —  The  allowance  in  a  sailing  ship  for  a 
bridge-house  in  addition  to  a  poop  or  forecastle,  or  in  addition 
to  a  forecastle  only,  is  obtained  by  the  rules  laid  down  in  paras. 
12  and  13,  as  the  case  may  be,  and  is  calculated  upon  the  differ- 
ence between  the  freeboards  of  Tables  A  and  C;  in  other  words, 
the  allowance  for  a  forecastle,  bridge-house,  and  poop,  or  for  a 
forecastle  and  bridge-house  in  a  sailing  ship,  is  the  same  as 
would  be  given  for  similar  erections  in  a  steamer  of  the  same 
dimensions. 

Para.  13.  —  When  the  combined  length  of  the  top-gallant 
forecastle  and  bridge-house  is  xV  of  the  length  of  the  ship,  a  de- 
duction from  the  freeboard  may  be  made  of  Tfo>  and  this  is 
the  maximum  deduction  for  this  type  of  vessel. 

For  erections  which  extend  over  less  than  T%  of  the  length  of 
the  ship  the  allowance  is  to  be  in  proportion. 

For  instance,  ^  covered  allow  §  of  19  per  cent. 

In  all  the  rules  governing  the  deductions  to  be  made  from  the 
freeboard  it  is  to  be  understood  as  follows:  When  the  top- 
gallant forecastle  is  not  closed  by  an  efficient  bulkhead  at  the 
after  end  the  length  is  never  to  be  estimated  at  a  greater  full 
value  than  f  the  length  of  the  ship,  but  any  extension  beyond 
this  may  be  estimated  at  one-half  the  value.  For  instance,  if  a 
vessel  240  feet  long  has  an  open  forecastle  80  feet  long,  its  value 
for  deductions  is  30  +  25  =  55  feet.  When  the  top-gallant  fore- 
castle has  an  efficient  bulkhead  with  an  elongation  abaft  that 
bulkhead  not  enclosed  at  the  after  end,  the  full  value  of  the 
closed-in  portion  is  to  be  estimated  either  as  |  the  length  of  the 
ship,  or  the  entire  length  of  the  enclosed  portion,  whichever 
may  be  the  greatest. 

Open-bridge  House. — -When  the  bridge-house  extends 
from  side  to  side  of  the  ship  its  value  for  deductions  must  be 
considered  on  its  merits,  which  will  depend  upon  the  security  of 
all  deck  openings,  doors,  bunker  lids  or  otherwise. 

Where  these  are  all  properly  protected  and  the  bridge-house 
is  open  at  both  ends,  one-half  the  length  may  be  estimated  as 
the  value  for  deductions.  Where  in  addition  the  fore  end  is 
enclosed  by  an  efficient  bulkhead  f  the  length  may  be  estimated 
as  the  value  for  deductions. 

If  the  openings  in  the  bulkhead  at  the  after  end  of  a  bridge 
erection,  having  its  fore  end  closed,  are  efficiently  protected  by 
weather  boards  properly  fitted  to  at  least  half  the  height  of  the 
erection,  the  full  length  of  the  erection  may  be  allowed  in  esti- 
mating its  value  for  freeboard.  This  does  not  apply,  however, 
to  the  case  of  a  long  erection  falling  to  be  dealt  with  under 
paragraph  11,  as  in  well-decked  vessels  having  the  well  aft, 


Notes  on  the  Tables  of  Freeboard        95 


except  in  shelter-decked  vessels  having  efficient  means  pro- 
vided for  temporarily  closing  the  openings  in  the  shelter-deck  in 
bad  weather. 

In  the  case  of  steamers  coming  under  paragraphs  12  and  13, 
when  the  engine  and  boiler  openings  are  not  covered  by  an 
erection  extending  from  side  to  side,  bridge-houses  may  have 
an  allowance  not  exceeding  that  which  would  be  given  for  half 
the  length  of  a  bridge-house  of  the  same  character  covering  en- 
gines and  boilers. 

Paras.  14  and  15.  —  When  the  poop  has  no  efficient  bulk- 
head, or  the  bulkhead  does  not  extend  across  the  vessel,  one- 
half  its  length  may  be  allowed,  provided  always  proper  freeing 
ports  are  fitted. 

When  the  openings  in  the  bulkhead  are  provided  with  efficient 
weather  boards  or  other  efficient  temporary  means  of  closing, 
and  extending  the  full  height  of  the  openings,  then  the  full 
length  of  the  poop  may  be  allowed. 

In  no  case,  however,  shall  shifting  boards  or  any  other  tem- 
porary means  of  closing  the  openings  in  the  bulkheads  at  the 
after  end  of  a  bridge-house,  or  fore  end  of  a  poop  be  considered 
satisfactory,  unless  the  means  of  their  attachment,  whether  by 
channels,  hooks,  cleats,  or  otherwise,  are  permanently  secured 
to  the  bulkheads. 

The  standard  heights  of  forecastles  and  raised  quarter-decks, 
as  defined  in  para.  11,  pages  6  and  16,  apply  also  to  these 
paragraphs. 

Paras.  16  and  17.  —  In  the  case  of  a  sailing  vessel  having 
a  forecastle  and  raised  quarter-deck,  or  a  raised  quarter-deck 
only,  the  latter  of  less  than  4  feet  in  height,  the  length  of  raised 
quarter-deck  to  be  allowed  should  be  in  proportion  to  its  height 
as  compared  with  the  standard  height  of  4  feet. 

The  provisions  of  the  preceding  paragraphs  relating  to  the 
height  of  forecastles,  bulkheads  at  the  after  end  of  forecastles 
and  at  the  fore  end  of  poops,  and  the  means  of  closing  openings 
in  poop  bulkheads,  are  also  to  be  applied  to  sailing  vessels  dealt 
with  under  paras.  16  and  17. 

"Para.  18.  Sheer.  —  Sheer  of  a  gradual  character  is  to  be 
defined  as  follows:  — 

"At  £  the  length  of  the  vessel  from  the  stem  or  sternpost  the 
sheer  is  to  be  55  per  cent  of  the  sheer  at  stem  or  sternpost;  at 
\  the  length  from  stem  to  sternpost  26  per  cent,  and  at  f  the 
length  7  per  cent. 

"In  those  cases  in  which  the  sheer  is  required  to  be  taken  at  the 
stem  and  sternpost  and  the  sheer  is  found  to  be  not  of  the  grad- 


96  The  Naval  Constructor 


ual  character,  the  following  method  of  computing  the  effective 
mean  sheer  is  to  be  used:  — 

"Let  S  =  mean  of  the  actual  sheers  at  stem  and  sternpost; 

"Let  Si  =  mean  of  sheers  at  £  length  from  stem  and  sternpost 
-*-.55. 

"If  S  is  greater  than  Si  the  effective  mean  sheer  to  be  used  in 
the  computation  of  freeboard  is  Si. 

C     i      g 

"  If  S  is  less  than  Si  the  effective  mean  sheer  to  be  used  is  — =—• 

"In  those  cases  in  which  the  sheer  is  required  to  be  taken  at  £ 
of  the  vessel's  length  from  stem  or  from  sternpost  the  sheer  as 
actually  measured  at  the  prescribed  point  may  be  used  in  ordi- 
nary cases  without  any  correction  on  account  of  a  departure  of 
the  sheer  line  from  the  gradual  character. 

"When  correcting  the  depth  of  hold  for  excess  or  deficiency  of 
sheer  (paragraph  3,  page  23),  the  mean  of  the  sheers  at  £  of 
vessel's  length  from  stem  and  from  sternpost  divided  by  .55 
should  in  all  cases  be  taken  as  the  vessel's  actual  sheer  for  this 
purpose. 

In  cases  where  there  is  no  forecastle  the  sheer  is  to  be  meas- 
ured at  the  stem  and  sternpost,  and  corrections  made  for  it  in 
all  respects  as  in  the  case  of  flush-decked  vessels. 

When  the  bridge-house  is  enclosed,  the  sheer  should  be  taken 
at  the  stem  and  sternpost  and  the  freeboard  corrected  for  sheer 
in  estimating  the  allowance  for  erections.  When  the  bridge- 
house  is  not  enclosed  at  both  ends,  the  sheer  should  be  measured 
as  if  there  were  no  bridge-house,  and  the  freeboard  should  or 
should  not  be  corrected  for  sheer  in  estimating  the  allowance 
for  erections,  according  as  the  sheer  is  measured  at  the  stem  or 
at  £  length  from  the  stem. 

Sub-para.  (a).  —  Surveyors  should  note  that  paras.  11  and 
12  apply  either  to  vessels  of  the  ordinary  well-decked  type  or  to 
vessels  having  a  poop  and  forecastle  with  a  disconnected  bridge- 
house. 

Sub-para.  (d).  —  The  extent  of  the  depressed  part  of  the 
sheer  covered  by  deck  erections  is  to  be  allowed  for  in  applying 
this  rule. 

Sub-para.  (e).  —  In  vessels  obtaining  an  allowance  for  deck 
erections  under  para.  11  and  having  considerably  less  than  the 
normal  sheer,  the  freeboard  should  be  modified  in  consideration 
of  the  decrease  of  height  of  deck  in  the  "well." 

Sub-para.  (/).  —  In  flush-deck  vessels  the  total  standard 
means  the  sheer  measured  at  the  stem  and  sternpost.     In  vessels 


Notes  on  the  Tables  of  Freeboard        97 

having  poops  and  forecastles,  it  means  the  sheer  measured  at 
points  distant  £  of  the  vessel's  length  from  stem  and  stern- 
post. 

In  vessels  obtaining  an  allowance  for  deck  erections  under 
para.  11,  where  the  sheer  drops  abaft  amidships,  the  height  of 
the  raised  quarter-deck  is  to  be  taken  from  the  level  of  the  top 
of  the  midship  beam. 

Para.  19  —  Round  of  Beam.  —  In  flush-deck  sailing  vessels 
the  excess  of  round  of  beam  for  which  an  allowance  is  made 
6hall  not  exceed  the  standard  round  of  beam;  and  for  sailing 
vessels  having  erections  on  deck  the  allowance  shall  be  further 
reduced  in  proportion  to  the  extent  of  the  main  deck  uncovered. 

Table  A. 

The  deductions  for  summer  in  vessels  having  deck  erections 
is  to  be  intermediate  between  those  required  by  Tables  A  and  C 
in  proportion  to  the  length  of  the  ship  covered  by  those  erections. 

Table  B. 

All  vessels  equal  in  strength  to  Lloyd's  spar-decked  rule,  or 
which,  although  in  excess  of  that  rule,  do  not  come  up  to  Lloyd's 
requirements  for  ships  of  full  scantlings  to  the  upper  deck,  are 
to  be  considered  as  spar-decked  ships,  the  freeboard  for  which 
will  vary  with  their  strength. 

When  the  height  between  decks  is  greater  or  less  than  7  feet, 
the  consequent  modification  in  freeboard  will  vary  from  i  to  § 
the  excess  or  deficiency  of  height,  the  exact  proportion  to  de- 
pend upon  the  strength  of  the  vessel. 

In  spar-decked  vessels  where  the  height  between  main  and 
spar  deck  exceeds  7  feet,  the  numbers  for  scantlings  should  be 
found  assuming  the  height  between  decks  to  be  7  feet;  if  both 
these,  numbers  are  in  the  same  grades  as  the  actual  scantling 
numbers  of  the  vessel,  the  correction  for  height  between  decks 
is  to  be  I  of  the  excess  of  height  above  7  feet.  If  both  the 
scantling  numbers  so  found  are  in  higher  grades  than  those  of 
the  actual  vessel,  §  of  the  excess  of  height  is  to  be  added,  and  if 
either  one  of  these  scantling  numbers  is  in  a  higher  grade,  \  of 
the  excess  of  height  is  to  be  added.  The  same  principle  will 
apply  in  cases  where  the  height  between  decks  is  less  than  7 
feet. 

Since  the  freeboard  is  measured  from  the  spar  deck,  it  will  be 
increased  if  the  'tween  deck  height  is  more,  and  decreased  if  it 
is  less  than  7  feet. 


98  The  Naval   Constructor 

In  computing  the  freeboard  of  spar-decked  vessels  having 
scantlings  in  excess  of  Lloyd's  requirements,  a  comparison  is  to 
be  made  between  their  scantlings,  the  scantlings  of  vessels  of 
the  same  dimensions  classed  100  A  built  to  the  three-decked 
rule,  and  of  vessels  built  to  the  100  A  spar-decked  rule,  and  the 
freeboard  is  to  be  proportionate  between  that  given  in  Table  A 
and  that  given  in  Table  B,  after  deducting  12  per  cent  from  the 
former;  but  in  no  case  must  the  freeboard  so  assigned  be  less 
than  that  provided  in  Table  A,  for  a  vessel  of  the  same  dimen- 
sions, sheer,  and  camber,  or  round  of  beam,  and  deck  erec- 
tions. 

In  the  comparison  of  scantlings  and  assignment  of  freeboard 
to  spar-decked  vessels  having  scantlings  in  excess  of  Lloyd's  re- 
quirements, the  following  method  is  to  be  adopted: 

1.  The  difference  between  the  freeboard  by  Table  A  (less  12 
per  cent)  and  that  by  Table  B  to  be  divided  by  five,  f  of  it  be- 
ing considered  with  reference  to  the  longitudinal  strength, 
and  |  of  it  with  reference  to  the  transverse  strength,  these  al- 
lowances to  be  the  maximum  deduction  on  each  account. 

2.  In  the  comparison  of  steel  ships,  notwithstanding  the 
general  reduction  of  20  per  cent  for  steel  as  compared  with  iron 
thicknesses,  outside  plating  in  the  way  of  the  double  bottoms  is 
not  to  be  further  reduced  by  ^  unless  its  thickness  is  \%  or 
over.  No  reduction  is  to  be  made  in  any  case  unless  there  are 
floors  connected  with  every  frame. 

3.  In  the  calculation  of  strength  the  following  method  is  to 
be  adopted: 

(a)  Thin  iron  or  steel  plating  in  weather  decks  and  the  inner 
plating  of  double  bottoms  are  to  have  their  sectional  area  re- 
duced for  the  purpose  of  the  strength  calculation  as  follows: 

1.  When  the  deck  beams  or  floors  are  fitted  on  every  frame 
of  the  usual  spacing: 

Thickness  in  20ths 5     6    7     8     9 

.6   .7   .9     1     1 

2.  When  the  deck  beams  or  floors  are  fitted  on  alternate 
frames: 

Thickness  in  20ths 5     6     7     8    9 

.4   .5  .6   .7   .8 

When  the  decks  are  sheathed  with  wood,  with  fastenings  not 
more  than  24  inches  apart,  the  factors  given  in  (1)  are  to  be 
used,  whether  the  beams  are  on  every  frame  or  on  alternate 
frames,  but  if  the  fastenings  are  48  inches  apart,  then  the  fac- 


Notes  on   the  Tables  of  Freeboard         99 


tors  in  (2)  are  to  be  used  unless  the  beams  are  fitted  on  every 
frame. 

(6)  A  deduction  of  \  is  to  be  made  for  rivet  holes  in  steel,  and 
\  in  iron  for  the  parts  in  tension. 

(c)  Iron  or  steel  decks  which  cover  not  less  than  §  of  the  mid- 
ship length  of  the  vessel  are  to  be  considered  in  the  calculation 
just  as  they  would  be  if  of  the  full  length. 

(d)  Such  portions  of  wood  weather  decks  as  are  continuous 
throughout  the  midship  portion  of  the  ship  are  to  be  considered 
as  equivalent  to  steel  of  ^V  the  section  area  of  the  wood. 

(e)  For  the  purpose  of  comparison  of  strength  the  breadth  of 
the  hatchways  in  the  standard  vessel  shall  be  deemed  to  be  5  the 
breadth  of  the  deck,  and  the  tie-plates  should  be  assumed  to  be 
fitted  at  the  side  of  the  hatchways. 

Table  C. 

The  standard  of  strength  for  awning-decked  vessels  is  that 
provided  by  Lloyd's  Rules  (1885)  for  100  A  awning-deck  class, 
as  modified  and  extended  by  the  following  table  showing  the 
thicknesses  of  topside  plating,  etc. 

All  vessels  equal  in  strength  to  the  above  standard,  or  which, 
although  in  excess  of  that  standard,  do  not  come  up  to  Lloyd's 
requirements  for  a  spar-decked  vessel,  are  to  be  considered  as 
awning-decked  vessels,  the  freeboard  of  which  will  vary  with 
their  strength. 

No  modification  is  necessary  in  respect  of  the  height  of  'tween 
decks  of  awning-decked  vessels. 

In  comparing  the  freeboard  for  awning-decked  vessels  having 
scantlings  in  excess  of  the  standard  requirements,  a  comparison 
is  to  be  made  between  their  scantlings,  the  scantlings  of  vessels 
of  the  same  dimensions  built  to  the  100  A  spar-decked  rule, 
and  of  vessels  built  to  the  standard  awning-decked  rule,  and  the 
freeboard  is  to  be  proportionate  between  that  given  in  Table  B 
and  that  given  in  Table  C. 

In  vessels  where  the  superstructure  is  of  less  strength  than 
that  required  for  the  standard  awning-decked  vessel,  additions 
are  to  be  made  to  the  freeboard  in  the  same  proportion. 

In  the  comparison  of  scantlings  and  assignment  of  freeboard 
to  awning-deck  vessels  having  scantlings  in  excess  of  the  stand- 
ard awning-decked  vessel,  the  method  of  procedure  to  be  similar 
to  that  stated  above  for  spar-deck  vessels  having  scantlings  in 
excess  of  those  provided  by  the  spar-decked  rule. 

The  thickness  of  the  side  plating  above  the  main  deck  of 
standard  awning-decked  vessels,  for  half  the  vessel's  length 
amidships,  is  to  be  in  accordance  with  the  following  table. 


100 


The  Naval  Constructor 


Ratio  -=. 

Under 
13. 

13-14 

14-15 

Plating  Number 
10,000  and  under  13,100 
13,100    "        "      15,500 
15,500    "        "      16,600 
16,600    "        "      18,700 
18,700    "        "      26,400 
26,400    "        "      30,900 
30,900    "        "      35,200 
35,200    "        "      40,000 

5 
6 
6 

7 

8 

8 

9* 

9* 

5  and  6 
6 

6  and  7 

7  and  8 

8  and  9* 

9* 
10* 

lot 

6 
6 

7 

8 

9* 

9  and  10* 

iot 
iot 

*  The  butts  of  the  awning-deck  sheer  strake  to  be  treble  riveted,  and  the  landing 
edges  of  the  side  plating  to  be  double  riveted. 

f  The  butts  of  the  strake  of  side  plate  below  the  awning-deck  sheer  strake  to  be 
treble  riveted  in  addition. 

Note. — For  iron  read  sixteenths  and  for  steel  read  twentieths  of  an  inch. 
When  two  thicknesses  are  given  the  greater  is  that  of  the  awning-deck  sheer 
Btrake.  The  depth  and  length  are  to  be  measured  as  defined  in  Lloyd's  Register 
Rules  for  estimating  the  scantling  numbers. 

When  Section  46  of  the  above  rules  (relating  to  vessel's  pro- 
portions) applies  to  these  vessels,  the  increased  thicknesses  re- 
quired for  sheer  strakes,  stringers,  etc.,  are  to  be  added  to  those 
of  the  main  deck. 

When  one  steel  deck  is  required,  it  is  to  be  fitted  at  the  main 
deck,  and  when  two  steel  decks  are  required  they  are  to  be 
fitted  at  the  awning-deck  and  the  main-deck,  for  the  purpose  of 
comparison  of  strength  for  determination  of  freeboard. 

For  vessels  having  a  plating  number  exceeding  40,000  the 
scantlings  necessary  for  the  standard  awning-decked  vessel  for 
the  Table  C  freeboard  are  to  be  determined  so  that  the  stress 
per  square  inch  upon  the  material  of  the  hull  amidships  shall 
not  exceed  that  of  a  standard  vessel  of  the  same  dimensions 
and  form,  and  having  scantlings  equal  to  the  requirements  of 
the  100  A  class  in  Lloyd's  Register  for  three-deck  vessels  when 
loaded  to  the  freeboard  given  in  Tables  A  after  deducting  12 
per  cent  from  the  same. 

In  part  awning-decked  vessels  with  raised  quarter-decks  and 
long  superstructures  with  the  extra  strength  given  in  Section  44, 
Lloyd's  Rules  for  1889  for  iron  and  steel  vessels,  where  the 
break  of  the  quarter-deck  is  fo  the  vessel's  length  abaft  amid- 
ships, and  the  continuity  of  strength  is  suitably  maintained  at 
such  break,  a  reduction  may  be  made  from  the  freeboard  re- 
quired by  Table  C  in  accordance  with  the  following  scale. 


Notes  on  the  Tables  or*  Freeboard      101 


When  the  break  of  the  quarter-deck  is  not  less  than  T3¥  the 
length  of  the  vessel  abaft  amidships,  twice  the  above  men- 
tioned allowance  may  be  made,  and  for  intermediate  lengths  of 
erection  the  allowance  is  to  be  obtained  by  interpolation. 

Vessels  with  plating  number  under  18,000,  2\  inches. 
Vessels  with  plating  number  18,000  to  21,000,  3  inches. 
Vessels  with  plating  number  21,000  to  24,000,  3£  inches. 
Vessels  with  plating  number  24,000  to  27,000,  2>\  inches. 

In  part  awning-deck  vessels  the  standard  height  of  the  raised 
quarter-deck  is  4  feet;  for  raised  quarter-decks  of  less  height, 
extending  over  y%  of  the  length,  the  allowance  for  the  erections 
should  be  diminished  as  shown  in  the  following  table: 


Height  of  R. 

Moulded  Depth  of  Vessel  in  Feet. 

Quar.  Dk. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

10    0 

12    0 

14     0 

16      0 

18      0 

20      0 

22      0 

Ft.     Ina. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

3       6 

t 

i 

2 

l 

2 

i 

t 

1 

4 

3       0 

i 

2 

i 

1 

1 

H 

lj 

A4 

2       6 

1 

if 

« 

If 

2 

n 

3 

2      0 

H 

if 

2} 

2i 

H 

'Si 

4± 

^2 

1      6 

2 

2j 

3 

3f 

4J 

5 

6 

For  shorter  or  longer  lengths  of  raised  quarter-decks  a  pro- 
portionate correction  should  be  made. 

Table  D. 

Sailing  vessels  classed  A  (black)  in  Lloyd's  Register  are  to  be 
regarded  as  first-class  ships  in  applying  the  tables. 

Hard  wood  ships,  i.e.,  other  than  fir  or  pine,  classed  A  (red) 
in  Lloyd's  are  to  have  their  freeboards  by  the  tables  increased 
by  8  per  cent. 

Hard  wood  ships  classed  (E  in  Lloyd's  are  to  have  their  free- 
boards by  the  tables  increased  15  per  cent. 

Hard  wood  ships  without  class  are  to  have  their  freeboard  by 
the  tables  increased  by  20  per  cent,  unless  opened  out  for  survey, 
when  their  freeboards  will  depend  upon  their  condition. 

Soft  wood  ships  will  require  to  have  their  coefficient  of  fine- 
ness modified  in  respect  of  the  excess  of  the  registered  breadth 
caused  by  the  extra  thickness  of  side.  That  for  hard  wood 
ships  is  already  provided  for  in  the  tables. 


102  The  Navral  Constructor 

Soft  wood  ships  classed  A  (red)  in  Lloyd's  are  to  have  their 
freeboards  by  the  tables  increased  10  per  cent. 

Soft  wood  ships  classed  (E  in  Lloyd's  are  to  have  their  free- 
boards increased  20  per  cent. 

Soft  wood  ships  without  class  are  to  have  their  freeboards  by 
the  tables  increased  25  per  cent  unless  opened  out  for  survey 
when  their  freeboards  will  depend  upon  their  condition. 

Iron  and  steel  sailing  vessels  having  a  greater  rate  of  rise  of 
floor  than  1|  inches  per  foot  of  half  breadth  may  have  the 
moulded  depth  to  be  used  with  the  tables  reduced  by  half  the 
difference  between  the  total  rise  of  floor  at  the  half  breadth  and 
the  total  rise  at  the  standard  rate  of  1|  inches  per  foot;  2\ 
inches  per  foot  of  half  breadth  is  to  be  the  maximum  rate  of  rise 
on  which  an  allowance  is  to  be  made.  When  the  reserve  buoyancy 
is  calculated,  the  percentage  taken  shall  be  that  corresponding 
to  the  depth  reduced  as  above,  but  in  no  case  shall  the  free- 
board be  less  than  that  given  in  the  top  line  of  Table  D  for  such 
percentage.  Whichever  method  be  adopted  the  correction  for 
length  is  to  be  applied  in  relation  to  the  reduced  moulded  depth. 

RULES  TO  REGULATE  THE  DEPTH  OP  LOADING 

OF  TURRET-DECK  VESSELS  AND  VESSELS 

OF  SIMDLAR  TYPES. 

1.  A  turret  is  a  strongly-constructed  continuous  erection  at 
the  middle  line  of  the  vessel,  forming  with  the  main  or  harbour 
deck  an  integral  part  of  the  hull,  having  a  breadth  not  less  than 
r5ff  of  the  greatest  breadth  of  the  vessel  and  a  height  not  less 
than  25  per  cent  of  the  moulded  depth.  In  assigning  free- 
boards to  turret-deck  vessels,  the  following  rules  should  be 
observed: 

2.  Hatch  coamings  at  least  2  ft.  high  and  casings  to  engine 
and  boiler  openings  at  least  4  ft.  6  ins.  high  to  be  fitted  above 
the  " turret"  deck. 

Any  scuttles  or  other  openings  in  the  harbour  deck  are  to  be 
closed  water-tight  by  means  of  iron  or  steel  plates  not  less  in 
thickness  than  the  harbour  deck,  suitably  stiffened  and  strongly 
bolted  in  place.  The  following  method  of  computing  the  free- 
board is  based  on  the  consideration  that  the  turret-deck  hatch- 
ways are  provided  with  permanent  means  of  closing  them,  as 
described  in  clause  8  of  the  rules  for  shelter-decked  steamers. 

3.  The  volume  of  the  turret  to  be  estimated  from  a  normal 
beam  line  drawn  through  the  point  where  a  vertical  line  at  the 
quarter  breadth  of  vessel  cuts  the  upper  surface  of  the  vessel's 
deck.     Where  the  turret  is  nearly  one-half  the  breadth  of  the 


Rules  for  Loading  of  Turret-deck  Vessels  103 

vessel,  and  its  transverse  section  is  of  rounded  form  at  its  base, 
the  base  line  of  the  turret  is  to  be  drawn  through  the  point 
where  the  vertical  line  at  the  quarter  breadth  cuts  the  upper 
surface  continued  in  the  same  curve  as  the  normal  line  of  beam. 

4.  The  reserve  buoyancy  required  by  the  tables  to  be  esti- 
mated by  taking  70  per  cent  of  the  volume  of  the  turret.  The 
height  of  the  turret  allowed  for  is  not  to  exceed  25  per  cent  of 
the  moulded  depth.  (It  is  to  be  understood  that  no  correction 
is  to  be  made  for  an  unsheathed  iron  harbour  deck  in  applying 
the  buoyancy  method.) 

5.  The  moulded  depth  of  the  vessel  to  be  taken  to  be  the 
depth  at  side  from  the  beam  line,  as  before  defined,  to  the  top 
of  the  keel. 

6.  If  a  vessel  has  sheer,  to  determine  the  volume  of  the  turret, 
the  turret  base  line  to  be  drawn  at  each  section  as  described 
above.  At  the  extreme  fore  end  of  the  vessel  the  base  of  the 
turret  to  be  parallel  to  the  turret  deck. 

7.  Where  a  poop  and  forecastle  or  a  forecastle  only  are  fitted 
on  the  top  of  a  turret,  the  allowance  for  them  is  to  be  as  follows: 

When  the  effective  length  of  these  erections  is  equal  to  \  of 
the  vessel  s  length,  deduct  8  per  cent  of  the  difference  between 
the  freeboards  in  Table  A  (after  correction  for  sheer)  and  Table  C. 

For  erections  of  greater  or  less  length  the  allowance  is  to  be 
in  proportion  to  the  length.  The  allowance  for  such  erections 
is  not  to  exceed  10  per  cent  of  the  difference  between  the  free- 
boards in  Table  A  (after  correction  for  sheer)  and  Table  C. 

The  effective  length  of  a  poop  or  forecastle  is  to  be  obtained 
by  multiplying  its  actual  length  by  the  ratio  which  its  breadth 
bears  to  the  breadth  of  the  ship  at  the  after  end  of  the  fore- 
castle or  fore  end  of  the  poop  respectively. 

The  provisions  of  the  freeboard  tables  regarding  the  height 
of  forecastles,  the  bulkheads  at  the  after  end  of  forecastles  and 
at  the  fore  end  of  poops,  and  the  means  of  closing  the  openings 
in  poop  bulkheads,  are  to  be  applied  in  these  cases. 

8.  The  method  described  above  is  only  applicable  when  it  is 
possible  to  obtain  a  correct  drawing  of  the  "lines"  of  the  ves- 
sel, and  it  is  only  to  be  employed  when  facilities  are  given  for 
verifying  the  drawing  by  actual  measurements  at  the  ship,  in 
accordance  with  para.  6  of  the  freeboard  tables.  When  a  veri- 
fied drawing  is  obtainable,  either  the  foregoing  or  the  following 
method  may  be  employed  at  the  option  of  the  owner,  but  if  a 
verified  drawing  is  not  obtainable,  the  following  method  only 
is  to  be  employed. 

9.  The  depth  of  hold  to  be  used  in  obtaining  the  coefficient 
of  fineness  in  vessels  having  either  an  excess  or  deficiency  of 
sheer  is  to  be  modified  as  described  in  para.  3,  and  the  coeffi- 


104  The  Naval  Constructor 


cient  thus  obtained  is  to  be  modified  when  the  vessel  is  of  rounded 
form  at  the  gunwale,  the  necessary  addition  in  ordinary  cases 
being  .01. 

10.  The  length  correction  under  para.  9  of  the  load-line 
tables  is  to  be  |  of  that  specified  in  Table  A,  where  the  breadth 
of  the  turret  is  T%  of  the  breadth  of  the  vessel,  but  the  table 
correction  is  to  be  halved  where  the  breadth  of  the  turret  is  A 
or  more  of  the  breadth  of  the  vessel.  For  turrets  having  breadths 
between  -^  and  -j*v,  the  length  correction  is  to  be  in  proportion. 

11.  In  making  the  sheer  correction  in  accordance  with  para. 
18  of  the  load-fine  tables,  the  sheer  is  to  be  measured  at  the 
ends  of  the  vessel. 

12.  The  effective  length  of  the  turret  is  to  be  obtained  by 
multiplying  its  length  by  the  ratio  of  the  mean  breadth  of  the 
turret  to  the  breadth  of  the  vessel  amidships. 

13.  The  deduction  from  the  freeboard  shown  in  the  tables  on 
account  of  the  turret  is  to  be  as  follows: 

Where  the  effective  length  of  the  turret  is  A  of  the  length  of 
vessel  deduct  45  per  cent  of  the  difference  between  the  free- 
boards in  Table  A  (after  correction  for  sheer)  and  Table  C. 
Where  the  effective  length  is  •&,  deduct  55  per  cent,  and  so  on 
in  proportion.  For  intermediate  lengths  intermediate  per- 
centages are  to  be  taken. 

14.  In  those  vessels  having  unsheathed  harbour  or  main 
decks,  a  correction  should  be  made,  when  employing  the  linear 
method  of  computation,  as  described  in  para.  6  (6). 

15.  The  transverse  and  longitudinal  strength  of  the  vessel  are 
to  be  regulated  by  that  required  for  a  "three-deck"  vessel  of 
the  same  length,  breadth,  moulded  depth,  and  coefficient  of 
fineness,  and  the  scantlings  of  the  turret  are  to  be  determined  so 
that  the  stress  per  square  inch  upon  the  material  of  the  turret 
amidships  shall  not  exceed  that  of  a  standard  vessel  of  the  same 
dimensions  and  form,  and  having  scantlings  equal  to  the  require- 
ments of  the  100  A  class  in  Lloyd's  Register  (1885)  for  three- 
deck  vessels  when  loaded  to  the  freeboard  given  in  Table  A 
after  deducting  12  per  cent  from  the  same. 

16.  Should  a  vessel  be  constructed  with  a  turret  less  than  A 
the  breadth  of  the  vessel  or  less  in  height  than  \  of  the  moulded 
depth,  or  should  the  radius  of  curvature  at  the  gunwale  exceed 
20  per  cent  of  the  moulded  depth,  or  should  the  centre  line  of 
the  disc  when  ascertained  reach  a  point  above  the  junction  of 
the  vertical  side  with  a  rounded  gunwale,  full  particulars  and 
calculations  with  the  proposed  assignment  are  to  be  submitted 
to  the  Board  of  Trade  before  freeboards  are  assigned. 

17.  The  freeboards  in  the  certificates  issued  are  to  be  set  off 
in  feet  and  inches  from  the  line  of  the  turret  deck. 


Rules  for  Shelter-decked  Steamers       105 


RULES    FOR   THE   DETERMINATION    OF   THE 
FREEBOARD    OF   SHELTER-DECKED 
STEAMERS 

By  the  term  "shelter-decked  steamer"  is  meant,  for  the 
purpose  of  the  following  instructions,  a  steam  vessel  having  a 
complete  superstructure  of  a  substantial  character  extending 
over  the  whole  length  of  the  vessel,  the  superstructure  deck 
(hereinafter  called  the  shelter-deck)  being  continuous  and  un- 
broken at  the  sides  of  the  vessel,  but  having  one  or  more  open- 
ings at  the  middle  line,  which  have  no  permanent  means  of 
closing  them,  but  which  may  not  have  means  for  temporarily 
closing  them. 

All  hatchways  in  the  deck  immediately  below  the  shelter- 
deck  should  be  properly  framed  with  substantial  coamings, 
hatch  covers,  and  shifting  beams,  etc.,  as  described  in  para- 
graph 24.  The  hatchways  should  have  efficient  means  of 
battening  down  as  described  in  clause  7  of  these  rules  and  any 
stairways  or  similar  openings  should  have  efficient  means  of 


In  assigning  freeboards  to  shelter-decked  vessels,  the  follow- 
ing rules  should  be  observed: 

(1)  In  making  the  sheer  correction  in  accordance  with  para. 
18  of  the  load-line  tables,  the  sheer  is  to  be  measured  at  the 
ends  of  the  vessel,  and  the  freeboard  corrected  for  sheer  in  esti- 
mating the  allowance  for  erections. 

(2).  (a)  In  the  case  of  shelter-decked  vessels  having  only 
one  opening  in  the  shelter-deck,  the  length  correction  under 
para.  9  of  the  load-line  tables  is  to  be  one-half  that  specified  in 
Table  A;  and  the  allowance  for  deck  erections  is  to  be  deter- 
mined under  para.  11  in  the  manner  specified  below,  provided 
that  the  effective  length  of  the  deck  erections,  when  assessed 
on  the  assumption  that  the  opening  in  the  deck  is  an  open  well, 
and  in  accordance  with  the  different  regulations  contained  in 
the  load-line  tables  affecting  poops,  bridges,  and  forecastle, 
open  or  closed,  is  not  less  than  T%  of  the  length  of  the  vessel. 

(6)  In  the  case  of  shelter-decked  vessels  having  an  opening 
at  each  end  of  the  vessel,  and  also  in  the  case  of  vessels  having 
more  than  two  openings  in  the  shelter-deck,  the  allowance  for 
deck  erections  is  to  be  determined  under  para.  12  of  the  tables, 
the  length  correction  under  para.  9  of  the  load-line  tables  is  to 
be  one-half  that  specified  in  Table  A,  provided  that  the  effective 
length  of  the  deck  erections,  when  assessed  on  the  assumption 
that  each  opening  in  the  deck  is  an  open  well,  and  in  accordance 
with  the  different  regulations  contained  in  the  load-line  tables 


106  The  Naval  Constructor 


affecting  poops,  bridges,  and  forecastles,  open  or  closed,  is  not 
less  than  T'c  of  the  length  of  the  vessel. 

(3)  The  effective  length  of  the  deck  erections  is  to  be  cal- 
culated in  the  following  manner,  provided  the  openings  in  the 
shelter-deck  do  not  exceed  half  the  vessel  s  breadth  at  the  mid- 
dle of  the  length  of  the  opening.  The  length  to  be  taken  in  the 
first  instance  as  if  each  opening  were  an  open  well,  the  value 
of  each  part  being  assessed  on  that  assumption  in  accordance 
with  the  different  regulations  contained  in  the  load-line  tables 
affecting  poops,  bridge-houses,  and  forecastles,  open  or  closed, 
and  also  in  accordance  with  the  regulations  regarding  bridge- 
houses  not  covering  the  engine  and  boiler  space.  The  final 
allowance  for  erections  will  depend  upon  whether  or  not  tem- 
porary but  efficient  means  are  provided  for  closing  the  openings 
in  the  shelter-deck. 

(a)  If  efficient  means  as  specified  below  are  provided  for  tem- 
porarily closing  the  openings  in  the  shelter-deck,  the  effective 
length  of  the  deck  erections  is  to  be  reckoned  as  the  length 
computed  as  prescribed  above,  plus  half  the  difference  between 
that  length  and  the  length  of  the  vessel. 

(6)  If  efficient  means  for  temporarily  closing  the  openings 
are  not  provided,  the  effective  length  of  the  erections  is  to  be 
computed  by  adding  to  the  length  computed  as  above  one-fourth, 
instead  of  one-half,  the  difference  between  that  length  and  the 
length  of  the  vessel. 

(c)  If  the  openings  in  the  shelter-deck  are  wider  than  as 
specified  above,  the  addition  to  the  assumed  length  of  erections 
is  to  be  modified  in  proportion  to  the  relation  which  the  actual 
opening  holds  to  the  specified  breadth  and  to  a  complete  well. 

4.  Means  for  temporarily  closing  the  openings  in  the  shelter- 
deck  may  be  regarded  as  efficient,  if  they  are  at  least  equivalent 
to  the  following  in  strength  and  security.  The  portable  planks 
for  closing  the  openings  to  be  not  less  in  thickness  than  re- 

auired  by  para.  43  of  Lloyd's  Rules  (1885)  for  the  flat  of  awning- 
ecks.  The  planks  to  be  supported  by  portable  beams,  fitted 
either  longitudinally  or  athwartships,  spaced  not  wider  than 
5  feet  apart,  and  efficiently  secured  at  their  ends,  and  the  deck 
in  way  of  the  openings  to  be  efficiently  supported  by  pillars 
from  the  deck  below.  The  portable  planks  to  be  provided  with 
eye  bolts  and  lashings,  or  some  other  equally  efficient  means  of 
securing  them  in  place. 

5.  If  efficient  means  are  provided  for  temporarily  closing  the 
openings  in  the  shelter-deck  in  heavy  weather,  the  freeing  ports 
required  by  para.  11  (e)  need  not  be  provided.  If,  however, 
efficient  means  for  closing  the  openings  are  not  provided,  whether 
in  vessels  with  one  or  more  than  one  opening  in  the  shelter- 


Rules  for  Shelter-decked  Steamers       107 


deck,  then  freeing  ports  with  shutters  properly  hung  are  to  be 
fitted,  having  a  minimum  area  as  follows: 


Length  of  Opening 

Freeing  Port  Area  on 

in  the  Shelter-deck, 

Each  Side  in  Square 

Feet. 

Feet. 

5 

4.5 

10 

6.5 

15 

7.5 

20 

8.5 

25 

9.0 

If  the  freeing  port  area  is  less  than  that  stated  above,  an 
addition  is  to  be  made  to  the  freeboard  of  \  per  cent  of  the  vessel's 
moulded  depth,  provided,  however,  that  in  the  case  of  vessels 
treated  under  para.  12,  the  freeboard  is  not  to  be  increased  be- 
yond that  due  to  deck  erections  of  the  same  length  and  character, 
but  with  open  wells,  as  determined  by  the  different  regulations 
contained  in  the  load-line  tables  affecting  poops,  bridge-houses, 
and  forecastles. 

6.  The  deduction  for  summer  to  be  intermediate  between 
Tables  A  and  C,  in  proportion  to  the  effective  length  of  erections 
finally  allowed  for  freeboard  purposes,  and  the  freeboards 
assigned  to  those  vessels  must  never  be  less  than  would  be 
assigned  for  a  complete  awning-decked  vessel  of  the  same  dimen- 
sions. 

7.  For  the  purpose  of  the  assignment  of  freeboards,  a  hatch- 
way having  strong  iron  or  steel  coamings,  with  hatch  rest  bars 
of  the  usual  description,  and  also  cleats  for  battening  down  bars 
securely  riveted  to  the  coamings,  thwartship  beams  and  fore 
and  afters,  substantial  hatch  covers  and  tarpaulins,  shall  be  con- 
sidered to  have  "permanent  means  of  closing."  And  a  deck 
erection  having  no  openings  in  it,  except  so  protected,  shall  be 
held  to  be  "permanently  enclosed." 

The  above  reduction  in  freeboard  for  summer  voyages  from  European  and 
Mediterranean  ports  is  to  be  made  from  April  to  September  inclusive.  In  other 
parts  of  the  world  the  reduced  freeboard  shall  be  used  during  the  corresponding 
or  recognised  summer  months.  Double  the  above  reduction  to  be  allowed  for 
voyages  in  the  fine  season  in  the  Indian  seas,  between  the  limits  of  Suez  and 
Singapore.  An  additional  freeboard  of  two  inches  should  be  required  for  all 
vessels  up  to  and  including  330  feet  in  length  when  entering  the  North  Atlantic, 
when  sailing  to,  or  from,  the  Mediterranean,  or  any  British  or  European  port, 
and  which  may  sail  to,  or  from,  or  call  at,  ports  in  British  North  America,  or 
eastern  ports  in  the  United  States,  north  of  Cape  Hatteras,  from  October  to 
March  inclusive. 


108  The  Naval  Constructor 

Load  Draught  Diagrams. 

(Based  on  British  Freeboard  Tables.) 

It  is  often  necessary  to  get  an  approximation  to  the  load  draught 
in  estimating  on  proposed  vessels,  when  in  many  cases  there  is 
insufficient  time  to  calculate  the  freeboard  in  the  regular  way. 
For  this  purpose  the  adjoining  diagrams  have  been  prepared  for 
cargo  vessels  from  the  freeboard  tables,  and  from  these  the  mean 
moulded  load  draught  may  be  scaled  off  with  accuracy,  always 
observing  that  the  proper  allowances  for  excess  of  sheer,  erec- 
tions on  deck,  and  uncovered  iron  deck,  strength,  etc.,  must  be 
made  afterwards.  These  diagrams  being  graphic  reproductions 
of  the  various  tables,  will  be  found  to  facilitate  the  estimating  of 
load  draughts  where  a  sufficiently  close  approximation  only  is  re- 
quired. It  should  also  be  borne  in  mind  that  fullness  of  form 
influences  the  freeboard  to  a  considerable  extent,  therefore  the 
diagram  will  only  read  correctly  for  vessels  having  coefficients  of 
under  deck  tonnage  from  .78  to  .82,  and  judgment  must  be  used 
when  dealing  with  vessels  of  finer  forms,  the  freeboards  of  which 
are  less  than  in  the  case  of  fuller  vessels. 


Types  of  Vessels 


SKETCHES  ILLUSTRATING  THE  DIFFERENT  TYPES  OF  VESSELS 


TO  WHICH  FREEBOARDS  ARE  ASSIGNED 


P'Il 


FLUSH  DECK  VESSEL. 
ENGINE^BpnER_CASINGS.  MAINJiECKj- 


3 


VESSELS  HAVING  MONKEY  FORECASTLE,   BRIDGE  HOUSE,  AND  HOOD  FOR 


THE  PROTECTION  Or  8TEERING  GEAR. 
HOOD  g.D 


NO.2 


VESSEL  HAVING  TOP-GALLANT  FORECASTLE,  BRIDGE  HOUSE,  AND  POOP 

F 


^JO.3 


— li 


em *j ^ 


_ 


oca 


VESSEL   HAVING  TOP   GALLANT  FORECASTLE,  BRIDGE  HOUSE,  AND  A 
SHORT  RAISED    QUARTER  DECK. 

_R.Q.D.  B.D 


MO.4 


1         ■ 


BRIDGE   HOUSE — i 
AMIDSHIPS 

SHORT   RAISED! 

QUARTER   DECK    P"™ 


40.5 


VESSEL   HAVING  TOP   GALLANT  FORECASTLE,  WITH  A  LONG  POOP  AND 
BRIDGE  HOUSE  COMBINED.  KNOWN  AS  A  "  WELL  DECKED  VESSEL' 

WELL  „ 


Figs.  18-22. 


110 


The  Naval  Constructor 


VESSEL  HAVING  TOP-GALLANT  FORECASTLE    WITH  A  LONG  RAISED 


TRANVERSE 
SECTION9. 

QUARTER  DECK  AND   BRIDGE    HOUSE   COMBINED  ALSO  KNOWN  AS  A  WELL  LONG  RAUEO 

DECKED  VESSEL  a    r> 


QUARTER    DECK 


l 


, -  1  EXTENDING 


SHADE  DECKED  VESSEL  THIS  TYPE  OF  VESSEL  HAS  A    CONTINUOUS  UPPER- 


N°-7     I 


DECK  OF  LIGHT  CONSTRUCTION  AND  WITH    OPENING8  IN  THE  SIDES. 
OPENING  SHADE  DECK  T"""""         j 


•AWNING  DECKED  VEB8EL'  THIS  TYPE  OF  VESSEL  HAS  A  CONTINOUS  UPPER 
DECK  OFLIGHTCONSTRUCTION  AND  THE  SIDES  COMPLETELY  CLOSED  ABOVE 
ENGINE^*   BPJLER_CA8ING9.  AWNINGJ>ECJ< 


THE  MAIN  DECK- 

_AWNING   DECK 


* -t. r.",rl 


DECK  ' 


AWNING  DECK. 


'SPAR  DECK  VESSEL"THIS  TYPE  OFVESSEL  IS  CONSTRUCTED    WITH  THE 
6CANTLING8  ABOVE   THE  MAIN  DECK  HEAVIER  THAN  IN  AN"AWNING  DECKED" 
VESSEL  BUT  NOT  SO  HEAVY  AS  IN  A  "THREE  DECKED  VES8EL" 

B.D, 


SPAR    DECK . — 


t 


3 


L^. 


TURRET  DECK  VESSEL 
ENGINE   *_BpiLi?_ 


_CASINGS. 

Asm 


5  m 


TRUNK  DECK  VESSEL 

B.D. 


Figs.  23-28. 


Freeboard   Marks  for  Steamers 


111 


Statutory  allowance  above  top  of  wood  deck  =  2" 
Centre  of  disc  below  statutory  deck  line         =    6'    7  \' 
Draught  of  water  moulded    *  =  26'  10|' 


DIAGRAMofFREEBOARD  MARKS forSTEAMERS. 

(FOR  FREEBOARD  SEE  TABLES) 


UPPER  DECK  LINE  (NOT  TO  BE  MARKED  ON  8HIP,) 


THE  MARKINGS  TO  BE  CUT  INTO 
PLATING  WITH  CENTRE-PUNCH 
MARKS  AS  SHOWN  AND  PAINTED 
WHITE 


METHOD  OF  MARKING  LINES 
AND  LETTERS  WITH  CENTRE- 
PUNCH. 


CENTRE  OF  DISC  TO  BE  PLACED  AT  THE 


MIDDLE  OF  THE  LENGTH  OF  THE  LOAD 
WATER  LINE 


— *l 


LINES  FOR  SMALL  LETTER8    Y  THICK. 


THESE  DIMENSIONS 
TO  BE  TAKEN  FROM 
CR.  OF  DISC  TO  TOP 
EACH  LINE 


ST'B'D.  SIDE  SHOWN-  PORT  SIDE  SIMILAR 

Fig.  30. 

(Fig.  29  in  this  edition  has  been  omitted.) 


112 


The   Naval   Constructor 


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DIAGRAM    Gl 

IN  FLUSH    Al 

PROPORTIONS  jj  IN  EACH  CASE  T 

LOAD  DRAFT  TO  CENTRE 
NOTE. -ALLOWANCES  FOR   EXCE 
DECK  (IN   FLUSH   DECK  S 
DRAFT  FOR  A  GIVEN   DEP 
DUE  TO  UNCOVERED  IRC 
FREEBOARD  TABLES. 

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Load   Draught  Diagrams 


113 


DIAGRAM  SHOWING  RELATIVE  DEPTHS  AND  LOAD 
DRAFTS  IN  VARIOUS  TYPES  OF  VESSELS. 

PROPORTIONS^)  IN  SPAR  DECK  SHIP  TAKEN  TO  SPAR  DECK  (7'-o"  ABOVE  MAIN  DECK*) 

•1              ii    ii AWNING     "       "          "        "    MAIN       " 

'•               "    "SAILING               "          "        "UPPER     " 
D     DEPTH  MOULDED  TO  RESPECTIVE    DECK8. 

^<^rf" 

NOTE:--ALLOWANCES  FOR  EXCESS  OF  SHEER  AND                                        V. 

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^-<^L. 

£ 

p. 

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MOULDED  DEPTH,  TO  MAIN  DECK    IN  SPAR  AND  AWNING  DECK  VESSELS 
«'               ««          "UPPER    <«      ««    SAILING  SHIPS. 

Fig.  32. 


114 


The  Naval   Constructor 


Table  A. 

Cargo-carrying  Steam  Vessels  Not  Having  Spar 

or  Awning  Decks. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Steam  Vessels  (in  Salt  Water). 


Coefficient  of 

Fineness. 

Percentage  Reserve  Buoyancy  (Winter). 

20.4 

20.6 

20.8 

21.0 

21.2 

21.4 

21.6 

21.8 

Corresponding  Height  of  Freeboard  Amidships 

(Winter). 

Measured  from  Top  of  Deck  at  Sides. 

Moulded  Depth  and  Length. 

6      0 

6      6 

7      0 

i      a 
7      6 

8      0 

8      6 

9      0 

/  // 
9      6 

72 

78 

84 

90 

96 

/ 

102 

/ 
108 

114 

0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 
0.82 

0      8 
0      8 
0      8J 
0      8} 
0      9 
0      9J 
0      9 
0      9i 

0      9 
0      9 
0      9J 
0      9} 
0    10 
0    10 
0    101 
0    101 

>      a 
0    10 
0    10 
0    101 
0    101 
0    11 
0    11 
0    111 
0    11* 

/      // 
0    11 
0    11 
0    111 

0  in 

1  0 
1      0 
1      01 
1      01 

1      0 
1      0 
1      01 
1      01 
1      1 

l     H 
1     U 

i      a 
1      1 

i    u 

1    u 

1      2 
1      2 
1      21 
1      21 

/      a 

1      2 
1      2 
1      21 
1      21 
1      3 
1      3 
1      31 
1      31 

1  3 
1  3 
1      3} 

1  31 
1  4 
1  4 
1  41 
1      41 

Correction     in 
inches   for  a  1 
change  of  10'  1 
in  the  length. 

0.7 

0.7 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

Deductions   in  1 
ins.  for  sum-  | 
mer  voyages.  J 

1 

1 

• 

1 

1 

■ 

• 

' 

Freeboard  Tables 


115 


Table  A.  —  (Continued.) 

Cargo-carrying  Steam  Vessels   Not  Having  Spar 

or  Awning  Decks. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Steam  Vessels  (in  Salt  Water). 


Percentage  Reserve  Buoyancy  (Winter). 

22. 0~ 

22.2 

22.4 

22.6 

22.8 

23.0 

23.2 

23.4 

Corresponding  Height  of  Freeboard  Amidships 

(Winter). 

Coefficient  of 

Measured  from  Top  of  Deck  at  Side. 

Moulded  Depth  and  Length. 

10      0 

10      6 

11      0 

11      6 

12      0 

12      6 

13      0 

13      6 

120 

/ 
126 

132 

138 

144 

150 

156 

162 

0.68 

1      4 

1      5 

1      6 

i    n 

1      8* 

1      9| 

1     11 

2      0 

0.70 

1      4 

1      5 

1      6 

i    n 

1      8£ 

1      9| 

1    11 

2      0* 

0.72 

1      4* 

1      5* 

1      6£ 

1      8 

1      9 

1     10 

1     111 

2      1 

0.74 

1      4| 

1      5£ 

1      6| 

1      8 

1      9 

1     10 

1     111 

2      1 

0.76 

1      5 

1      6 

1      7 

1      8* 

1      9* 

1     10J 

2      0 

2      li 

0.78 

1      5 

1      6 

1      7 

1      8} 

1      9* 

1     11 

2      0£ 

2      2 

0.80 

1      5* 

1      6* 

i    n 

1      9 

1     10 

1     11* 

2      1 

2      2i 

0.82 

1      5* 

1      6£ 

i    n 

1      9 

1     10 

i  m 

2      1 

2      2i 

Correction     in 

ins.      for      a  1 
change  of  10' j 

0.8 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

in  the  length. 

Deductions   in  j 

ins.  for  sum-  | 

1 

1 

1 

1 

1 

1 

1 

li 

mer  voyages.  J 

116 


The   Naval  Constructor 


Table  A.  —  (Continued.) 

Cargo-carrying  Steam  Vessels  Not  Having  Spar 

or  Awning  Decks. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Steam  Vessels  (in  Salt  Water). 


Coefficient  of 
Fineness. 

Pebcentage  Reserve  Buoyancy  (Winter). 

23.6 

23.8 

24.0 

24.2 

24.5 

24.7 

Corresponding  Height  of  Freeboard  Amidships 
(Winter). 
Measured  from  Top  of  Deck  at  Side. 

Moulded  Depth  and  Length. 

14      0 

14      6 

15      0 

15      6 

16      0 

16      6 

168 

174 

180 

186 

192 

198 

0.68 

0.70 
0.72 
0.74 
0.76 
0.78 
0.80 
0.82 

/        // 

2      1| 
2      14 
2      2 
2      24 
2      3 
2      3 
2      34 
2      4 

2      3 
2      3 
2      3} 
2      4 

2      44 
2      4i 
2      5 
2      54 

2      4 
2      4J 
2      5 
2      54 
2      6 
2      6 
2      6i 
2      7 

2      5i 
2      6 
2      6i 
2      7 
2      74 
2      74 
2      8 
2      84 

2      7 
2      74 
2      8 
2      84 
2      9 
2      9 
2      94 
2    10 

2      84 
2      9 
2      94 
2    10 
2    104 
2    11 

2  114 

3  0 

Correction  in  ins.  1 
for  a  change  of  > 
10' in  the  length.] 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

Deduction  in  ins. 
for  summer 
voyages.             J 

II 

li 

li 

14 

14 

2 

Freeboard  Tables 


117 


Table  A.  —  (Continued.) 

Cargo-carrying  Steam  Vessels  Not  Having  Spar 

or  Awning  Decks. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Steam  Vessels  (in  Salt  Water). 


Coefficient  of 

Fineness. 

Percentage  Reserve  Buoyancy  (Winter) 

25.0 

25.2 

25.5 

25.7 

26.0 

Corresponding  Height  of  Freeboard  Amid- 
ships (Winter). 
Measured  from  Top  of  Deck  at  Side. 

Moulded  Depth  and  Length. 

17      0 

17      6 

18      0 

18      6 

19      0 

204 

210 

216 

222 

t 

228 

0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 
0.82 

2      10J 

2      10 
2      11 

2  11} 

3  0 
3        0i 
3        1 
3        l\ 

2  Hi 

3  0 
3        0£ 
3        1 
3        1| 

3        2 
3        2J 
3        3 

3        1 
3        I* 
3        2 
3        2h 
3        3 
3        4 
3        4| 
3        5 

3        2J 
3        3 
3        3* 
3        4 
3        5 
3        5* 
3        6 
3        6i 

/        // 
3        4 
3      4 

3        5* 
3        6 
3      "6i 
3        1\ 
3        8 
3        8} 

Correction  in  ins.   for  | 
a   change  of   10'   in  [ 
the  length. 

1.1 

1.1 

1.1 

1.1 

1.1 

Deduction  in  ins.  fori 
summer  voyages. 

2 

2 

2 

2 

2 

118 


The  Naval  Constructor 


Table  A..  — (Continued.) 

Cargo-carrying  Steam  Vessels  Not  Having  Spar 

or  Awning  Decks. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Steam  Vessels  (in  Salt  Water). 


Coefficient  of 

Fineness. 

Percentage  Reserve  Buoyancy  (Winter). 

26.2 

26.5 

26.7 

27.0 

27.3 

27.5 

Corresponding  Height  of  Freeboard  Amidships 

(Winter). 

Measured  from  Top  of  Deck  at  Side. 

Moulded  Depth  and  Length. 

19    6 

20    0 

20    6 

21    0 

21    6 

22    0 

234 

240 

246 

252 

258 

264 

0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 
0.82 

3      5} 
3      «i 
3      7 
3      8 
3      8} 
3      9J 
3    10 
3    10i 

3      7i 
3      8 
3      8* 
3       9i 
3     10 
3    11 

3  Hi 

4  0 

3      9 
3     10 
3    10i 

3  11} 

4  0 
4      1 
4      1} 
4      2 

3     Hi 

3  Hi 

4  0 
4      1 
4      li 
4      2i 
4      3 
4      3i 

4      0i 
4      li 
4      2 
4      3 
4      3i 
4      4i 
4      5 
4      5i 

4      2i 
4      3i 
4      4 
4      5 
4      5i 
4      6i 
4      7 
4      7i 

Correction  in  ins.  ) 
for  a  change  of  / 
lCJin  the  length.  ) 

1.1 

1.2 

1.2 

1.2 

1.2 

1.2 

Deduction  in  ins.  ) 
for  summer         / 
voyages.              ) 

2* 

2* 

Si 

2i 

2i 

2i 

Freeboard  Tables 


119 


Table  A.  —  (Continued.) 

Cargo-carrying  Steam  Vessels  Not  Having  Spar 

or  Awning  Decks. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Steam  Vessels  (in  Salt  Water). 


Percentage  Reserve  Buoyancy  (Winter). 

27.8 

28.1 

28.3 

28.6 

28.9 

29.2 

Corresponding  Height  of  Freeboard  Amidships 

(Winter). 

Coefficient  op 

Fineness. 

Measured  from  Top  of  Deck  at  Side. 

Moulded  Depth  and  Length. 

22    6 

23    0 

23    6 

24    0 

24    6 

25    0 

270 

276 

282 

288 

i 
294 

300 

0.68 

4      4* 

4      6* 

4      8i 

4    10* 

5      1 

5      3J 

0.70 

4      5* 

4    n 

4      9* 

4  m 

5     ti 

5      4 

0.72 

4      6 

4      8 

4    10 

5      0 

5      2* 

5      5 

0.74 

4      7 

4      9 

4    11 

5      1 

5      3 

5      5i 

0.76 

4      7* 

4      9* 

4    m 

5      li 

5      4 

5      6* 

0.78 

4      8* 

4    10* 

5      0i 

5      2* 

5      4} 

5      7 

0.80 

4      9 

4    11 

5      1 

5      3 

5      5* 

5      8 

0.82 

4      9* 

4    111 

5      2 

5      4 

5      6* 

5      9 

Correction  in  ins.  ) 

for  a  change  of  > 

1.2 

1.2 

1.3 

1.3 

1.3 

1.3 

10' in  the  length.  ) 

Deduction  in  ins.  ) 

for  summer         £ 

3 

3 

3 

3 

3 

3} 

voyages.             ) 

120 


The  Naval  Constructor 


Table  A.  —  (Continued.) 

Cargo-carrying  Steam  Vessels  Not  Having  Spar 

or  Awning  Decks. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Steam  Vessels  (in  Salt  Water). 


Percentage  Reserve  Buoyancy  (Winter). 

29.5 

29.8 

30.1 

30.4 

30.8 

31.1 

Corresponding  Height  of  Freeboard  Amidships 

coeiticient  of 

Fineness. 

(Winter). 
Measured  from  Top  of  Deck  at  Side. 

Moulded  Depth  and  Length. 

25    6 

26    0 

26    6 

/     // 

27    0 

27    6 

28    0 

306 

312 

318 

324 

330 

336 

0.68 

5      5i 

5      8 

5     10 

6      0| 

6      3 

6      5 

0.70 

5      6 

5      8i 

5    10* 

6      1 

6      3| 

6      6 

0.72 

5      7 

5        «!J 

5    11| 

6      2 

6      4} 

6      7 

0.74 

5      7J 

5    10 

6      0} 

6      3 

6      5J 

6      8 

0.76 

5      8} 

5    11 

6      1| 

6      4 

6      6| 

6      9 

0.78 

5      9 

5     111 

6      2 

6      4* 

6      7 

6      9} 

0.80 

5     10 

6      0} 

6      3 

6      .V, 

6      8 

6    10J 

0.82 

5     11 

6      1} 

6      4 

6      6| 

6      9 

6    Hi 

Correction  in  ins.  ) 

for  a  change  of  > 

1.3 

1.4 

1.4 

1.4 

1.4 

1.4 

10' in  the  length.  ) 

Deduction  in  ins.  ) 
for  summer         / 
voyages.              ) 

H 

3* 

3J 

4 

4 

4 

Freeboard  Tables 


121 


Table  A.  —  (Continued.) 

Cargo-carrying  Steam  Vessels  Not  Having  Spar 

or  Awning  Decks. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Steam  Vessels  (in  Salt  Water). 


Percentage  Reserve  Buoyancy  (Winter). 

31.3 

31.5 

31.8 

32.0 

32.3 

32.6 

Corresponding  Height  of  Freeboard  Amidships 

(Winter). 

Coefficient  of 
Fineness. 

Measured  from  Top  of  Deck  at  Side. 

Moulded  Depth  and  Length. 

28    6 

29    0 

29    6 

30    0 

30    6 

31    0 

342 

348 

354 

360 

366 

372 

0.63 

6      7 

6      9 

6    11 

7      1| 

7      4 

7      6* 

0.70 

6      8 

6    10* 

7      0* 

7      3 

7      5£ 

7      8 

0.72 

6      9 

6    11) 

7     n 

7      4 

7      6i 

7      9 

0.74 

6    10 

7      Q\ 

7      2* 

7      5 

7      7* 

7    10 

0.76 

6    11 

i    w 

7      3* 

7      6 

7      8* 

7    11 

0.78 

7      0 

7      2\ 

7      5 

7      lh 

7    10 

8      0* 

0.80 

7      1 

7      Zh 

7      6 

7      8h 

7    11 

8      1* 

0.82 

7      2 

7      4* 

7      7 

7      91 

8      0 

8      2i 

Correction  in  ins.  ) 

for  a  change   of  ( 

1.5 

1.5 

1.5 

1.5 

1.5 

1.6 

10' in  the  length.  ) 

Deduction  in  ins.  ) 

for  summer          / 

4 

4} 

4* 

4* 

5 

5 

voyages.                ) 

122 


The  Naval  Constructor 


Table  A. —  {Continued.) 

Cargo-carrying  Steam  Vessels  Not  Having  Spar 

or  Awning  Decks. 


Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  a 

nd  Steel 

Steam  Vessels  (in  Salt  Water). 

Percentage  Reserve  Buoyancy  (Winter). 

32.8 

33.0 

33.3 

33.5 

33.8 

34.0 

Corresponding:  Height  of  Freeboard  Amidships 

Coefficient  of 

Fineness. 

(Winter). 
Measured  from  Top  of  Deck  at  Side. 

Moulded  Depth  and  Length. 

31    6 

32    0 

32    6 

33    0 

33    6 

34    0 

378 

384 

390 

396 

402 

408 

0.68 

7      9 

7    11| 

8      1} 

/      // 

8      4 

8      6* 

8      9 

0.70 

7    10} 

8      1 

8      3 

8      5} 

8      8 

8    10} 

0.72 

7    Hi 

8      2  • 

8      4 

8      6} 

8      9 

8    11} 

0.74 

8      0} 

8      3 

8      5} 

8      8 

8     10} 

9      1 

0.76 

8      1} 

8      4 

8      6} 

8      9 

8     11} 

9      2 

0.78 

8      3 

8      5J 

8      8 

8    10* 

9      1 

9      3} 

0.80 

8      4 

8      6} 

8      9 

8    11} 

9      2 

9      4} 

0.82 

8      5 

8      7} 

8    10 

9      0} 

9      3 

9      5} 

Correction  in  ins.  ) 

for  a  change  of  / 

1.6 

1.6 

1.6 

1.6 

1.7 

1.7 

10' in  the  length.   ) 

• 

Deduction  in  ins.  ) 

for  summer           > 

5 

5 

5} 

5} 

5} 

6 

voyages.                ) 

Freeboard  Tables 


123 


Table  A.  —  {Continued.) 

Cargo-carrying  Steam  Vessels  Not  Having  Spar 

or  Awning  Decks. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Steam  Vessels  (in  Salt  Water). 


Coefficient  of 

Fineness. 

Percentage  Reserve  Buoyancy  (Winter). 

34.2 

34.4 

34.6 

34.7 

34.9 

35.1 

35.3 

35.4 

Corresponding  Height  of  Freeboard  Amidships 
(Winter). 
Measured  from  Top  of  Deck  at  Side. 

Moulded  Depth  and  Length. 

34    6 

35    0 

35    6 

36    0 

36    6 

37    0 

37    6 

/    // 

38    0 

414 

420 

426 

432 

438 

444 

450 

456 

0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 
0.82 

8  Hi 

9  1 
9      2 
9      3* 
9      4* 
9      6 
9      7 
9      8 

9      2 
9      3 
9      4 
9      5* 
9      7* 
9      8 
9      9* 
9    10* 

9      4 
9      5 
9      6* 
9      8 
9      9 
9    10* 
9    n* 
10      1 

9      6 
9      7 
9      8* 
9    10 
9    11 J 
10      0i 
10      2 
10      3J 

9    8* 
9    9* 
9  11 
10    0* 
10    2 
10    3 
10    4* 
10    6 

9  11 
10    0 
10    1* 
10    3 
10    4* 
10    5* 
10    7 
10    8* 

10    \\ 

10    2* 
10    4 
10    5* 
10    7* 
10    8 
10    9* 
10  11 

10    3i 

10    5 
10    6* 
10    8 
10    9* 

10  10* 

11  0 
11     1* 

Correction  in 
ins.     for     a  1 
change  of  10' [ 
in  the  length. 

Deduction    in 
ins.  for 
summer 
voyages. 

1.7 

1.7 

1.7 

1.7 

1.7 

1.7 

1.7 

1.7 

6 

6 

6 

6* 

6* 

6* 

6J 

7 

124 


The  Naval  Constructor 


Table  A. —  (Continued.) 

Cargo-carrying  Steam  Vessels  Not  Having  Spar 

or  Awning  Decks. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Steam  Vessels  (in  Salt  Water). 


Percentage  Reserve  Buoyancy  (Winter) 

35.4 

35.5 

35.6 

35.6 

35.7 

35.7 

35.8 

35.8 

Corresponding  Height  of  Freeboard  Amidships 

Coefficient  op 

Fineness. 

(Winter). 
Measured  from  Top  of  Deck  at  Side. 

Moulded  Depth  and  Length. 

38    6 

39    0 

39    6 

40    0 

40    6 

41    0 

41    6 

42    0 

462 

468 

474 

480 

486 

492 

498 

504 

0.68 

10    5£ 

10    7J 

10    9} 

io  Hi 

11     1} 

11    3i 

11    6 

11    8 

0.70 

10    7 

10    9 

10  11 

n   i 

11    3 

11    5 

11    lh 

11    9* 

0.72 

10    Si 

10  .10* 

11    0* 

11     2J 

11    4! 

11    fij 

11    9 

11  11 

0.74 

10  10 

11    0 

11    2 

11    4 

11    6 

11    8 

11  10* 

12    0i 

0.76 

11  11} 

11    u 

11    3} 

11     5} 

11    7| 

11    9} 

12    0 

12    2 

0.78 

11    (I1. 

11    2i 

11    4* 

11    7 

11    9 

11  11 

12     1J 

12    3J 

0.80 

11     2 

11    4 

11    6 

11    .Si 

11    10.'. 

12    0} 

12    3 

12    5 

0.82 

11    3* 

11    5i 

ii  n 

11  10 

12    0 

12    2} 

12    5 

12    7 

Correction    in 

ins.     for     a  1 
change  of  10'  f 

1.7 

1.7 

1.7 

1.7 

1.7 

1.7 

1.7 

1.7 

in  the  length. 
Deduction    in 

ins.  for 
summer 

7 

7 

7 

7} 

7| 

71 

71 

8 

voyages. 

Freeboard  Tables 


125 


Table  A.  —  (Continued.) 

Cargo-carrying  Steam  Vessels  Not  Having  Spar 

or  Awning  Decks. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Steam  Vessels  (in  Salt  Water). 


Percentage  Reserve  Buoyancy  (Winter). 

35.8 

35.8 

35.8 

35.8 

35.8 

35.8 

35.8 

35.8 

Corresponding  Height  of  Freeboard  Amidships 

Coefficient  of 

Fineness. 

(Winter). 
Measured  from  Top  of  Deck  at  Side. 

Moulded  Depth  and  Length. 

42    6 

43    0 

43    6 

44    0 

44    6 

45    0 

45    6 

46    0 

510 

516 

522 

528 

534 

540 

546 

552 

0.68 

11  10i 

12    0 

12    2 

12    3* 

12    5 

12    7 

12    9 

12  10* 

0.70 

12    0 

12    2 

12    4 

12    5* 

12    7 

12    8i 

12  10£ 

13    0 

0.72 

12    fj 

12    3J 

12    5i 

12    7 

12    8i 

12  10 

13    0 

13    2 

0.74 

12    3 

12    5 

12    7 

12    8} 

12  10 

13    0 

13    2 

13    4 

0.76 

12    4* 

12    6* 

12    8i 

12  10 

13    0 

13    2 

13    4 

13    6 

0.78 

12    6 

12    8 

12  10 

13    0 

13    2 

13    Si 

13    5i 

13    7j 

0.80 

12    7i 

12    9£ 

12  Hi 

13    1} 

13    3* 

13    5 

13    7 

13    9 

0.82 

12    9* 

12  Hi 

13    1" 

13    8| 

13    5* 

13    7 

13    9 

13  10* 

Correction     in 

ins.     for     a  1 
change  of  10'  | 

1.7 

1.7 

1.7 

17 

1.7 

1.7 

1.7 

1.7 

in  the  length.] 

• 

Deduction    in 

ins.  for 
summer 

8 

8 

8 

8| 

8} 

8i 

8| 

9 

voyages. 

126 


The  Naval  Constructor 


Table  A.  —  (Continued.) 

Cargo-carrying  Steam  Vessels  Not  Having  Spar 

or  Awning  Decks. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Steam  Vessels  (in  Salt  Water). 


Percentage  of  Reserve  Buoyancy  (Winter). 

35.8 

35.8 

35.8 

35.8 

35.8 

35.8 

35.8 

35.8 

Corresponding  Height  of  Freeboard  Amidships 

Coefficient  of 
Fineness. 

(Winter). 
Measured  from  Top  of  Deck  at  Side. 

Moulded  Depth  and  Length. 

,     „ 

,     ,, 

,     „ 

t     n 

/     // 

i     // 

/     a 

/     ,, 

46    6 

47    0 

47    6 

48    0 

48    6 

49    0 

49    6 

50    0 

558 

564 

570 

576 

582 

588 

594 

600 

0.68 

13    0 

13     1* 

13    3 

13    5 

13    6* 

13    8 

13    9i 

13  11 

0.70 

13    1J 

13    3 

13    4J 

13    6* 

13    8 

13  10 

13  Hi 

14    1 

0.72 

13    3} 

13    5 

13    6J 

13    .s.J 

13  10 

13  11* 

14    1 

14    3 

0.74 

13    5i 

13    7 

13    8i 

13  10* 

14    0 

14    1* 

14    3 

14    4} 

0.76 

13    1\ 

13    9 

13  10* 

14    0* 

14    2 

14    3* 

14    5 

14    6i 

0.78 

13    9 

13  10£ 

14    0 

14    2 

14    3* 

14    5 

14    6} 

14    8i 

0.80 

13  10* 

14    0 

14    \\ 

14    3* 

14    5 

14    6i 

14    8 

14  10 

0.82 

14    0J 

14    2 

14    3i 

14    5* 

14    7 

14    8i 

14  10 

15    0 

Correction    in 

ins.     for     a  1 
change  of  10' 

1.7 

1.7 

1.7 

1.7 

1.7 

1.7 

1.7 

1.7 

in  the  length. 

" 

Deduction  in 

ins.  for 
summer 

9 

9 

9 

H 

9* 

9J 

9J 

H 

voyages. 

Freeboard  Tables 


127 


Table  B. 
Cargo-carrying  Spar  Deck  Vessels. 

Table  of  Freeboard  to  Spar  Deck  for  First-class  Sea-going  Spar  Deck  Steam 
Vessels  (in  Salt  Water). 


Coefficient  of 

Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Spar  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

13    0 

13    6 

14    0 

14    6 

15    0 

15    6 

240 

246 

252 

258 

264 

270 

0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0  80 
0.82 

5      5 
5      5* 
5      6 
5      6* 
5      7 

5    7* 

5      8 
5      8} 

5      6 
5     H 

5      7 
5      7* 
5      8 
5      8* 
5      9 
5      9* 

5      7 
5      7* 
5      8 
5      8* 
5      9 
5      9* 
5    10 
5    10* 

5      8 
5      8* 
5      9 
5      9* 
5    10 
5    10i 
5    11 
5    Hi 

5      9 
5      9* 
5    10 
5    10* 
5    11 

5  Hi 

6  0 
6      0* 

5    10 
5    10* 
5    11 

5  11* 

6  0 
6      0* 
6      1 
6      1* 

Correction  in  ins.    ) 
for  a  change  of     / 
10'  in  the  length .  ) 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

Deduction  in  ins.   ) 
for  summer           / 
voyages.                ) 

2 

2 

2 

2 

H 

2* 

128 


The  Naval  Constructor 


Table  B.  —  (Continued.) 
Cargo-carrying  Spar  Deck  Vessels. 

Table  of  Freeboard  to  Spar  Deck  for  First-class  Sea-going  Spar  Deck  Steam 
Vessels  (in  Salt  Water). 


Coefficient  of 

Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Spar  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

16    0 

16    6 

17    0 

17    6 

18    0 

18    6 

276 

282 

288 

294 

300 

306 

0.68 
0.70 

0.72 
0.74 
0.76 
0.78 
0.80 
0.82 

5    11 

5  ill 

6  0 
6      0} 
6      1 
6      1} 
6      2 
6      2\ 

/      // 

6      0 
6      0i 
6      1 
6      1| 

6      2 
6      2\ 
6      3 
6      3* 

6      1J 
6      2 
6      2J 
6      3 
6      3h 
6      4 
6      4§ 
6      5 

6      2i 
6      3i 
6      4 
6      4i 
6      5 
6      5h 
6      6 
6      H 

6      4 
6      5 
6      5J 
6      6 
6      6* 
6      7 
6      1\ 
6      8 

6      5| 
6      6* 
6      7 
6      7} 
6      8 
6      8} 
6      9 
6      9£ 

Correction  in  ins.   ) 
for  a  change  of    / 
10' in  the  length.  ) 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

Deduction  in  ins.   ) 
for  summer            > 
voyages.                ) 

2J 

n 

3 

3 

3 

3 

Freeboard  Tables 


129 


Table  B.  —  (Continued.) 
Cargo-carrying  Spar  Deck  Vessels. 

Table  of  Freeboard  to  Spar  Deck  for  First-class  Sea-going  Spar  Deck  Steam 
Vessels  (in  Salt  Water). 


Coefficient  of 

Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Spar  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

19    0 

19    6 

20    0 

20    6 

21    0 

21    6 

312 

318 

324 

330 

336 

342 

0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 
0.82 

6    n 

6      8* 
6      9 
6      9* 
6    10 
6    10* 
6    11 
6    Hi 

6      9 
6    10 
6    10j 

6    11 

6  ll| 

7  0 
7    0* 
7      1 

6  11 

7  0 
7      0* 
7      1 
7     H 
7      2 
7      2* 
7      3 

7      0J 
7      1§ 
7      2 
7      3 
7      3* 
7      4 
7      4* 
7      5 

7      2J 
7      3i 
7      4 
7      5 
7      5* 
7      6 
7      6* 
7      7 

7      4* 
7      5* 
7      6 
7      7 
7      7i 
7      8 
7      8i 
7      9 

Correction  in  ins.    ) 
for  a  change  of     / 
10'  in  the  length.  ) 

1.1 

1.1 

1.1 

1.1 

1.1 

1.2 

Deduction  in  ins.   ) 
for  summer            > 
voyages.                 ; 

3* 

3* 

3* 

4 

4 

4 

130 


The  Naval  Constructor 


Table  B.  —  (Continued.) 
Cargo-carrying  Spar  Deck  Vessels. 


Table  of  Freeboard  i 


Spar  Deck  for  First<lass  Sea-going  Spar  Deck  Steam 
Vessels  (in  Salt  Water). 


Coefficient  of 

Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Spar  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

22    0 

22    6 

23    0 

23    6 

24    0 

24    6 

348 

354 

360 

366 

372 

378 

0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 
0.82 

/      // 

7     7 
7      8 
7      81 
7      91 
7    10 
7    10* 
7    11 
7    11| 

7      9 
7    10 
7    101 

7  Hi 

8  0 
8      01 
8      1 
8      lj 

/      // 

7  111 

8  01 
8      1 
8      2 
8      21 
8      3 
8      31 
8      4 

8      2 
8      3 
8      31 
8      41 
8      5 
8      51 
8      6 
8      7 

i      a 

8      41 
8      51 

8      6 
8      7 
8      71 
8      8 
8      81 
8      91 

8      7 
8      8 
8      81 
8      91 
8    10 
8    11 

8  111 

9  01 

Correction  in  ins.  ) 
for  a  change  of    / 
10'  in  the  length.  ) 

1.2 

1.2 

1.2 

1.2 

1.3 

1.3 

Deduction  in  ins.   ) 
for  summer           / 
voyages.               ) 

41 

41 

41 

5 

5 

5 

Freeboard  Tables 


131 


Table  B.  —  (Continued.) 
Cargo-carrying  Spar  Deck  Vessels. 

Table  of  Freeboard  to  Spar  Deck  for  First-class  Sea-going  Spar  Deck  Steam 
Vessels  (in  Salt  Water). 


Coefficient  o» 

Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Spar  Deck  at  Side. 

Moulded  Depth  (  Main  Deck)  and  Length. 

25    0 

25    6 

26    0 

26    6 

27    0 

27    6 

384 

390 

i 
396 

402 

/ 

408 

414 

0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 
0.82 

8      94 
8    104 

8  11 

9  0 
9      04 
9      l| 
9      2 
9      3 

9      0 
9      1 
9      2 
9      3 
9      3* 
9      4* 
9      5 
9      6 

9      24 
9      34 

9    a 

9      5* 
9      6 
9      7 

9    n 

9      84 

9      54 
9      6} 
9      7* 
9      8} 
9      9 
9    10 
9    104 
9    m 

9      8 
9      9 
9    10 
9    11 
10      0 
10      1 
10     14 
10      24 

9  11 
10    0 
10    1 
10    2 
10    3 
10    4 
10    4J 
10    54 

Correction  in  ins.   ) 
for  a  change  of    / 
10'  in  the  length.  ) 

1.3 

1.3 

1.3 

1.4 

1.4 

1.4 

Deduction  in  ins.   ) 
for  summer           > 
voyages.               ) 

. 

54 

54 

54 

6 

6 

132 


The  Naval  Constructor 


Table  B.  —  (Continued.) 
Cargo-carrying  Spar  Deck  Vessels. 

Table  of  Freeboard  to  Spar  Deck  for  First-class  Sea-going  Spar  Deck  Steam 
Vessels  (in  Salt  Water). 


Coefficient  of 
Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Spar  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

28      0 

28      6 

29      0 

29      6 

30      0 

420 

426 

432 

438 

444 

0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 
0,82 

10      2 
10      3 
10      4 
10      5 
10      6 
10      7 
10      7i 
10      8i 

10      5 
10      6 
10      7 
10      8 
10      9 
10    10 
10    10i 
10    111 

/       // 

10      81 
10      91 
10    101 

10  111 

11  01 
11      11 
11      2 
11      3 

10  111 

11  01 
11      11 
11      21 
11      31 
11      41 
11      51 
11      61 

11      3 
11      4 
11      5 
11      6 
11      7 
11      8 
11      9 
11     10 

Correction  in  ins.  ) 
for  a  change  of  > 
10'in  the  length.  J 

1.4 

1.5 

1.5 

1.5 

1.5 

Deduction  in  ins.  1 
for  summer          > 
voyages.              ; 

6 

6 

61 

61 

61 

Freeboard  Tables 


133 


Table  C. 
Cargo-carrying  Awning  Deck  Vessels. 

Table  of  Freeboard  for  First-class  Sea-going  Awning  Deck  Steam  Vessels 
(in  Salt  Water). 


Coefficient  of 

Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Main  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

8      0 

8      6 

9      0 

9      6 

10      0 

10      6 

96 

102 

108 

114 

120 

126 

0  66 
0  68 
0.70 
0  72 
0  74 
0  76 
0.78 
0.80 

0      1 
0      1 
0      1 
0      li 
0      1J 
0      li 
0      If 
0      2 

0      1 
0      1 
0      1 
0      t| 
0      li 
0      li 
0      li 
0      2 

0      li 
0      li 
0      li 

0      2 
0      2 
0      2 
0      2 
0      2* 

0      li 
0      li 
0      li 
0      2 

0      2 
0      2i 
0      2i 
0      3 

0      2 
0      2 
0      2 
0      2i 
0      2i 
0      2i 
0      2i 
0      3 

0      2 
0      2 
0      2 
0      2| 
0      2i 
0      3 
0      3 
0      3i 

Correction  in  ins.    ) 
for  a  change  of  / 
10'  in  the  length    ) 

0.4 

0.4 

0.4 

0.4 

0.4 

0.5 

Deduction  in  ins.    ) 
for  summer            > 
voyages.                ) 

2 

2 

2 

2 

2 

2. 

134 


The   Naval  Constructor 


Table  C.  —  (Continued.) 
Cargo-carrying  Awning  Deck  Vessels. 

Table  of  Freeboard  for  First-class  Sea-going  Awning  Deck  Steam  Vessels 
(in  Salt  Water). 


Coefficient  of 

Fineness. 

Heioht  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Main  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

11    0 

11    6 

12    0 

12    6 

13    0 

13    6 

132 

138 

/ 
144 

150 

/ 

156 

162 

0.66 
0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 

0      2i 
0      2i 
0      2J 
0      3 
0      3 
0      3 
0      3 
0      3i 

0      2J 

o    -i\ 

0      2i 
0      3 
0      3 
0      3} 
0      3i 
0      4 

0      3 
0      3 
0      3 
0      3} 
0      3J 
0      4 
0      4 
0      4* 

0    3} 

0    3} 
0    3i 
0    4 
0    4 

0    4J 
0    4} 
0    5 

0    4 
0    4 
0    4 
0    4} 
0    4J 
0    5 
0    5 
0    5} 

0    4} 

0    41 
0    4} 
0    5 
0    5 
0    5J 
0    51 
0    6 

Correction  in  ins.  ) 
for  a  change  of  / 
10' in  the  length.  ) 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

Deduction  in  ina.    ) 
for  summer            > 
voyages.               ) 

2 

2 

2 

2 

2 

2 

Freeboard  Tables 


135 


Table  C  —  (Continued.) 
Cargo-carrying  Awning  Deck  Vessels. 

Table  of  Freeboard  for  First-class  Sea-going  Awning  Deck  Steam  Vessels 
(in  Salt  Water). 


Coefficient  of 

Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Main  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

14    0 

14    6 

15    0 

15    6 

16    0 

16    6 

168 

174 

180 

186 

192 

198 

0.66 
0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 

0    5 
0    5 
.0    51 
0    5* 
0    6 
0    6 
0    61 
0    6* 

0    51 
0    5} 
0    6 
0    6 
0    61 
0    61 
0    7 
0    7 

0    6 
0    6 
0    6* 
0    6* 

0    7 
0    7 

o  n 

0    71 

/      // 

0    6* 
0    6* 

0    7 
0    7 
0    71 
0    7* 
0    8 
0    8 

0    7 
0    7 
0    71 
0    8 
0    8 
0    8} 
0    9 
0    9 

0    71 
0    7* 
0    8 
0    81 
0    81 
0    9 
0    91 
0    91 

Correction  in  ins.   ) 
for  a  change  of  £ 
10' in  the  length.   ) 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

Deduction  in  ins.    ) 
for  summer            > 
voyages.                ) 

2 

2 

2 

2 

2 

21 

136 


The  Naval  Constructor 


Table  C  —  (Continued.) 
Cargo-carrying  Awning  Deck  Vessels. 

Table  of  Freeboard  for  First-class  Sea-going  Awning  Deck  Steam  Vessels 
(in  Salt  Water). 


Coefficient  of 

Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Main  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

17    0 

17    6 

18    0 

18    6 

19    0 

19    6 

204 

210 

216 

222 

228 

234 

0  66 
0.68 
0  70 
0  72 
0.74 
0.76 
0.78 
0  80 

0      8} 
0      8§ 
0      9 
0      9i 
0      9i 
0    10 
0     101 
0     10-5 

0      9 
0      9 
0      9i 
0    10 
0    10 
0    10i 
0    11 
0    11 

0    10 
0    10 
0    10| 
0    11 
0    11 

0  iii 

1  0 
1      0 

0    11 
0    11 

0  11} 

1  0 
1      0 
1      0} 
1      1 
1      1 

1    0 
1    0 
1    0} 

1   1 
1   1 
1  11 

1    2 
1    2 

1     1ft 

1     1J 
1    2 
1    2i 
1    2} 
1    3 
1    3} 
1    3£ 

Correction  in  ins.    ) 
for  a  change  of     > 
10' in  the  length.    ) 

0  5 

0  5 

0  5 

0.6 

0.6 

0.6 

Deduction  in  ins.    ) 
for  summer           ? 
voyages.                ) 

2| 

2ft 

2ft 

3 

3 

3 

Freeboard  Tables 


137 


Table  C.  —  (Continued.) 
Cargo-carrying  Awning  Deck  Vessels. 

Table  of  Freeboard  for  First-class  Sea-going  Awning  Deck  Steam  Vessels 
(in  Salt  Water). 


Coefficient  of 

Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Main  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

20    0 

20    6 

21    0 

21    6 

22    0 

22    6 

240 

246 

252 

258 

264 

270 

0.66 
0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 

1    2* 
1    2* 
1    3 
1    3* 
1    8} 
1    4 
1    4* 
1    5 

1    4 
1    4 
1    4* 
1    5 
1    5 
1    5* 
1    6 
1    6} 

1    5 
1    5 
1    bh 
1    6 
1    6 
1    6£ 
1    7 
1    7* 

l   H 

1    6i 
1    7 

l   H 

i  n 

1    8 
1    Sh 
1    9     . 

1  n 

1    7i 
1    8 
1    B| 

1    8i 

1    9 
1    9 
1  10 

1      8i 
1      9 
1      9* 
1     10 
1     10 
1     10* 
1     11 
1    111 

Correction  in  ins.    ) 
for  a  change  of   / 
10' in  the  length.    ) 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

Deduction  in  ins.   ) 
for  summer           / 
voyages.                ) 

Si 

H 

3* 

3* 

4 

4 

138 


The  Naval  Constructor 


Table  C.  —  (Continued.) 

Cargo-carrying  Awning  Deck  Vessels. 

Table  of  Freeboard  for  First-class  Sea-going  Awning  Deck  Steam  Vessels 
(in  Salt  Water). 


Coefficient  or 

Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Main  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

23    0 

23    6 

24    0 

24    6 

25    0 

25    6 

276 

282 

288 

294 

300 

306 

0.66 
0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 

1    10 
1    10* 
1    11 

i   m 

1  nj 

2  0 
2      0} 
2      1 

1  11* 

2  0 
2      0* 
2      1 
2      1 
2      U 
2      2 
2      2* 

2    1 
.    2    U 
2    2 
2    2* 
2    3 
2    3* 
2    4 
2    4* 

2    3 
2    31 
2    4 
2    41 
2    5 
2    51 
2    6 
2    61 

2    41 
2    5 
2    51 
2    6 
2    61 
2    7 
2    71 
2    8 

2    61 

2    7 
2    71 
2    8 
2    81 
2    9 
2    91 
2  10 

Correction  in  ins.  ) 
for  a  change  of  / 
10' in  the  length.  ) 

0.6 

0.6 

0.6 

0.7 

0  7 

0.7 

Deduction  in  ins.  ) 
for  summer          > 
voyages.              ) 

4 

M 

41 

41 

5 

5 

Freeboard  Tables 


139 


Table  C. —  (Continued.) 
Cargo-carrying  Awning  Deck  Vessels. 

Table  of  Freeboard  for  First-class  Sea-going  Awning  Deck  Steam  Vessels 
(in  Salt  Water). 


Coefficient  of 

Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Main  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

26    0 

26    6 

27    0 

27    6 

28    0 

28    6 

312 

318 

324 

330 

336 

342 

0.66 
0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 

2      8 
2      8| 

2      9 

2    n 

2    10 
2    11 

2  11| 

3  0 

2    10 
2    10* 
2    11 

2  m 

3  0 
3      1 
3      U 
3      2 

3    0* 
3    1 
3    U 

3    2 
3    2* 
3    3* 
3    4 
3    4* 

3    2\ 
3    3 
3    3* 
3    4 
3    4* 
3    5* 
3    6 
3    8* 

3    4* 
3    5 
3    5* 
3    6 
3    6* 

3  n 

3    8 
3    6* 

3      6* 
3      7 
3      7* 
3      8 
3      8* 
3      9* 
3     10 
3    10* 

Correction  in  ins.   ) 
for  a  change  of    ? 
10' in  the  length.    ) 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

Deduction  in  ins.   ) 
for  summer           / 
voyages.                ) 

5 

5* 

5* 

5* 

5i 

6 

140 


The  Naval   Constructor 


Table  C  —  (Continued.) 
Cargo-carrying  Awning  Deck  Vessels. 

Table  of  Freeboard  for  First-class  Sea-going  Awning  Deck  Steam  Vessels 
(in  Salt  Water). 


Coefficient  of 
Fineness. 

Height  of  Freeboard  Amidships  (Winter). 
Measured  from  Top  of  Main  Deck  at  Side. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

29    0 

29    6 

... 

30    0 

30    6 

31    0 

31    6 

348 

354 

360 

366 

372 

378 

0.66 
0.68 
0.70 
0.72 
0.74 
0.76 
0.78 
0.80 

3      8} 
3      9 
3      9} 
3    10 
3    10| 

3  Hi 

4  0 
4      0* 

3    10| 
3    11 

3  Hi 

4  0£ 
4      1 
4      2 
4     H 
4      3 

4    0J 
4    1| 

4    2 
4    3 
4    3* 
4    4J 
4    5 
4    5i 

4    3 
4    4 
4    4i 
4    5* 

4    6 

4    7 
4    7i 
4    8 

4      5i 
4      6§ 
4      7 
4      8 
4      8J 
4      9* 
4    10 
4    10J 

4      8 
4      9 
4      9* 
4    10* 

4  11 

5  0 
5      0J 
5      1 

Correction  in  ins.   ) 
for  a  change  of-    / 
10' in  the  length.    ) 

0.7 

0.8 

0.8 

0.8 

0.8 

0.8 

Deduction  in  ins.   ) 
for  summer            > 
voyages.                ) 

6 

6 

6 

6                6 

6* 

Freeboard  Tables 


141 


Table  C.  —  (Continued.) 
Cargo-carrying  Awning  Deck  Vessels. 

Table  of  Freeboard  for  First-class  Sea-going  Awning  Deck  Steam  Vessels 
(in  Salt  Water). 


Height  of  Freeboard  Amidships 

3epth 
from 
A  to 
C. 

(Winter). 
Measured  from  Top  of  Main  Deck  at  Side. 

For  Steamers  above  34'  Moulded  '. 
Deduct  the  Following  Amount 
the  Freeboards  Given   in  Table 
Obtain  the  Freeboards  for  Table 

Coefficient  of 

Fineness. 

Moulded  Depth  (to  Main  Deck)  and  Length. 

32    0 

32    6 

33    0 

33    6 

34    0 

384 

390 

396 

402 

408 

0.66 

4    10* 

5    1 

5    3} 

5      6 

5      8 

3      0 

0.68 

4.    11} 

5    2 

5    4* 

5      7 

5      9 

3      0 

0.70 

5      0 

5    2} 

5    5 

5      7} 

5      9} 

3      1 

0.72 

5      1 

5    3} 

3    6 

5      8} 

5    10} 

3      1 

0.74 

5      1} 

5    4 

5    6} 

5      9 

5    11 

3      2 

0.76 

5      2} 

5    5 

5    7} 

5    10 

6      0 

3      2 

0.78 

5      3 

5    5} 

5    8 

5    10} 

6      0} 

3      3 

0.80 

5      3* 

5    6 

5    8} 

5    11 

6      1} 

3      3 

Correction  in  ins.   ) 

for  a  change  of    £ 

0.8 

0.8 

0.8 

0.8 

0.8 

10'  in  the  length.    ) 

Deduction  in  ins.    ) 

for  summer            / 

6} 

6} 

6} 

6} 

6} 

voyages.                ) 

142 


The  Naval  Constructor 


Table  D. 
Sailing  Vessels. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 

Sailing  Vessels  and  Composite  and  Wood  Vessels  of  the  Highest  Class 

(in  Salt  Water). 


Pebcentage  Reserve  Buoyancy 

Coefficient  or 

(Iron  Vessels). 

21.7 

21.9 

22.1 

22.3 

22.5 

Fineness. 

Corresponding  Height  or  Freeboard 

Amidships. 

Measured  from  Top  of  Deck  at  Side. 

Wood. 

Com- 

Moulded Depth  and  Length. 

,      „ 

/      // 

,      „ 

/      // 

,      „ 

posite. 

5      6 

6      0 

6      6 

7      0 

7      6 

55 

60 

65 

70 

75 

0.64 

0      Si 

0      9i 

0    10i 

0    Hi 

1    Oi 

0.64 

0.66 

0      8i 

0      9i 

0    10i 

0    Hi 

1    0i 

0.66 

0.68 

0      9 

0    10 

0    11 

1      0 

1     1 

0.64 

0.68 

0.70 

0      9 

0     10 

0    11 

1      0 

1     1 

0.66 

0.70 

0.72 

0      lij 

0    10i 

o  Hi 

1      0i 

1    li 

0.68 

0.72 

0.74 

0      9i 

0    10i 

0    Hi 

1      0i 

l    li 

0.70 

0.74 

0    10 

0    11 

1      0 

1    1 

1    2 

0.72 

0    10 

0    11 

1      0 

1     1 

1    2 

Correctio 

l   in   ins. 

for    a  ) 

change 

of    10'    ii 

i    the  > 

0.8 

0.8 

0.8 

0.8 

0.8 

length. 

) 

Freeboard  Tables 


143 


Table  D.  —  (Continued.) 
Sailing  Vessels. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 

Sailing  Vessels  and  Composite  and  Wood  Vessels  of  the  Highest  Class 

(in  Salt  Water). 


Percentage  Reserve  Buoyancy 
(Iron  Vessels). 

Coefficient  of 

Fineness. 

22.7 

22.9 

23.1 

23.3 

23  5 

Corresponding  Height  of  Freeboard 

Amidships. 

Measured  from  Top  of  Deck  at  Side. 

Wood. 

Com- 
posite. 

Iron. 

Moulded  Depth  and  Length. 

8      0 

/      // 
8      6 

9      0 

9      6 

10    0 

80 

85 

90 

95 

100 

0.64 
0.66 

0.68 
0.70 
0.72 

0.64 
0.66 
0.68 
0.70 
0.72 
0.74 

0.64 
0.66 
0.68 
0.70 
0.72 
0.74 

l    \\ 
i    U 

1    2 
1    2 
1    2\ 
1    2* 
1    3 
1    3 

1    2J 
1    2i 
1    3 
1    3 
1    Z\ 
1    3* 
1    4 
1    4 

1    3* 
1    3J 
1    4 
1    4 
1    4J 
1    4J 
1    5 
1    5 

1    4J 
1    4J 

1    5 
1    5 
1    5} 
1    5* 
1    6 
1    6 

1    5* 
1    5i 
1    6 
1    6 
1    6J 
1    « 
1    7 
1    7 

Correction    in    ins.    for    a   ) 
change    of    10'    in    the   ? 
length.                                 ) 

0.8 

0.9 

0.9 

0.9 

0.9 

144 


The  Naval   Constructor 


Table  D.  —  (Continued.) 

Sailing  Vessels. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 

Sailing  Vessels  and  Composite  and  Wood  Vessels  of  the  Highest  Class 

(in  Salt  Water). 


Percentage  Reserve  Buoyancy 

Coefficient  of 

(Iron  Vessels). 

23.7 

23.9 

24.2 

24.4 

24.6 

] 

Fineness. 

Corresponding  Height  of  Freeboard 

Amidships. 

Measured  from  Top  of  Deck  at  Side. 

Wood. 

Com- 
posite. 

Iron. 

Moulded  Depth  and  Length. 

10    6 

11    0 

11    6 

12    0 

12    6 

105 

110 

115 

120 

125 

0.64 

1    6* 

1      7* 

1      9 

1     10* 

1     11* 

0.64 

0.66 

1    6* 

i    n 

1      9 

1     10* 

2      0 

0.66 

0.68 

1    7 

1      8 

1      9* 

1     11 

2      0* 

0.64 

0.68 

0.70 

1    7 

1      8* 

1     10 

1     11* 

2      1 

0.66 

0.70 

0.72 

i  n 

1      9 

1     10* 

2      0 

2      1* 

0.68 

0.72 

0.74 

i  « 

1      9 

1    10* 

2      0 

2      1* 

0.70 

0.74 

1    8 

1      9* 

1     11 

2      0* 

2      2 

0.72 

1    8* 

1     10 

1     11* 

2      1 

2      2* 

Correctio 

i    in  ins. 

for    a   ) 

change 

of    10'    ii 

i    the   > 

0.9 

0.9 

1.0 

1.0 

1.0 

length. 

> 

Freeboard  Tables 


145 


Table  D.  —  (Continued.) 

Sailing  Vessels. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 

Sailing  Vessels  and  Composite  and  Wood  Vessels  of  the  Highest  Class 

(in  Salt  Water). 


Coefficient  of 

Fineness. 


Wood. 

Com- 

posite. 

0.64 

0.66 

0.64 

0.68 

0.66 

0.70 

0.68 

0.72 

0.70 

0.74 

0.72     . 

Iron. 


0.64 
0.66 
0.68 
0.70 
0.72 
0.74 


Correction  in  ina.  for  a 
change  of  10'  in  the 
length. 


Percentage  Reserve  Buoyancy 
(Iron  Vessels). 


24.9  25.1  25.3  25.5  25.7 


Corresponding  Height  of  Freeboard 

Amidships. 

Measured  from  Top  of  Deck  at  Side. 


Moulded  Depth  and  Length. 


130 


1.0 


13    6 


14    6 


15    0 


150 


2  8* 

2  9 

2  9| 

2  10 


146 


The  Naval   Constructor 


Table  D.  —  (Continued.) 

Sailing  Vessels. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 

Sailing  Vessels  and  Composite  and  Wood  Vessels  of  the  Highest  Class 

(in  Salt  Water). 


Percentage  Reserve  Buoyancy 

(Iron  Vessels). 

Coefficient  of 

26.0 

26.2 

26.4 

26.6 

26.8 

Fineness. 

Corresponding  Height  of  Freeboard 

Amidships. 

Measured  from  Top  of  Deck  at  Side. 

Wood. 

Com- 

Moulded Depth  and  Length. 

,     „ 

,     „ 

,     „ 

,  ;, 

posite. 

15    6 

16    0 

16    6 

17    0 

17    6 

155 

160 

165 

170 

175 

0  64 

,      „ 

,      „ 

,      „ 

,      „ 

,     „ 

0.64 
0  66 

0.66 
0  68 

2      8 

2      81 

2      91 
2    10 

2    11 
2    111 

3    01 
3    1 

3    2 
3    21 

0.64 

0.63 

0.70 

2      9 

2    101 

3      0 

3    H 

3    3 

0.66 

0.70 

0.72 

2      91 

2    11 

3      01 

3    2 

3    31 

0.68 

0.72 

0.74 

2    10 

2    11 

3      1 

3    21 

3    4 

0.70 

0.74 

2    101 

3      0 

3      11 

3    3 

3    41 

0.72 

2    11 

3      01 

3      2 

3    31 

3    5 

2    llj 

3      1 

3      21 

3    4 

.3    51 

Correction    in    ins. 

for   a   ) 

change    of    10'    ii 

i    the  / 

1.1 

1.1 

1.1 

1.1 

1.1 

length 

'1 

Freeboard  Tables 


147 


Table  D. —  (Continued.) 
Sailing  Vessels. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 

Sailing  Vessels  and  Composite  and  Wood  Vessels  of  the  Highest  Class 

{in  Salt  Water). 


Percentage  Reserve  Buoyancy 
(Iron  Vessels). 

Coefficient  of 

Fineness. 

27.1 

27.3 

27.4 

27.5 

27.6 

Corresponding  Height  of  Freeboard 

Amidships. 

Measured  from  Top  of  Deck  at  Side. 

Com- 
posite. 

Iron. 

Moulded  Depth  and  Length. 

Wood. 

18    0 

18    6 

19    0 

19    6 

20    0 

180 

185 

190 

195 

200 

0.64 
0.66 
0.68 
0.70 
0.72 

0.64 
0.66 
0.68 
0.70 
0.72 
0.74 

0.64 
0.66 
0.68 
0.70 
0.72 
0.74 

3    3* 
3    4 
3    4} 
3    5 
3    5£ 
3    6 
3    6£ 
3    7 

3    5 
3    5| 
3    6 
3    6| 
3    7} 
3    8 
3    8£ 
3    9 

3      6* 
3      7 
3      7* 
3      8 
3      9 
3      % 
3     10 
3    10* 

3      8 
3      8* 
3      9 
3      9| 
3    10£ 
3     11 

3  in 

4  0 

3      9* 
3    10 
3    10i 

3  11 

4  0 
4      0J 
4      1 
4      li 

Correction    in    ins.    for    a   ) 
change    of    10'    in    the   ? 
length.                                 ) 

1.1 

1.1 

1.2 

1.2 

1.2 

148 


The  Naval   Constructor 


Table  D.  —  (Continued.) 
Sailing  Vessels. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 

Sailing  Vessels  and  Composite  and  Wood  Vessels  of  the  Highest  Class 

(in  Salt  Waief). 


Percentage  Reserve  Buoyancy 

Coefficient  of 

(Iron  Vessels). 

27.7 

27.9 

28.0 

28.2 

28.3 

Fineness. 

Corresponding  Height  of  Freeboard 

Amidships. 

Measured  from  Top  of  Deck  at  Side. 

Wood. 

Com- 
posite. 

Iron. 

Moulded  Depth  and  Length. 

20    6 

21    0 

21    6 

22    0 

22    6 

205 

210 

215 

220 

225 

0.64 

3    11 

.  4    0i 

4    2 

4    3} 

4      5 

0.64 

0.66 

3    11} 

4    1 

4    3 

4    4} 

4      6 

0.66 

0.68 

4      0 

4  n 

4    3} 

4    5 

4      6} 

0.64 

0.68 

0.70 

4      0} 

4    2 

4    4 

4    .li 

4      7 

0.66 

0.70 

0.72 

4      1* 

4    3 

4    5 

4    6* 

4      8 

0.68 

0.72 

0.74 

4      2 

4    3} 

4    5i 

4    7 

4      8i 

0.70 

0.74 

4      2} 

4    4i 

4    6 

4    8 

4      9} 

0.72 

4      3 

4    5 

4    7 

4    8| 

4    10 

Correction    in    ins. 

for   a   ) 

change    of    10'    ii 

i    the  > 

1.2 

1.2 

1.2 

1.2 

1.2 

length. 

> 

Freeboard  Tables 


149 


Table  D.  —  (Continued.) 
Sailing  Vessels. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 

Sailing  Vessels  and  Composite  and  Wood  Vessels  of  the  Highest  Class 

(in  Salt  Water). 


Percentage  Reserve  Buoyancy 
(Iron  Vessels). 

Coefficient  of 

Fineness. 

28.5 

28.6 

28.8 

28.9 

29.1 

Corresponding  Height  of  Freeboard 

Amidships. 

Measured  from  Top  of  Deck  at  Side. 

Com- 
posite. 

Iron. 

Moulded  Depth  and  Length. 

Wood. 

23    0 

23    6 

24    0 

24    6 

25    0 

230 

235 

240 

245 

250 

0.64 
0.66 
0.68 

0.70 
0.72 

0.64 
0.66 
0.68 
0.70 
0.72 
0.74 

0.64 
0.66 
0.68 
0.70 
0.72 
0.74 

4      6* 
4      71 
4      8 
4      81 
4      91 
4    10 

4  11 

5  0 

4      8 
4      9 
4      91 
4    10 
4    11 

4  111 

5  01 
5      11 

4    10 
4    101 

4  111 

5  0 
5      1 
5      11 
5      21 
5      31 

4  111 

5  0 
5      1 
5     H 
5      21 
5      3 
5      4 
5      5 

/      a 

5    11 
5    2 
5    3 
5    31 
5    41 
5    5 
5    6 
5    7 

Correction    in    ins.    for   a   ) 
change    of    10'    in    the  £ 
length.                                 ) 

1.3 

1.3 

1.3 

1.3 

1.3 

150 


The  Naval  Constructor 


Table  D.  —  (Continued.) 

Sailing  Vessels. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 

Sailing  Vessels  and  Composite  and  Wood  Vessels  of  the  Highest  Class 

(in  Salt  Water). 


Percentage  Reserve  Buoyanct 

Coefficient  of 

(Iron  Vessels). 

29.2 

29.4 

29.5 

29.7 

Fineness. 

Corresponding:  Height  of  Freeboard 

Amidships. 

Measured  from  Top  of  Deck  at  Side. 

Wood. 

Com- 

Moulded Depth  and  Length. 

,     „ 

,       „ 

.     „ 

,     „ 

posite. 

25    6 

26      0 

26    6 

27    0 

255 

260 

265 

270 

0.64 

5      3 

5      5 

5      61 

5      81 

0.64 

0.66 

5      3J 

5      51 

5      71 

5      91 

0.66 

0.68 

5      4J 

5      6f 

5      81 

5    101 

0.64 

0.68 

0.70 

5      5 

5      7 

5      9 

5    11 

0.66 

0.70 

0.72 

5      6 

5      8 

5    10 

6      0 

0.68 

0.72 

0.74 

5      61 

5      81 

5    10* 

6      01 

0.70 

0.74 

5      71 

5      91 

5    111 

6      U 

0.72 

5      81 

5    101 

6      01 

6      21 

Correctioi 

l    in     ins. 

for    a   ) 

change 

of     10'    i 

n    the   / 

1.3 

1.3 

1.3 

1.4 

length. 

) 

Freeboard  Tables 


151 


Table  D.  —  (Continued.) 
Sailing  Vessels. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Sailing  Vessels  (in  Salt  Water). 


Coefficient  of 
Fineness. 

Percentage  Reserve  Buoyancy. 

29.8 

30.0 

30.2 

30.4 

Corresponding  Height  of  Freeboard 

Amidships. 

Measured  from  Top  of  Deck  at  Side. 

Iron. 

Moulded  Depth  and  Length. 

27      6 

28      0 

28      6 

29      0 

275 

280 

285 

290 

0.64 
0.66 
0.68 
0.70 
0.72 
0.74 
0.76 

5      101 

5  111 

6  01 
6        1 
6        21 
6        31 

6        01 
6        11 
6        2 
6        3 
6        41 
6        51 

6        2 
6        3 
6        4 
6        5 
6        6 
6        7 

6        4 
6        5 
6        6 

6        7 
6        8 
6        9 

Correction  in  ins.  for  a  ) 
change   of    10'    in  the  / 
length.                              ) 

1.4 

1.4 

1.4 

1.4 

152 


The  Naval  Constructor 


Table.  D.  —  (Continued.) 
Sailing  Vessels. 

Table  of  Reserve  Buoyancy  and  Freeboard  for  First-class  Sea-going  Iron  and  Steel 
Sailing  Vessels  (in  Salt  Water). 


Coefficient  of 
Fineness. 

Percentage  Reserve  Bdoyanct. 

30.6 

30.8 

31.1 

31.4 

Corresponding  Height  of  Freeboard 
Amidshdts. 
Measured  from  Top  of  Deck  at  Side. 

Iron. 

Moulded  Depth  and  Length. 

29      6 

30      0 

30      6 

31      0 

295 

300 

305 

310 

0.64 
0.66 
0.68 
0.70 
0.72 
0.74 
0.76 

6        6 
6        7 
6        8 
6        9 
6        9* 
6      10 
6      11 

6        8 
6        9 
6      10 
6      U 

6  111 

7  0 
7        1 

6      10 

6  11 

7  0 
7        1 
7        U 
7       2 
7       3 

/        // 

7       0 

7       2 
7       3 
7       31 
7       4 
7       5 

Correction   in  ins.   for  a  ) 
change   of    10'   in  the  / 
length.                             ) 

1.4 

1.5 

1.5 

1.5 

Kirk's  Analysis  153 


CHAPTER  V. 

KIRK'S   ANALYSIS. 

{Trans.  Inst,  of  Nav.  Arch.) 

The  following  was  the  method  adopted,  and  here  I  may  premise 
that  for  ordinary  purposes  I  assumed  that  the  length  of  entrance 
and  run  were  equal  —  in  fact  I  contented  myself  by  finding  the 
mean  of  the  lengths  and  angles  of  entrance  and  run  —  but  the 
method  is  equally  applicable  to  finding  them  separately  when 
greater  accuracy  is  required. 

I  shall  now  give  the  process  for  finding  the  mean  length  and 
angle  of  entrance  and  run. 

Construct  a  block  ship  having  the  same  displacement,  mean 
draught,  and  area  of  midship  section  as  the  ship  under  considera- 
tion, but  with  rectangular  sections,  parallel  middle  body  (if  neces- 
sary) and  straight-sided  wedge-shaped  ends.  Fig.  34  shows  by  the 
curved  line  IBK  the  midship  section  of  the  actual  ship,  and  by  the 
rectangle  CLME  the  midship  section  of  the  block  ship,  both  sec- 
tions being  equal  in  area  and  depth,  having  a  common  water  line 
IK.  The  depth  AB  is  the  mean  draught  of  the  ship.  Fig.  35 
represents  the  block  ship,  and  ABDG  is  the  half-breadth  plan, 
the  sides  being  vertical,  the  transverse  sections  all  rectangular,  and 
the  keel  parallel  to  the  water  line.  The  sides  CD  and  EF  which 
form  the  middle  body,  are  parallel  to  the  keel  (or  to  the  centre 
line  AB),  and  the  half-breadth  GC  or  LTD  is  equal  to  AC,  Fig. 
34,  the  half-breadth  of  the  equivalent  rectangular  midship  section 
(which  is  in  fact  the  midship  section  of  the  block  ship),  EL  being 
also  equal  to  AB.  The  angles  CA  G  and  DBH  are  equal,  and  while 
the  length  AB  is  equal  to  the  length  of  the  ship,  the  length  A  G  or 
HB  of  equal  wedges  which  form  the  ends  is  such  that  the  area  of 
the  figure  ACDBFE  multiplied  by  the  mean  depth  AB,  is  equal 
to  the  volume  of  the  displacement  of  the  actual  ship. 

Complete  the  rectangle  COPE  as  in  the  dotted  lines.  It  is 
obvious  that  the  rectangular  solid  COPELQ  is  equal  in  volume  to 
that  of  the  block  ship,  in  fact  to  the  volume  of  the  displacement  of 
the  actual  ship,  and  that  the  length 

-,-,.-    .    ,  Displacement  in  cubic  feet 

GB  in  feet  = * . -— , 

Area  of  midship  section  in  square  feet 

and  the  mean  length  of  entrance  and  run 

An     i       tu    m  vi        Displacement 

AG  —  length  of  ship  —  „.  ,  .  . » 

Midship  area 


154 


The  Naval  Constructor 


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Kirk's  Analysis 


155 


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156 


The  Naval  Constructor 


also, 


The  breadth  CE  = 


Area  midship  section 

Mean  draught  (ex.  keel) 

and  the  tangent  of  the  mean  half-       >\t 

angle  of  entrance  and  run, 

—- & 

Thus  from  the  length,  breadth, 
draught,  area  of  midship  section, 
and  displacement,  the  mean 
length  of  entrance  and  run  and 
the  mean  angle  can  be  got.  There 
are  other  methods  of  working  this 
out,  which  will  occur  to  any  one, 
but  the  method  given  is  perhaps 
the  simplest. 

In  order  to  get  the  length  and 
angle  of  entrance  and  run  sepa- 
rately (instead  of  the    mean  as 
stated),  it  is  necessary  to  have  in 
addition,  the  displacement  in  two 
portions,  one  forward  of  the  mid- 
ship section,  and  one  aft,  the  dis-     „ 
tance  of  the  midship  section  from    « 
one  end  of  the  ship,  and  the  mean     I 
draught  of  each  of  these  portions ;     : 
treating  them,   in  fact,   as  two 
separate  ships,  one  of  which  has 
no  run  and  one  no  entrance. 

In  my  earlier  attempts  I  re- 
tained the  actual  breadth  of  the 
ship  as  the  breadth  of  the  block 
ship,  and  varied  the  depth,  but 
I  prefer  the  plan  before  given  of 
using  for  the  block  ship  the  mean 
draught  of  the  actual  ship.  In 
ships  with  extremely  raking 
sterns  or  stern  posts,  I  take  the 
length  at  half  depth  when  that 
can  be  got  (or  the  mean  length) 
as  the  length  of  the  block  ship. 
In  single  screw  steamers,  I  take 
the  length  to  the  forward  stern 
post. 

The  block  ship  will  often  be 
found  of  use  in  forming  first  or 


/  I 

m     Ip 

\ 

\  ~ 

\      1      / 

A    i    / 

Wetted  Surface  157 


ipproximate  designs,  and  in  this  view  it  may  be  interesting  to 
joinpare  the  wetted  skin  surface  of  actual  ships  with  that  of  the 
squivalent  block  ships,  this  being  an  important  element  in  speed 
:alculations  and  otherwise. 

In  the  foregoing  table  I  have  selected  fourteen  ships  of  very 
liverse  types,  giving  their  dimensions,  block  models,  actual 
vetted  surface  (exclusive  of  that  of  keels  or  rudder),  and  wetted 
lurface  of  block  ship,  and  the  ratio  of  one  to  the  other. 

From  this  it  will  be  seen  that  in  first  approximations  in  compar- 
ng  one  ship  with  another  we  shall  not  commit  a  grievous  error 
n  using  the  surface  of  the  block  ship,  and  also  that  a  very  close 
ipproximation  indeed  may  be  made  to  the  actual  wetted  surface 
>y  multiplying  the  surface  of  the  block  ship  by  one  of  the  coeffi- 
ients  in  the  table,  according  to  the  type  of  the  ship.  In  the 
econd  column  SS  means  single  screw,  TS  means  twin  screw,  and 
°  paddle.  In  No.  10  I  ought  to  explain,  that  not  only  was  the 
udder  of  exceptional  breadth,  part  of  which,  to  make  the  com- 
>arison  with  the  others  more  even,  has  been  included,  but  there 
pas  a  peculiar  overhanging  portion  under  water  near  the  top  of 
he  stern  post,  by  which  the  mean  length  taken  for  the  block  ship 
xceeds  that  of  the  actual  ship  between  perpendiculars. 

To  show  more  clearly  the  relation  of  the  block  model  to  that  of 
he  actual  ship,  I  have  selected  No.  4  in  the  table,  as  being  a  fair 
xample  of  a  merchant  mail  steamer  of  considerable  speed,  and  in 
•Mg.  36  I  have  given  the  curve  of  areas  of  transverse  sections ;  and 
have  put  it  in  this  form  that  the  ordinates  are  equal  to  the  half 
reas  of  the  corresponding  transverse  sections  divided  by  the 
.raught  of  water  (less  depth  of  keel)  at  the  several  sections. 
?his  is  in  fact  the  curve  of  form,  or  fineness  of  model. 

Above  this  I  have  drawn  the  half-breadth  plan  of  the  block 
hip,  the  length,  breadth,  and  area  of  this  being  of  course  equal  to 
hose  of  the  curve,  and  the  length  and  angle  of  entrance  and  run 
i  mean  of  those  of  the  actual  curve  of  form. 

Wetted  Surface  Formula. 

W.S.=Lx(~+dr)xc. 


(!+* 


Vhere  W.S.  =  wetted  surface  of  hull  proper  in  square  feet,  ex- 
cluding bossing,  rudder,  bar  keel,  etc. 

L  —  length  on  load  water  line. 

B  =  extreme  breadth. 

dr  =  extreme  draught  in  flat  plate  keel  vessels,  and 
draught  corrected  to  fiat  plate  keel  conditions  in 
bar  keel  vessels. 

c  =  constant  from  the  following  table  : 


158 


The  Naval  Constructor 


Ratio  of 

#  =5.00 
dr 

3.33 

2.50 

2.00 

1.667 

Block  Co- 
efficient. 

■\ 

ralues  of  "c 

.40 

1.120 

1.130 

1.158 

1.180 

1.200 

.45 

1.167 

1.184 

1.211 

1.240 

1.260 

.60 

1.215 

1.238 

1.270 

1.300 

1.320 

.55 

1.272 

1.299 

1.330 

1.360 

1.380 

.60 

1.330 

1.360 

1.390 

1.420 

1.440 

.65 

1.397 

1.427 

1.456 

1.480 

1.500 

.70 

1.465 

1.494 

1.522 

1.541 

1.560 

.75 

1.542 

1.565 

1.588 

1.604 

1.620 

.80 

1.620 

1.637 

1.655 

1.668 

1.680 

.85 

1.708 

1.715 

1.724 

1.733 

1.740 

"Wetted  Surface  (Taylor's  Formula). 

W.S.  =c  V-Dx^- 
where  W.S.  =  wetted  surface  in  square  feet,  excluding  rudde 

bossing,  etc.: 
D  =  displacement  in  tons  of  35  cubic  feet. 
L  =  mean  immersed  length. 
B  =  breadth  extreme. 
H  =  draught  of  water,  extreme  in  flat  plate  keel  vessel 

and  corrected  to  flat  plate  keel  conditions  in  b 

keel  vessels. 
c  =  constant  found  from  the  following  table  : 


Ratio  -=• 

Constant  "c." 

Ratio  ■==• 

H 

Constant  "c." 

2.0 

15.63 

2.8 

15.55 

2.1 

15.58 

2.9 

15.58 

2.2 

15.54 

3.0 

15.62 

2.3 

15.51 

3.1 

15.66 

2.4 

15.50 

3.2 

15.71 

2.5 

15.50 

3.3 

15.77 

2.6 

15.51 

3.4 

15.83 

2.7 

15.53 

3.5 

15.89 

Note.  —  This  formula  becomes  unreliable  when  the  block  coefficient 
beyond  the  limits  of  .45  and  .75,  or  when  the  ratio  of  —  is  outside  the  limi 
given  in  the  table. 


Launchi 


ing 


159 


CHAPTER   VI. 

LAUNCHING* 

The  form  of  ways  for  ordinary  merchant  ships  is  of  compara- 
tively little  importance  ;  but  in  special  cases,  such  as  armored  war 
vessels  or  long,  light  river  boats,  if  there  is  too  little  water  on  the 
way  ends,  the  vessel  is  liable  to  tilt  as  soon  as  her  C.G.  gets  over 
the  way  ends,  and  being  as  it  were  pivoted  at  this  point,  a  great 
pressure  is  put  upon  the  bottom  of  the  vessel,  causing  undue  local 
strains,  which  might  possibly  force  in  the  bottom  plating,  frames, 
etc.,  in  those  vessels  which  are  not  so  strongly  constructed  as  ordi- 
nary merchant  vessels,  or  the  ways  might  collapse  here  and  then 

1-     COMMENCEMENT  OF  1ST  PERIOD 

2.    CHANGE  BETWEEN  1ST*&  2N°  PERIODS 

3-    END  OF  2nd  pER|OD 


267  250     210  200 

Fig.  36. 

the  vessel  would  be  left  to  slide  off  the  remaining  distance  on  her 
keel.  To  guard  against  this  danger,  it  is  desirable  to  ascertain  by 
calculations  and  diagrams  if  the  form  of  the  ways  is  such  that  the 
vessel  may  be  launched  without  fear  of  tilting. 

The  time  that  a  vessel  takes  to  travel  down  the  ways  may  be 
divided  into  two  periods  —  the  first  lasts  while  she  rests  entirely 

*  Paper  by  H.  G.  Gannaway,  Trans.  E.  Coast,  Eng.,  and  Shipb'd,  1887. 


160  The  Naval  Constructor 


on  the  ways,  and  the  second,  when  the  stern  is  afloat  and  the  fore 
end  of  the  ship  is  bearing  on  the  fore  end  of  the  sliding  ways. 

A  base  line  is  first  drawn,  the  measurements  along  which  repre- 
sent distances  travelled  by  the  ship  down  the  ways,  the  total 
length  in  this  case  being  267  feet.  The  line  AA  drawn  parallel 
to  the  base  represents  the  moment  of  the  ship  about  the  fore 
end  of  the  sliding  ways.  In  this  example  the  ship's  weight  is 
865  tons,  which  being  multiplied  by  97.2  feet,  the  distance  of  the 
C.G.  of  the  ship  from  the  fore  end  of  the  sliding  ways,  =  84,121 
foot-tons.  The  buoyancy  moments  about  the  same  point  are  rep- 
resented by  curve  B.  The  position  of  intersection  of  this  curve 
with  the  line  A  A  will  indicate  where  the  vessel  will  be  when  her 
stern  commences  to  float  aft.  At  this  point  the  first  period  ends 
and  the  second  commences,  which  in  the  example  is  when  the 
vessel  has  travelled  208'  6"  down  the  ways.  Although  this  is  the 
point  where  the  moments  of  buoyancy  and  weight  about  the  fore 
end  of  sliding  ways  become  equal,  the  vessel's  stern  does  not 
actually  lift  until  she  has  .moved  a  few  feet  beyond  this,  because 
an  additional  amount  of  displacement  is  required  to  overcome  the 
vertical  component  of  the  ship's  momentum. 

Observations  of  the  dip  of  the  vessel's  keel  have  proved  that 
this  additional  displacement  is  so  trifling  that  a  complete  investi- 
gation of  its  amount  is  unnecessary  for  ordinary  purposes. 

The  displacement  of  the  vessel  throughout  the  first  period  is 
shown  by  curve  D1,  and  for  the  second  period  by  curve  JD2.  Dur- 
ing the  second  period,  the  after  end  of  the  vessel  being  afloat,  and 
the  fore  end  resting  on  the  sliding  ways,  it  is  evident  that  the 
buoyancy  moment  about  that  point  will  remain  the  same  as  the 
weight  moment  all  throughout  this  period.  The  displacement,  of 
course,  increases  as  the  vessel  moves  down  the  ways,  but  the 
gradual  lifting  of  the  stern  and  lowering  of  the  bows  brings  the 
C.B.  further  forward,  and  so  reduces  the  leverage  while  the  dis- 
placement is  increasing,  thus  retaining  practically  a  constant  mo- 
ment. The  distance  that  the  line  CG  is  above  the  base,  represents 
the  weight  of  the  ship,  the  weight  on  the  fore  end  of  the  sliding 
ways  being  proportional  to  the  distance  between  this  line  and 
curve  of  displacement  D2.  This  weight  is  225  tons  at  the  begin- 
ning of  the  period,  and  is  reduced  to  115  tons  at  the  end.  It  is 
important,  therefore,  that  the  fore  end  of  the  cradle  should  be 
made  sufficiently  strong  to  carry  the  load  which  is  thus  put  upon 
it.  It  will  be  seen  then  that  it  is  desirable  to  reduce  the  duration 
of  the  second  period  as  much  as  practicable,  for,  since  the  longer 
it  is,  the  greater  the  weight  will  be  on  the  fore  end  of  the  sliding 
ways,  which  in  the  case  of  heavy  vessels  renders  them  liable  to 
come  down  to  the  ground  and  damage  their  fore  ends. 

In  considering  the  subject  of  tipping,  we  take  the  moments 


Launching 


161 


rat  the  end  of  the  standing  ways,  and  as  long  as  the  buoyancy 
ment  remains  in  excess  of  the  weight  moment  about  this  point, 
re  is  no  fear  of  the  vessel  tipping  ;  but  if  in  any  position  the 
mer  moment  falls  short  of  the  latter,  it  is  evident  that  in  order 
restore  equilibrium,  the  stern  will  drop,  and  thus  increase  the 
placement  until  both  moments  are  equal.  Tipping,  if  occurring 
ill,  must  take  place  after  the  C.G.  of  the  ship  has  passed  the 
1  of  the  standing  ways,  and  before  the  commencement  of  the 
ond  period.     In  the  example,  the  C.G.  of  the  ship  has  passed 


B 
FTTON8 

E 
PTTON8 

0 
TONS. 

*\^ 

A 

80,000 

16,000 

800 

V^8 

1 





E^-"" 

--^D 

10,000 

2,000 

100 

Fig.  37. 


cjjAT  WAYEND8 


way  ends  when  she  has  moved  174  feet.  From  about  that 
nt  to  a  little  beyond  the  end  of  the  first  period,  the  buoyancy 
L  weight  moments  about  the  end  of  the  standing  ways  are  cal- 
led at  several  intervals,  and  at  each  interval  the  latter  moment, 
ng  deducted  from  the  former,  gives  the  moments  against  tip- 
g.  These  moments  are  shown  by  curve  E.  If  this  curve  at 
-  part  were  to  run  below  the  base  line,  it  would  show  that  the 
sel  will  tilt.  The  point  where  this  curve  is  nearest  to  the  base 
)  gives  the  position  of  the  vessel  when  she  has  least  longitudi- 

stability,  which  in  this  case  is  when  the  vessel  has  travelled 
ra  the  ways  189  feet,  the  minimum  margin  against  tipping  be- 

9,700  foot-tons. 

t  is  desirable  that  the  margin  be  not  too  small  for  uncertain 
sels ;  where  this  was  the  case  they  actually  did  tilt  slightly, 
ch  shows  that  a  moderate  margin  is  required  in  calculation  to 
>w  for  the  error  introduced  by  treating,  as  it  is  convenient  to 
in  practice,  those  moments  statically  instead  of  dynamically, 
calculating  the  buoyancy  moments  no  account  is  taken  of  the 
lie,  which  would  only  alter  the  results  slightly  ;  the  variations 
lg  on  the  right  side,  may  be  safely  ignored.     Besides,  the  after 


162 


The  Naval  Constructor 


Table  of 


INDEX   LETTER. 

A 

B 

c 

D 

sT.- 

s23 

Description  • 

«x 

fa 

2x 

3* 

of  Vessel  and  Moulded  Dimen- 

£8 

CG  W 

a  3 

&$ 

sions  in  Feet. 

^x 

£>< 

*x 

i*x 

ccb 

W^ 

|i 

oo 

(iv 

H" 

02 

Declivity  of  keel  per  foot  .     . 

9  It 

TJ 

8  // 

TS 

8    ft 

T~5 

8  // 

IS 

Declivity  of  standing  ways  per 

foot 

8     to   18 
Iff  lo  IS 

A  toil 

8     fnll 
TS  l0  TS 

i'2" 

AtoH 
ro" 

Camber  of  standing  ways  .     . 

2' 3" 

ro" 

Length    of    standing    j  Inner 
ways \  Outer 

345' 

288' 

|367' 

395' 

370' 

Length     of      sliding    (  Inner 
ways \  Outer 

240' 
165' 

I  284' 

330' 

305' 

Breadth     of    sliding    (  Inner 
ways (  Outer 

V  10" 

1'8"' 

J** 

1'9" 

vv 

Area  of  sliding  ways  in  square 

feet 

1,430 

904 

1,155 

1,067 

Total  fall  in  length  of  standing 

ways 

23' 0" 

18' 9" 

19'7" 

18'  6" 

Water  on  way  ends  .... 

8'  7" 

6'0" 

4' 4" 

2'6" 

Draught  of  ship  forward   .     . 

11' 2" 

11' 6" 

7'0" 

8' or 

Draught  of  ship  aft .     .     .     . 

16'  6" 

14' 0" 

10'  10£ 

10'  5" 

Draught  of  ship  mean  .     .     . 

13'  10" 

12'  9" 

9'0f" 

vq» 

Displacement  in  tons    .     .     . 

2,850 

2,500 

2,157 

2,240 

Mean  pressure  per  square  foot 

on  sliding  ways  in  tons  .     . 

2.00 

2.51 

1.9 

2.09 

Length  of  first  period   .     .     . 

278.0 

283 

250.5 

279.5 

Length  of  second  period    .     . 

67 

84 

144.5 

90.5 

Ratio  of  length  of  2d  period  to 

length  of  sliding  ways    .     . 

28% 

30% 

44% 

30% 

mencement  of  2d  period 

520 

550 

640 

630 

Weight  on  sliding  ways  at  end 

of  second  period  (in  tons)   . 

250 

290 

300 

380 

Margin  against  tipping  .     .     . 

10,500 

33,250 

80,000 

35,300 

Table  of  Launching  Data 


163 


Launching  Data. 


E 

F 

G 

H 

J 

K 

ii 

M 

coco 

Is 
1* 

cc$ 

£* 
^x 

CO$ 

cox 

8 

g35 

pf  • 

Wo 

^X 

St 

Sfe 

COM 

*x 

(So 
^>3 

co 

£X 

go 

HE 

co 

£X 

CO 

ccSi 

HX 

Si 

< 
As 

£x 

CO 

B0 

9  // 

8  // 

A" 

9  // 

A" 

9  " 

A" 

A" 

A  t0  If 

A  to  If 
r  io" 

A  to^-f 

1'  10" 

8     tn  14 
TS  l°  T6 

ro" 

A  toft 

10" 

10   fn   14 
TS  uo  TS 

Atoll 

l'O" 

A  to  H 

6" 

348' 

302' 

300' 

267' 

250' 

195' 

259' 

276' 

240' 

200' 

200' 

180' 

170' 

150' 

207' 

190' 

r  io'' 

i'8" 

1'9" 

1'9" 

1'9" 

1'8" 

1'9" 

1'9" 

880 

666 

700 

630 

595 

375 

725 

665 

21'  6" 

18'  10" 

15' 6" 

15' 4" 

14'  6" 

12' 0" 

15'  0" 

16'  0" 

8'  9" 

3'  10" 

3'  7" 

2' 8" 

4'5" 

2' 9" 

1'9" 

2'0" 

6' 6  J" 

6'0" 

5' 7" 

5' 9" 

8' 7" 

4'0" 

6'  11" 

9' 2" 

9'5£" 

8'  2" 

10' 8" 

9,0" 

7'1" 

3'  10" 

9'  11" 

12'  0" 

r<r 

7'1" 

8'ir 

7'4r 

7'  10" 

3' 11" 

8' 5" 

10'  7" 

1,660 

1,100 

1,000 

865 

700 

215 

1,015 

1,750 

1.89 

1.65 

1.40 

1.37 

1.16 

.57 

1.4 

2.63 

237.5 

202 

249 

208.5 

190 

122 

212 

110.5 

100 

51 

58.5 

60 

73 

47 

46% 

50% 

25i% 

32£% 

35% 

49% 

23% 

560 

400 

215 

225 

225 

75 

235 

255 

125 

110 

115 

115 

25 

170 

53,500 

39,000 

5,400 

9,700 

12,300 

5,500 

164  The  Naval  Constructor 


and  of  the  sliding  ways  often  rises  to  the  surface  shortly  after  the 
vessel  has  entered  the  water.  In  the  diagram  a  complete  set  of 
jurves  has  been  given  to  fully  illustrate  the  matter,  but  for  prac- 
ical  purposes  only  that  part  of  the  diagram  where  the  vessel  is 
represented  to  be  moving  from  the  position  where  the  C.G.  is  at 
,he  way  ends,  to  ffhe  end  of  the  second  period,  is  required. 

As  the  minimum  moment  against  tipping  is  a  very  important 
hing,  it  will  be  useful  to  know  what  variation  will  be  made  in  its 
imount  by  any  alteration  to  the  length  and  form  of  the  standing 
vays  of  this  vessel : 

Lengthening  the  standing  ways  10  feet  increases  the  moment 
!rom  9,700  to  13,700  foot-tons. 

Shortening  the  ways  10  feet  decreases  the  moment  to  5,300  foot- 
ons. 

Increasing  the  camber  from  12  inches  to  18  inches  increases  the 
noment  to  14,500  foot-tons. 

Decreasing  the  camber  to  6  inches  decreases  the  moment  to  4,000 
oot-tons. 

If  with  a  certain  declivity  of  ways  for  the  launching  of  a  vessel, 
t  is  found,  by  calculation,  she  will  tilt,  the  standing  ways  must  be 
sxtended  further  out  into  the  water,  or,  if  this  cannot  be  done 
jonveniently,  their  outer  ends  must  be  lowered,  or  ballast  put  into 
he  fore  end  of  the  vessel.  The  first  two  increase  the  buoyancy 
noment  about  the  end  of  the  standing  ways,  and  the  third 
lecreases  the  weight  moment  about  the  same  point. 

_  W  sin  5  -fW  cos  5 

Pressure  on  dog  shores  = -— 

cos  /3 

W  =  weight  of  vessel. 

5  =  mean  angle  of  declivity  of  ways  under  vessel. 

/S  =  angle  between  ways  and  dog  shores. 

/  =  coefficient  of  friction  (between  1.0  and  .7). 

The  ratio  of  second  period  to  length  of  sliding  ways  cannot  be 
jot  lower  than  about  25  per  cent  without  danger  of  tipping. 


Rudders 


165 


RUDDERS. 

In  determining  the  most  suitable  area  of  rudder  it  is  usual  to  take 
the  same  as  a  percentage  of  the  immersed  longitudinal  plane  of 
the  ship,  which  percentage  will  vary  with  the  degree  of  fineness 
of  the  vessel. 

Percentage  for  Rudder  Area  in  Various  Types. 


Type  of  Vessel. 

Per  Cent  of 
Immersed  Longi- 
tudinal Plane. 

Fast  ocean  liners 

Freighters 

Yachts 

Paddle  steamers 

1.25 
1.50 
1.10 
2.0 

Having  fixed  upon  the  area,  the  diameter  of  stock  may  be 
calculated  by  various  formulae,  some  of  them,  unfortunately,  of  a 
very  approximate  character,  and  on  this  account,  where  high 
speed  will  be  attained,  it  is  advisable  to  carefully  calculate  the 
required  diameter  irrespective  of  the  result  obtained  by  the  classi- 
fication societies'  formulae.  For  this  purpose  it  is  necessary  to 
know,  (1)  the  hard  over  angle  of  rudder,  (2)  centre  of  pressure  on 
rudder  blade,  (3)  maximum  pressure  exerted  at  hard  over  with 
ship  at  full  speed.  The  angle  of  helm  being  usually  35°,  the 
pressure  on  blade  at  this  angle  at  full  speed  may  be  found  from 
the  formula,  — P  representing  the  pressure  in  lbs. 

P  =  AV2XshiaXp. 

It  should  be  stated  that  V=  speed  of  vessel  in  knots  per  hour 
plus  20  per  cent  to  allow  for  the  slip ;  A  =  area  of  rudder  in 
square  feet,  including  emerged  surface ;  and  p  =  pressure  in  lbs. 
per  sq.  foot  at  1  knot,  =3.19  lbs.  per  sq.  foot. 

Before,  however,  the  twisting  moment  on  the  stock  can  be 
solved,  the  centre  of  pressure  must  be  located.  This  centre  being 
\  the  breadth  from  the  leading  edge  with  the  helm  amidships,  does 
not  arrive  at  the  centre  of  gravity  of  rudder  until  90°  is  reached, 
and  as  35°  is  the  usual  angle,  it  will  be  sufficiently  close  to  take  .37 
of  the  breadth  of  the  rectangle  equalling  the  rudder  area : 

A 

Centre  of  pressure  from  centre  of  stock  =  I—  -j-  .37. 


166 


The  Naval  Constructor 


The  twisting  moment  T  would  then  be 

T=  A  V*  X  sin  36°  x  3.19  x  I  as  inch-pounds, 

and  equivalent  diameter  of  stock  "  d  "  in  inches  with  a  fibre  stress 
k  of  6,000  lbs., 

8 


d=\"-lmt 


5000 

The  subjoined  table  gives  torsional  moments  with  their  equiva- 
lent diameters  calculated  as  above,  with*  6,000  lbs.  per  square 
inch,  being  a  sufficiently  high  fibre  stress  to  allow  for  a  twisting 
stress,  alternating  between  right  and  left,  for  wrought  iron. 

In  a  rudder  of  rectangular  form  the  centre  of  pressure  from  the 
leading  edge  is  equal  to 

6  (.195 +  .305  sin  o)=  5c, 

where  b  is  the  mean  breadth  of  rudder,  and  c  a  coefficient,  as  under. 


Angle  of 
Rudder,  a. 

c. 

Angle  of 

KUDDEK,  a. 

c. 

10° 

.248 

35° 

.370 

20° 

.300 

40° 

.391 

30° 

.347 

45° 

.410 

Rudder  Stocks  per  Lloyd's  Rule. 

The  following  is  the  formula  prescribed  by  Lloyd's  Register  for 
estimating  diameters  of  rudder  stocks,  but  in  no  case  must  the 
result  be  less  than  the  tabulated  rule  size,  which  see.  It  should 
not,  however,  be  used  unless  the  ship  is  intended  for  classification 
in  that  society's  register,  as  for  very  high  speed  vessels  the 
results  obtained  would  be  too  weak.  One  of  the  factors  is  draught 
of  water,  which  has  little  or  no  value  in  computing  the  strength 
of  rudder  stock  for  a  rudder  of  ordinary  type  hung  on  a  post.  Of 
course,  in  a  rudder  with  no  bottom  bearing,  as  in  destroyers  and 
such  craft,  the  case  would  be  entirely  different,  as  then  the  stock 
would  be  figured  for  bending,  the  moment  for  such  being  much  in 
excess  of  the  torsional  one. 


*  Take  7,000 


for  steel. 


Rudder  Stock  Diameters 

167 

Rudder  Stock  Diameters. 

16y 

Torsional 
Moment 
"T"  in 

Inch-lbs. 

Diame- 
ter of 
Stock 
in  Ins. 

Torsional 
Moment 

"7"'  IN 

Inch-lbs. 

Diame- 
ter of 
Stock 
in  Ins. 

Torsional 
Moment 

**T"   IN 

Inch-lbs. 

Diame- 
ter of 
Stock 
in  Ins. 

20,000 

2| 

500,000 

8 

3,250,000 

15 

25,000 

3 

550,000 

H 

3,500,000 

15| 

50,000 

3f 

600,000 

8j 

3,750,000 

15| 

75,000 

H 

650,000 

8J 

4,000,000 

16 

100,000 

*H 

700,000 

9 

4,250,000 

m 

120,000 

5 

800,000 

»l 

4,500,000 

16| 

140,000 

H 

900,000 

9f 

4,750,000 

17 

160,000 

H 

1,000,000 

10 

5,000,000 

m 

180,000 

H 

1,200,000 

lOf 

5,500,000 

171 

200,000 

51 

1,400,000 

HJ 

6,000,000 

18} 

220,000 

6 

1,600,000 

Hf 

6,500,000 

181 

240,000 

6i 

1,800,000 

12} 

7,000,000 

m 

260,000 

H 

2,000,000 

m 

7,500,000 

19f 

280,000 

H 

2,200,000 

13 

8,000,000 

20* 

300,000 

H 

2,400,000 

13| 

8,500,000 

20| 

320,000 

»i 

2,600,000 

131 

9,000,000 

21 

360,000 

n 

2,800,000 

14} 

9,500,000 

21| 

400,000 

n 

3,000,000 

14| 

10,000,000 

21f 

450,000 

n 

11,000,000 

22| 

Note.  — Di 
fibre  stress  of 

ameters  a 
5,000  lbs. 

re  calculated 

to  nearest 

eigbtbs  of  an 

inch  with  a 

168  The  Naval  Constructor 


D  =  draught  in  feet. 

B  =  greatest  distance  in  inches  from 

centre  of  pintle  to  back  of  rudder. 
b  =  greatest  breadth  of  rudder  in  inches. 
V  =  speed  in  knots. 
d  =  diameter  of  stock  in  inches. 


Then,  ^  =  -h  V  ■*»  (2  B  -  b)  V*. 

Rudder  Stock  per  Germanischer  Lloyd  Formula. 

This  rule  is  a  much  more  correct  one  than  Lloyd's  Register, 
using,  as  it  does,  truer  factors.  It  is  given  here  converted  for 
English  measure  as  well  as  for  metric. 

Let  d  =  diameter  of  stock  in  centimeters. 
F=area  of  rudder  in  square  meters. 
r—  distance  from  centre  of  gravity  of  area  to  axis  of 

stock  in  centimeters. 
V=  speed  in  knots. 
Then,  d  =  .42  ?/FrV2. 

For  English  measure  let 

d  =  diameter  of  stock  in  inches. 
A  —  area  of  rudder  in  square  feet. 
r  =  distance  from  e.g.  to  axis  in  inches. 
V  =  speed  in  knots. 

Then,  d  =  .103  ^aTV*. 

British  Corporation  Formula. 

The  "B.C.,"  or  British  Corporation,  Rule  is  slightly  different 
from  the  foregoing,  but,  like  it,  takes  the  true  factors  into  account, 
and  gives  a  more  correct  result  than  either  of  the  foregoing  for- 
mulae. 

d=.26\/rZF2. 

Note.  —  "  r  "  is  here  taken  in  feet. 

PROPELLER   STRUTS. 

Simpson's  Formula. 

Propeller  "  A  "  brackets  or  struts  are  not  dealt  with  in  any  of 
the  classification  societies'  rules,  and  in  deciding  on  a  suitable  area 
of  section  for  these,  it  is  the  invariable  practice  to  base  it  on  ex- 
perience.    Such  being  the  case,  a  great  divergence  is  found  in  the 


Propeller  Struts  169 

proportions  and  dimensions  of  them  in  vessels  of  similar  size  and 
power.  To  insure  greater  uniformity  in  their  design  and  weight 
consistent  with  ample  strength  to  meet  the  stresses  to  which  they 
are  subjected,  the  writer  has  prepared  the  formula  following,  based 
on  the  results  of  a  varied  experience  with  struts  for  all  sizes  of 
vessels  with  a  range  of  I.H.P.  of  10  to  7,000  per  shaft  and  revolu- 
tions of  70  to  600,  and  from  observation  of  some  which  were 
actually  carried  away.  It  should  be  stated  that  the  smaller  pow- 
ers were  not  for  twin  screws  but  for  small  craft  with  cut-away 
deadwoods  necessitating  a  bracket  to  support  the  outer  end  of 
shaft.  From  the  formula  given,  the  area  is  obtained,  and  with  it 
the  following  proportions  determined  :  — 

SECTION  OF  ARM 


FOR  WD. 
*«M 


Fig.  38. 

Let  R  =" revolutions  of  engines  per  minute. 

P  =  indicated  horse  power. 
I  =  outboard   length  of  shaft  from  stern  tube  outer 

bearing  to  centre  of  boss,  in  inches, 
k  =  coefficient  =  .0633  B. 


Then,  — =  area  in  square  inches. 

Of  course  the  horse  power  is  that  transmitted  through  one  shaft 
only,  and  the  area  obtained  is  for  one  arm.  The  proportions  of 
the  pear-shaped  arm  are  as  under. 

L=  V5.3X  Area. 
B  =  .25L.  R=.25B. 

l=.SSL.  r  =  .50R. 

For  the  lesser  powers  and  for  brackets  intended  for  wood  or 
composite  vessels,  the  brackets  should  be  of  gun  metal  or  bronze, 
and  for  higher  powers  and  steel  ships  of  cast  steel. 


170 


The  Naval  Constructor 


Spectacle  Frames. 

For  the  larger  classes  of  twin  screw  steamers  what  are  known 
as  spectacle  frames  are  bolted  to  body  post  to  take  the  outer  end 
of  shaft,  and  the  shell  plating  webbed  out  to  enclose  what  other- 
wise would  be  the  outboard  length  of  shafting,  as  described  in  the 
chapter  on  design.  These  frames  are  of  cast  steel  and  semi-pear- 
shaped  in  section.  The  area  of  this  section  may  be  found  from 
the  same  formula  as  if  the  ship  were  to  be  fitted  with  "A" 


Bossing  adds  l\%  to 
wetted  surface  and  .84% 
to  displacement. 


Fig.  39. 

brackets  and  the  result  multiplied  by  2.  This  greater  area  is 
accounted  for  by  the  fact  that  there  is  only  one  arm  and  the 
greater  breadth  of  same  required  to  permit  of  working  the  shell 
plating  and  also  obtaining  the  necessary  section  modulus.  The 
weight,  however,  will  be  found  to  approximate  very  closely  to  the 
open  struts.  Experiments  have  shown  that  better  results  are 
obtained  by  inclining  the  spectacle  frame  downwards  at  an  angle 
of  about  30°  from  the  horizontal. 


The  Transport  of  Cattle  171 


Proportions. 

A  =  2L.  F  =  %D. 

B  =  \  A.  L  =  Length    of   pear-shaped 
C  =  B.  section  as  got  for  '■'•A  " 

E  =  \D.  bracket. 

The  outside  diameter  D  of  the  boss  will  be  fixed  in  conjunction 
with  the  engineer. 


THE  TRANSPORT   OP   CATTLE. 

In  arranging  the  ship  for  the  transport  of  cattle  in  conformity 
with  the  United  States  Department  of  Agriculture,  care  should  be 
exercised  in  first  providing  for  the  main  cattle  gangways.  A  good 
location  for  these  would  be  at  the  ends  of  engine  or  boiler  casings 
opposite  which  the  cattle  doors  should  be  placed.  The  webs, 
webframes,  and  any  other  structural  obstructions  should  be  ar- 
ranged with  a  view  to  working  them  in  as  boundaries  for  blocks 
of  4  cattle  if  practicable,  and  if  the  ship  be  a  new  one,  the  frame 
spacing  should  be  fixed  to  work  out  with  the  legal  dimension  for 
cattle  pens  to  obviate  waste  of  space,  unsuitable  pillaring,  and 
division  boards  coming  off  beams.  If  the  ship  be  of  such  dimen- 
sion as  to  require  30"  spacing  ordinarily,  then  by  increasing  this 
to  30 1",  a  very  good  arrangement  of  pens  will  be  obtained.  Coal- 
ing ports,  mucking  ports,  and  all  thwartship  passages  in  connection 
therewith,  should  next  be  located,  bearing  in  mind,  in  arranging 
these,  the  4-cattle  blocks  previously  mentioned.  The  stalls  may 
be  then  outlined,  followed  by  the  pillars,  which,  of  course,  will  be 
placed  to  suit  these,  working  downwards  from  the  cattle  deck  to 
the  other  hold  pillaring. 

The  following  are  the  dimensions  of  cattle  spaces  required  by 
the  Department  of  Agriculture  : 

Cattle  per  head  on  upper,  spar,  or  weather  decks  : 

8'  0"  long  X  2'  6"  wide  X  6'0"  high  in  the  clear. 

Cattle  loaded  under  decks  will  require  2  inches  more  width  unless 
in  regular  cattle  ships  with  satisfactory  ventilation. 

Pens  must  be  arranged  for  4  cattle,  unless  at  the  ends  of  a  row 
of  pens,  where  5  may  be  stowed. 

Special  permission  must  be  obtained  to  carry  cattle  on  lower 
deck,  and  in  all  cases  where  this  is  granted,  the  width  allotted 
must  be  2'  8",  the  ventilation  sufficient,  and  no  animals  are  allowed 
on  hatches. 


172  The  Naval  Constructor 


Slieep,  per  head,  4'0"  long  X  14"  wide  in  the  clear.  Pens  must 
not  exceed  20  feet  X  8  feet  where  two  tiers  are  carried,  and  each 
tier  to  have  a  clear  vertical  space  not  less  than  3  feet. 

Horses,  per  head,  8  feet  long  X  2'6"  wide  x  6'3"  high  in  the  clear, 
and  as  far  as  possible  arranged  between  the  overhead  athwartship 
beams.  Each  horse  must  have  a  separate  stall,  and  where  22  or 
more  horses  are  carried,  a  hospital  8  feet  X  10  feet  square  must  be 
reserved. 

Alleyways  for  feeding  and  watering  to  be  3  feet  wide,  but  where 
obstructions  less  than  3  feet  long  occur,  and  at  ends  of  ship,  they 
may  be  reduced  to  a  minimum  of  18  inches. 

Thwartship  alleyways  to  scuppers  to  be  18  inches  wide. 

Headboards  not  less  than  2  x  10  inches  or  3  x  8  inches,  of  spruce 
or  yellow  pine. 

Footboards,  same  dimensions  as  headboards. 

Division  boards  of  2x8  inches,  spruce  or  yellow  pine  fitted 
vertically  for  cattle. 

Division  boards  for  horses,  2x9  inches  x  8  feet,  planed  and 
placed  horizontally. 

FooUocks,  2  inches  above  cement  X  4  inches  wide  of  spruce,  yel- 
low pine,  or  hardwood,  ranged  fore  and  aft,  and  placed  12  inches, 
14  inches,  26  inches,  and  14  inches  apart ;  the  first  one  being  12 
inches  distant  from  the  inside  of  footboard;  but  when  troughs  are 
used,  the  footlocks  will  be  placed  17",  16",  22"  and  16"  apart. 

Outside  planking  on  open  and  closed  rail  ships  to  be  not  less 
than  2  inches  spruce  or  1^  inches  yellow  pine. 

Ventilators.  Each  under  deck  compartment  not  exceeding  50 
feet  in  length,  must  have  at  least  four  18-inch  diameter  cowl  ven- 
tilators, with  tops  7  feet  above  shelter  deck,  two  being  placed  at 
each  end  of  the  compartment.  If  compartments  be  over  60  feet 
long,  additional  ventilators  must  be  fitted. 


Weight  of  Fittings  per  Head  of  Cattle  Carried. 


Item. 


Weight  in 
Lbs. 


Cementing  on  deck  \\"  thick 185.00 

Total  woodwork,  including  bolts     ....  139.62 

Angle  steel  footlock  clips 11.43 

Castings  and  fittings,  including  bolts  .     .     .  37.19 

Gnawing  strips  of  segmental  iron   ....  6.00 

Solid  cattle  pillars        9.74 

Hollow  cattle  pillars          11.02 

Total  per  head  of  cattle       =400.00 


Weight  of  Hull  173 

Light.  Sufficient  light  must  be  provided  for  the  proper  tending 
of  animals  at  all  times. 

Ventilation  for  horses.  Under  deck  canvas  bags  should  be  fitted 
to  ventilators,  provided  with  iron  rings  at  bottom,  and  reaching 
within  18  inches  of  the  deck  under  foot. 

In  estimating  the  weight  of  cattle  fittings,  comprising  cement, 
cattle  pillars,  footlocks,  head  and  rumpboards,  castings,  etc.,  the 
following  will  be  found  reliable  :  — 

Weight  of  Fittings  per  Horse  Carried. 

Item.  Weilgbhst  in 

Cementing  on  deck  \\"  thick 185.00 

Total  woodwork,  including  bolts    ....     273. 55 

Kicking  pieces  and  bolts 34.11 

Castings  and  fittings,  including  bolts  .     .     .     200.34 

Total  per  horse  (London  regulation).     .  =693.00 
Leaving  an  American  port,  deduct  close  divi- 
sion boards 135.00 

Total  per  horse  (American  regulation)     =  558.00 


WEIGHT   OF   HULL. 

In  estimating  for  displacement  purposes,  the  weight  of  a  ship's 
hull  is  usually  divided  broadly  into  two  parts,  viz. :  (1)  finished 
steel  and  (2)  weight  of  wood  and  outfit. 

There  are  various  methods  by  which  the  steel  may  be  estimated 
approximately,  but  where  great  accuracy  is  required  the  weights 
of  the  structure  should  be  calculated  in  detail  systematically,  and 
the  results  summarized  in  convenient  form  for  future  reference. 

The  arrangement  shown  in  the  table  will  be  found  useful  when 
the  cost  estimate  is  being  figured,  as  the  parts  of  structure  item- 
ized are  those  which  generally  show  variations  in  labor  prices. 
The  summary  of  material  is  given  for  a  similar  reason,  and  also 
for  the  variation  in  scrap  between  the  different  items. 

Of  course  the  structural  parts  considered  in  the  table  must  each 
be  dealt  with  in  detail,  but  by  having  some  such  form  as  that 
here  presented  the  chances  of  omission  will  be  minimized,  the 
weights  put  in  a  convenient  form  for  prime  cost,  and  also  usefully 
arranged  if  the  centre  of  gravity  should  afterwards  require  calcu- 
lating. 

The  most  common  method  to  approximate  the  weights  of  hull 
steel  when  there  is  insufficient  time  to  figure  in  detail,  is  to  take 
the  ratio  between  the  weight  and  the  cubic  number  of  a  known 


174 


The  Naval  Constructor 


Calculated  Finished  Steel  Weight. 


Part  of 
Structure. 


if.  s 

: « 


X^ 


I 


Summary. 


Keel  bars  and  stem  .... 
Stern  post,  rudder  frame  and 

struts 

Frames,  reverse  frames,  and 

doublings 

Floors  and  tail  plates  .  .  . 
Beams  and  carlings      .     .     . 

Keelsons 

Bulkheads  (W.T.)   .... 

Bunker  casings 

Engine  and  boiler  seats  .  . 
Shaft  tunnel  and  stools  .  . 
Inner  bottom  plating  .  .  . 
Shell  plating,  including  bhd. 

liners 

Stringers  and  ties     .... 

Deck  plating 

Cargo  and  coal  hatches  .  . 
Engine  and  boiler  casings 

Deck  houses 

Sundry  deck  and  hold  work  . 
Fresh-water  tanks   .... 

Slip  iron 

Moulding  and  copes  .  .  . 
Rivet  heads 

Finished  steel  weight     .  = 


Tons. 
3.5 

20.0 

275.0 

301.0 

225.4 

142.5 

102.7 

40.0 

25.0 

37.7 

119.4 

734.2 

217.6 

305.3 

37.5 

77.6 

140.0 

25.0 

13.2 

57.0 

46.5 

44.0 


Tons. 
6.0 


Forgings 
Angles  . 
Plates  . 
Bulb  tee 
Slips 

Mouldings 

Castings 

Rivet  heads      44.0 

Total     =  2990.0 


587.0 
2063.6 

168.4 
57.0 
46.5 
17.5 


2990.0 


vessel  of  similar  type  and  degree  of  fineness  and  use  the  coeffi- 
cient so  obtained  on  the  proposed  ship.  For  example,  a  known 
ship  of  length  330  feet,  breadth  41'  9",  and  depth  moulded  28'  3", 
has  a  total  steel  weight  of  1,680  tons,  then 

LxBxD     330X41.75X28.25       ,0, 
SX100    =         1680X100     -  = M1  coefecient- 
The  proposed  steamer  is  320  X  42  X  29 1  and  the  coefficient  of 
steel  weight  being  .431,  we  get 


Hull  Steel  Weights 


175 


320  x  42  x  29^ 
100 


x  .431  =  1709  tons. 


This  rough  method  requires  good  judgment  and  practice,  as  it  is 
obvious  from  the  example  given  that  although  1,709  tons  is  a  fair 
approximation  it  is  still  too  heavy. 

Kecognizing  this  fact  and  the  necessity  for  a  quick  approxima- 
tive rule  which  would  give  fairly  close  results,  Mr.  J.  Johnson 
(vide  Trans.  Inst.  Nav.  Arch.  Vol.  39)  devised  a  method  based  on 
Lloyd's  longitudinal  number  (modified  for  some  types)  and  by 
plotting  down  known  steel  weights  opposite  their  numeral,  draw- 
ing curves  through  the  mean  values  of  each  type,  he  analyzed 
them  and  found  their  equations.  By  means  of  curves  prepared  in 
this  way  from  actual  weights,  the  amount  of  steel  is  easily  read  off 
and  the  increase  or  decrease  due  to  an  alteration  in  the  numeral  is 
readily  seen.     Johnson's  formula  is  as  under, 


W=cN    or  W 


"(«)' 


where 

W  =  Finished  weight  in  tons  of  iron  or  steel  used  in  hull  construc- 
tion. 

N  =  Lloyd's  longitudinal  number  modified  as  follows :  In  3 
decked  vessels  the  girths  and  depths  are  measured  to  the 
upper  deck  without  deduction.  In  spar  and  awning 
decked  vessels  the  girths  and  depths  are  measured  to  the 
spar  or  awning  decks  respectively. 
In  one,  two  or  well  decked  vessels  the  girths  and  depths  are 
.   taken  to  the  main  deck  in  the  usual  way. 

C  and  K  are  coefficients  varying  with  different  types. 

X  is  an  exponent,  also  varying  with  different  types. 

Table    Giving    the    Mean    Values    for   c,    K,  and   x    for 
Vessels  Built  to  Lloyd's  or  Veritas'  Highest  Class. 


Type  of  Vessel. 


K. 


Three  deck,  with  complete  shelter  deck 

Three  deck 

Spar  deck 

Awning  deck 

One  deck,  two  deck,  and  well  deck 
Sailing  vessels 


.00359 
.00078 
.00115 
.00167 
.00215 
.00065 


.328 
.492 
.576 
.665 
.856 
.410 


1.48 
1.40 
1.35 
1.30 
1.30 
1.40 


176  The  Naval  Constructor 

Of  course  differences  in  the  arrangement  of  scantlings,  extent  of 
double  bottom,  number  of  bulkheads  or  length  of  erections  must 
be  calculated  as  extra. 

A  complete  set  of  curves  based  on  this  method,  but  extended  to 
embrace  the  largest  types  of  vessels  including  complete  shelter 
deck  steamers  is  given  opposite. 

The  second  part  of  the  finished  hull  weight,  viz.:  the  wood  and 
outfit,  embraces  everything  that  goes  to  finish  the  ship  excepting 
fresh  water,  coal  and  consumable  stores.  That  is,  it  comprises 
all  wood  work,  both  shipwright  and  joiner,  masts,  rigging,  sails, 
boats,  anchors,  chains,  cables,  hawsers,  furniture,  fixtures,  etc. , 
many  of  the  items  being  extremely  difficult  of  accurate  cal- 
culation. For  this  reason  it  is  necessary  where  these  fittings  are 
calculated  in  detail  to  carefully  check  the  result  obtained  by  a 
similar  method  to  that  used  for  the  approximated  steel  weight 
from  actual  wood  outfit  data  derived  from  known  ships  of  similar 
type.  The  value  of  this  coefficient  for  various  classes  will  be 
seen  from  the  Table  of  Elements  of  Ships. 

Regarding  this  weight,  Johnson  states  that  it  will  be  found  to 
vary  almost  directly  as  the  longitudinal  number. 


Hull  Steel  Weights 


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SIS 

"IJOONNHiOO'j;     00Pj(OHiO»M00 
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si  a 

c 

H   iO««   S   H   ifl     OIMNHICOMN 

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«  n  h  us  «  «  <q   q-*oo<N<©OJcot>. 

Tji    •*)<    id   »C   »C   d   d     t^l^t^OOQOOOOJOS 

eoeocococococo    coeocoeococococo 

odoHHNflfi    eo 

SIS 

WWCOWCOMCCCO    cococoeococococo 

q^N-H^oo«lO     OS 

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C0C0C0COCOC0Tj<t      ^i 

SIS 

OOHHHINININ 
MMMMMMP5CC 

co'coeoT)<TjiT)5id>d 
cococoeococococo 

qwqqeoqqeo    co 
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SIS 

NO»eO«(Off 

oooioiaoddc 

NfNNMMMMK 

NCOJNIOOOHK) 

fi     iH     ^H*     tN     <N     l>I     CO     CO 

cococoeococococo 

00l-4TjJlv.^H-^t>.O       CO 

CO^Tf^uJdldd     d 

cococoeococococo    eo 

SIS 

O»<?»W500rH^b.C 
dNNNMOOSOff 
(NCNCNtNCNtNtNCN 

eo«oosc^»qoOrHTij 

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NONiOXH^N     O 

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eocoeocoeocoeoco    co 

SIS 

H^oft«K)NC 
»d»d»o»d«o«dcDN 

cocqoqT-jTjjt^qc^ 
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iccxji-jcoqqtNrj'    t>. 

ddddddi-H--<    ri 
CNtNeococococoeo    eo 

SIS 

3  h   N  N   00  M   O   •■*     O>OH©NNn00 

niononiono    mioooqccioooq 

COCCCO'*-^-*-^«5     «5iO>0(0<OtdlCN 
CNJCNCNtNCNCNCNCN     CNtNCNCNCNCNCNCN 

27.34 
27.59 
27.85 
28.10 
28.36 
28.61 
28.87 
29.12 
29.38 

SIS 

HIOOOHIOOOH^I 

^(OOOHMiOMC 
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iflCOXOOHMTt 
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ddoidddd- 

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r-l_i,_I^H^H<N<N<N     <N(NCNCN<NCN<NCN     (M 

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TfHMWNatOM 
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cococoeococococo 

H»  .+»  **o  r^  «*«>**.  H» 

Weight  of  Steel  Tees 


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T 


185 


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ft 

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02 
H 

H 
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H 
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218 





518 





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818 





318 



218 

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318 

218 

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186 


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Weight  of  Steel  Tees 


T 


187 


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H 

f 

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ci 

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Cl 

cc 
cc 

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3 
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318 

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q 

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ci 

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Cl 

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CO 
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3 

cc 

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cc 
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05    CC 

318 

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318 

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188 


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The   Naval  Constructor 


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u 
fe 

to 

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o 

ao 

H 
W 

H 
to 
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H 
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00 
33 

w 

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M 
u 

s 

818 

WWWOOCCWMrt 

00(N<©0»CO>CO^ 

re   re   re   re   re   re   re   re 

SIS 

26.7 
27.1 
27.5 
27.9 
28.3 
28.7 
29.1 
29.5 

ood-HrtHiNfi 

NTOMMMMMW 

cdcd**-<t'*»d»d<d 
cococococoeoeoeo 

218 

iO00N«qp"*00'-; 

NNNNMMMW 

loqnNrt^MN 

^H    dlNMWMJ 

cocooocooocococo 

SIS 

t^r^^oooooooici 

<N<N<NC$Cv|<N<N(N 

©NqOMNO* 

ficoeocococococo 

SIS 

OOHi(5«Hi(500tj 
NNMNNNNN 

»q   00  <N    "5   OS  <N    »q   OS 

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wqqNqqcce 

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MNMMMMNN 

SIS 

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t^t^t^OOOOGCCOOi 

19.44 
19.69 
19.95 
20.20 
20.46 
20.71 
20.97 
21.22 

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OOOtCHJMINOO 

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cq 

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2 

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Weight  of  Steel  Tees 


T 


189 


w 

o 

< 

o 

00 

U 

H 

H 

b> 

H 
ft 

'SI 
CO 

3 

H 

cnIcm 

01 
X 

to 

38.6 
39.0 
39.4 

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co 

CO 

d 

d 

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co 

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191 


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24.23 
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20.47 
21.06 
21.66 
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14.77 
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8.77 
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8.69 
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11.07 
11.36 
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44.20 
45.05 
45.90 
46.75 

47.60 
48.45 
49.30 
50.15 

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39.08 
39.89 
40.70 
41.51 

42.31 
43.12 
44.93 
44.74 

45.54 
46.35 
47.16 
47.97 

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•    •  S  to 

:    :  22  SS 

37.33 
38.10 
38.86 
39.63 

40.39 
41.16 
41.92 
42.69 

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32.66 
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34.10 
34.82 

35.55 
36.27 
36.99 
37.71 

38.44 
39.16 
39.88 
40.60 

CO   tO   N.   OS 

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28.29 
28.97 
29.65 
30.33 

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33.73 
34.41 
35.09 
35.77 

36.45 
37.13 
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38.49 

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26.78 
27.41 
28.05 
28.69 

29.33 
29.96 
30.60 
31.24 

31.88 
32.51 
33.15 
33.79 

34.43 
35.06 
35.70 
36.34 

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27.61 
28.20 
28.80 
29.39 

29.99 
30.58 
31.18 
31.77 

32.37 
32.96 
33.56 
34.15 

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23.65 
24.20 
24.75 
25.30 

CO    --1    CO    H 

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CN    CN    CN    IN 

28.07 
28.62 
29.17 
29.72 

30.28 
30.83 
31.38 
31.93 

32.49 
33.04 
33.59 
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22.03 
22.54 
23.05 
23.56 

24.07 
24.58 
25.09 
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28.66 
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20.38 
20.85 
21.32 

21.79 

22.25 
22.72 
23.19 
23.66 

24.12 

24.59 
25.06 
25.53 

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27.86 
28.33 
28.80 
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20.40 
20.83 
21.25 
21.68 

22.10 
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16.98 
17.37 
17.75 
18.13 

18.51 
18.90 
19.28 
19.66 

20.04 
20.43 
20.81 
21.19 

21.57 
21.96 
22.34 
22.72 

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18.29 
18.63 
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13.45 
13.74 
14.04 
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11.63 
11.88 
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14.69 
14.94 
15.20 
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11.48 
11.69 
11.90 
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12.33 
12.54 
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193 


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73.95 

74.80 
75.65 
76.50 
77.35 

78.20 
79.05 
79.90 
80.75 

81.60 
82.45 
83.30 
84.15 

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64.92 
65.73 
66.54 
67.35 

68.15 
68.96 
69.77 
70.58 

71.38 
72.19 
73.00 
73.81 

74.61 
75.42 
76.23 
77.04 

77.84 
78.65 
79.46 
80.27 

218 

61.81 
62.58 
63.34 
64.11 

64.87 
65.64 
66.40 
67.17 

67.93 
68.70 
69.46 
70.23 

70.99 
71.76 
72.52 
73.29 

74.05 
74.82 
75.58 
76.35 

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58.67 
59.39 
60.11 
60.83 

61.56 
62.28 
63.00 
63.72 

64.45 
65.17 
65.89 
66.61 

67.34 
68.06 
68.78 
69.50 

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56.17 
56.85 
57.53 

58.21 
58.89 
59.57 
60.25 

60.93 
61.61 
62.29 
62.97 

63.65 
64.33 
65.01 
65.69 

66.37 
67.05 
67.73 
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52.28 
52.91 
53.55 
54.19 

54.83 
55.46 
56.10 
56.74 

57.38 
38.01 
58.65 
59.29 

59.93 
60.56 
61.20 
61.84 

62.48 
63.11 
63.75 
64.39 

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49.03 
49.62 
50.22 
50.81 

51.41 
52.00 
52.60 
53.19 

53.79 
54.38 
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45.75 
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47.96 
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50.17 
50.72 
51.27 
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44.69 
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35.70 
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38.40 
38.79 
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28.83 
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20.47 
20.77 
21.06 
21.36 
21.66 

21.96 
22.25 
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19.50 
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X   th   OS   "5 

Q  H   H   ci 

>5  io  io  io 

53.0 
53.6 
54.1 
54.7 

55.2 
55.8 
56.4 
56.9 

SIS 

X   CO    OS    ■* 
CN   CO   CO   T(5 

•*     Tft     T*     <* 

OS   tJ<    OS    ^}J 

«*  ■<*  ■*  * 

OS  ^*  OS  ^* 

d  t^  t^  oo 

49.0 
49.5 
50.0 
50.5 

OiOOiO 
rH   fH   CN   CN 

«5  "5   iO   ifl 

SIS 

CO   N   N   N 

ai  ai  <6  d 
CO  CO  •*  ^i 

H     «     H     IO 

f-5   rH   CN   CN 

T}<     Tj<     Tf     ■* 

q  »q  q  ^ 

CO   CO   CO    ^ 

Tf      Tj<     T«     «* 

q  co  oo  cq 
■*  id  id  d 

M*     ^     ^     ^ 

t>;  CN   t^  CN 

CO  N  N   00 

SIS 

35.70 
36.12 
36.55 
36.97 

37.40 
37.82 
38.25 
38.67 

©   CN    IO    t» 

f-;  iq  q  q 
OS   OS  OS   o 
CO  CO  CO   ■<* 

40.80 
41.22 
41.65 
42.07 

q  a  co  s 

CN   CN   CO   CO 
r*   rjt    ^    ^ 

«I8 

M    H    O    UJ 
rH    l«    00    CN 
(N    (N   CN    CO- 
CO  CO   CO    CO 

33.66 
34.04 
34.42 
34.81 

35.19 
35.57 
35.95 
36.34 

36.72 
37.10 
37.48 
37.87 

38.25 
38.63 
39.01 
39.40 

»I8 

28.56 
28.90 
29.24 
29.58 

29.92 
30.26 
30.60 
30.96 

31.28 
31.62 
31.96 
32.30 

Tf    X   CN    CO 

q  q  co  q 

CN   CN   CO  CO 

CO    CO   CO   CO 

34.00 
34.34 
34.68 
35.02 

H8 

OS   OS    X    X 
q   CN   U5   X 
rj<    id   id   id 
CN   <N   CN   CN 

X  x  b-  t^> 

h  ^  n  q 

(O   tO  (O  N 
CN   CN    CN    CN 

t~-  r-  co  co 
co  q  q  cn 
r>^  t^  t>l  x 

CN   CN    CN    CN 

CD   CD 

«5  X     •     • 
oo  oo     !     I 

CN   CN 

»I8 

cn  r^  co  x 

tJ<   co  OS  — i 

rH    ^H     ^    CN 

CN    CN    CN    CN 

»18 

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«I8 

«I8 

-IS 

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pin?  q»A\. 
jo  urns 

H*  HN  «t* 
CN    CN    CN    CN 

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CN    CN    CN    CN 

CN    CN    CN    CN 

CO    CO    CO    CO 
CN    CN    CN    CN 

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Tt<     Tf     T*     Tf 

CN    CN    CN    CN 

•+»  Hn  «+» 
IO    K5   ifl    K5 
CN    CN    CN    CN 

Weight  of  Steel  I   Sections 


209 


w 

o 

H 

K 
< 

b 

O 
ao 

w 

H 
H 

H 

H 

to 

02 

a 
?; 
M 
o 

X 

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88.4 

89.2 

0.1 

a 

d 
95 

X 

09 

CO   iO 
CN    CO 

as  as 

CO 
OS 

OI 
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a 

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oi 

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N.  q 

d  ■* 
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©  oq  q 

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00   00   00 

d 
x 

00 

q  oo 

00   00 
00    00 

03 

d 

X 

d 
5 

CN    .-h 
rJ   CN 

OS    OS 

a 

oi 

09 

l>    IO 

d  ■>* 

09    OS 

CO    pH 

d  d 

OS   OS 

a 

d 
a 

a 

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an? 

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d    ©    rH 
t^   X    X 

q 

00 

01 

00 

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00   00 

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d 

00 

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id 

X 

d  t^ 

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o 

i 

I>    IO 

oo  d 

X   X 

co  q 

os  os 

DO 

a 

CD 

oi 

CO    rH 
d    Tji 

OS   OS 

«8 

rH     05     CO 

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t-~  t^  l^ 

CO 

o 

00 

00   IO 

oo  d 

OI 

d 

X 

09 

q  tp 

r-I    CN 

X  X 

d 

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w  q 
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X   X 

d 

X 

X 

rH     OS 

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SIS 

N  ^J  H 

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oi 

co 

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01 

d 

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d  t^ 

01 
90 

a  co 
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cn  q 

X   X 

X 

co 
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d  d 

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CO   05    CO 
CO   CO   N 
CO   CO   CO 

ot 
X 
CO 

X 
00 
to 

IO     rH 

d  d 

CO  h- 

X 

q  t- 

CN    CN 

co 
d 

q  q 
d  ■* 

cn  q 
d  d 

iO 

d 

I- 

oo  ■* 

t>^   00 

SIS 

OS   iO    rH 

h  n  m 

CO  CO  CO 

co 

CO 

co 
-r 

q  tj; 
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CO    CD 

o 
d 
3 

CD 

d 

OS 

CN    00 

CO    CO 

X 
CO 

O  CO 

a  d 

CD   CD 

CN    X 

d  d 

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CO   CN 
CN  d 

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io  q  cq 
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d 

IO 

d 
10 

CN    00 

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CD    CD 

co 

co 

a 

3 

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CN    CO 

CO   CO 

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id  d 

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CO 

d 

io 

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CN    £> 

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CO    CD 

01 

to 

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CO 

CN    ^ 
CN    CN 

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10 

d 
as 

q  -<t 

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09 
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CN    CO 
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90 

d 

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CN    t>. 

IO   iO 

CN    CO 

d  d 

IO    IO 

i 

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d 

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q  q 

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SIS 

O   CM    IO 

cn  q  © 
t(5  tj<  d 

d 

5 

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CN    IO 
CO    t- 

d  d 

o 
9 

CN    IO 

q  tjh 

00   00 

00 
00 

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CO   f- 

a  d 

IO   t^ 

rH    IO 

8S 

§ 

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rH   d 
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00   CD    -# 

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5 

d 

CO 

os  h- 

CD   O 
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00 

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CN   o 

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CO   CO 

s 

d 

t^   IO 
CO   l> 

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CO   O   ^ 

n  no 
id  ic id 

co  co  co 

90 

CO 

90 

co 

HS 

•IS 

•IS 

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«IS        :::.":      :   :   :   :      :   :   :   :      :   :   :   :      :';■-:-; 

«IS  |     :   :   :   :      :   :   :   :      :   :   :   :      :   :   :   :      :   :   :   : 

-IS 

put?  qa^i 
jo  rang 

CO   CD   CO 
(N    CM    CN 

CO 

01 

CM 

CN   CM 

CM 

00 

OI 

X   X 
CN    CN 

•4* 

OS    OS 
CN    CN 

os  os 

CN    CN 

Q 

CO 

CD 

CO 

o  o 

CO    CO 

210 


The  Naval   Constructor 


w 

k 

>-. 

O 
» 

H 

s 

p 

E 

H 

£ 

OS 

■ 

M 
g 

5 

H 

SIS 

105.4 
106.2 
107.1 
107.9 

00   CO  «5   CO 

§§2S 

NOOI-. 
CN    CO    CO    Tji 

qf|MH 

>Q    <D   N   00 

O   X   I^    iC 

a>  ai  d>  ~ 

SIS 

100.1 
100.9 
101.7 
102.6 

•*  n  qoo 
cd  ^  >d  id 
o  o  o  o 

q  *  «  o 
o  o  o  o 

00   CO   ■*   CM 

d  d  --5  <n 

q  »  N  q 

cd  co  tf  id 

SIS 

94.9 
95.6 
96.4 
97.2 

97.9 

98.7 

99.4 

100.2 

OMOCO 
h   h   N  W 

o  o  o  o 

104.0 
104.8 
105.6 
106.3 

rH    OS    CO    T^ 

^  r^  oo  d 

o  o  o  o 

518 

89.6 
90.3 
91.0 
91.8 

iO   (N   OS   CO 

<n  cd  cd  -r 

OS   OS   OS   OS 

95.4 
96.1 
96.8 
97.5 

98.3 

99.0 

99.7 

100.4 

101.1 
101.9 
102.6 
103.3 

SIS 

COOS'* 

•*  id  id  d 

00   00   00   00 

87.0 
87.7 
88.4 
89.1 

89.8 
90.4 
91.1 
91.8 

iq  tN  oo  iq 
CN   CO  CO   -^5 
OS    OS    OS    OS 

<N   OS  CO  <N 

IO   «!   (6    N 

C-   C-   c.   c 

SIS 

onco  q 
d  d  d  i-J 

CO   <N   OS   "5 

00   X   00  00 

H     OOTfrt 

"t  ■<*  id  d 

X  X  X  X 

86.7 
87.3 
88.0 
88.6 

CN   OS   "3   CN 

d  d  d  i-5 

X   X   OS    OS 

SIS 

00   •*   O   CO 

cd  ■*  id  id 
t-  t>.  t>-  t-» 

CN   00   CO   OS 

d  d  s  s 
t~»  t^  s  r- 

78.5 
79.1 
79.7 
80.3 

80.9 
81.5 
82.1 
82.7 

CO  OS  iq  -h 

cd  cd  >t  id 

X   X   X   X 

SIS 

iq  -<  cq  CN 

oo  d  d  d 

CO  CO  CO  r» 

t>.   CO   00   «* 

O    ~*     H    CN 

s  s  s  s 

OS   iO   O   CO 
CN    CO    •*    rji 
t-   b-   t-    t- 

H   N   CN   00 

id  id  d  d 
i^  t^  h-  b- 

CO  OS  iO  o 

s  ^  x  d 
s  t>.  i>  s 

SIS 

CN   t>.   CO   X 
CO   CO   tj<   Tj< 

CO  cc  CO  CD 

65.3 
65.8 
66.3 
66.8 

CO   X   CO   X 
N   N   00   00 

CO   CO   CO   CO 

"^    OS    "^    OS 

<£  d>  d>  <6 

■^    OS    ^t4    OS 
rH    pH   tN    CN 
1^    t^   S   S 

SIS 

58.0 
58.4 
58.9 
59.4 

00«00N 
»66h 
iO  CO  CO   CO 

S    <N    CO   -J 
i-5    <N    CN   CO- 
CO   CD   CD   CO 

CO  o 

cd  <*    ;    ! 

CO   CD 

SIS 

© 

lO 

csIS 

»I8 

H8 

»I8 

»ta 

«I8 

«I8 

«I8 

H8 

puB  qaAi 
jo  rang 

H«  Hn  <*• 
CO    CO    CO   CO 

-4-f     -*<     <*» 

CN    CN    CM    CN 

CO    CO   CO    CO 

**•  •*•  «*• 
CO   CO    CO    CO 
CO   CO   CO   CO 

co  co  co  co 

-M    -*.    nHi 

*    iO   iO   iO 

co  co  co  co 

Round  and  Square  Bars 


211 


STEEL.  — ROUND    AND    SQUARE   BARS. 

Sectional  Area  in  Inches  x  3.4  =  Weight  per  Lineal  Foot  in  Pounds. 


IP 

S  "  a 

Weight  per 

« 

Weight  per 

Lineal  Foot  in 

i*i 

Lineal  Foot  in 

Pounds. 

Area 

*s« 

Pounds. 

Area 

£  *  w 

OF  lf|  IN 

Sq.  Ins. 

o 

OF  4§&  IN 

Sq.  Ins. 

Round. 

Square. 

Round. 

Square. 

0 

o 

□ 

o 

□ 

0 

To 

2 

A 

10.68 
11.36 

13.60 
14.46 

3.1416 
3.3410 

'    .010 

'    .013 

'  .0031 

| 

.042 

.053 

.0123 

1 

8 

12.06 

15.35 

3.5456 

_3_ 
1  6 

.094 

.119 

.0276 

A 

12.78 

16.27 

3.7583 

J 

.167 

.212 

.0491 

| 

13.51 

17.22 

3.9761 

A 

.261 

.332 

.0767 

A 

14.28 

18.19 

4.2000 

i 

.375 

.478 

.1104 

1 

15.06 

19.18 

4.4301 

A 

.511 

.651 

.1503 

A 

15.86 

20.20 

4.6664 

* 

.667 

.850 

.1963 

1 

16.69 

21.25 

4.9087 

9 

1~S 

.844 

1.076 

.2485 

A 

17.53 

22.33 

5.1572 

f 

1.043 

1.328 

.3068 

f 

18.40 

23.43 

5.4119 

11 

T^ 

1.261 

1.607 

.3712 

ii 

TT 

19.29 

24.56 

5.6727 

} 

1.502 

1.912 

.4418 

i 

20.20 

25.71 

5.9396 

1  3 

T<> 

1.762 

2.245 

.5185 

it 

21.12 

26.90 

6.2126 

i 

2.044 

2.603 

.6013 

I 

22.07 

28.10 

6.4918 

15 
1^> 

2.347 

2.989 

.6903 

if 

23.04 

29.33 

6.7771 

1 

2.670 

3.400 

.7854 

3 

24.01 

30.60 

7.0686 

T~5 

3.014 

3.838 

.8866 

A 

25.04 

31.88 

7.3662 

i 

3.379 

4.303 

.9940 

1 

26.08 

33.20 

7.6699 

A 

3.766 

4.795 

1.1075 

A 

27.13 

34.55 

7.9798 

1 

4.173 

5.312 

1.2272 

i 

28.20 

35.91 

8.2958 

A 

4.600 

5.857 

1.3530 

A 

29.30 

37.31 

8.6179 

§ 

5.049 

6.428 

1.4849 

i 

30.41 

38.73 

8.9462 

A 

5.518 

7.026 

1.6230 

A 

31.55 

40.18 

9.2806 

4 

6.008 

7.650 

1.7671 

i 

32.71 

41.65 

9.6211 

A 

6.520 

8.301 

1.9175 

9 

33.89 

43.15 

9.9678 

f 

7.051 

8.978 

2.0739 

f 

35.09 

44.68 

10.321 

H 

7.604 

9.682 

2.2365 

tt 

36.31 

46.24 

10.680 

f 

8.178 

10.41 

2.4053 

i 

37.55 

47.82 

11.045 

II 

8.773 

11.17 

2.5802 

it 

38.81 

49.42 

11.416 

1 

9.388 

11.95 

2.7612 

i 

40.10 

51.05 

11.793 

it 

10.024 

12.76 

2.9483 

H 

41.40 

52.71 

12.177 

212 


The  Naval  Constructor 


STEEL.  — ROUND    AND    SQUARE    BARS. 

Sectional  Area  in  Inches  x  3.4  =  Weight  per  Lineal  Foot  in  Pounds. 


g 

Weight  per 

M 

Weight  per 

Lineal 

Foot  in 

.'.  H  £ 

Lineal  Foot  in 

w  w  2 
fi  S  » 

Pounds. 

Area 

o 

Pounds. 

Area 

0 

OF©  IN 

Sq.  Ins. 

OF  (D  IN 

Sq.  Ins. 

Round. 

o 

Square. 
□ 

Round. 

o 

Square. 
□ 

4 

42.72 

54.39 

12.566 

6 

96.1 

122.4 

28.274 

tV 

44.07 

56.11 

12.962 

A 

98.1 

125.0 

28.866 

| 

45.44 

57.85 

13.364 

i 

100.2 

127.6 

29.465 

3 

46.83 

59.62 

13.772 

a 

102.2 

130.2 

30.069 

| 

48.23 

61.41 

14.186 

i 

104.3 

132.8 

30.680 

A 

49.66 

63.23 

14.607 

A 

106.4 

135.5 

31.296 

1 

51.11 

65.08 

15.033 

108.5 

138.2 

31.919 

A 

62.58 

66.95 

15.466 

A 

110.7 

140.9 

32.548 

| 

54.07 

68.85 

15.904 

} 

1128 

143.6 

33.183 

A 

55.59 

70.78 

16.349 

A 

115.0 

146.5 

33.824 

t 

57.12 

72.72 

16.800 

t 

117.2 

149.2 

34.472 

ft 

58.67 

74.70 

17.257 

ft 

119.4 

152.1 

35.125 

1 

60.25 

76.71 

17.721 

i 

121.7 

154.9 

36.786 

H 

61.84 

78.74 

18.190 

ft 

123.9 

157.8 

36.450 

I 

63.46 

80.80 

18.665 

I 

126.2 

160.7 

37.122 

« 

65.10 

82.89 

19.147 

if 

128.5 

163.6 

37.800 

5 

66.76 

85.00 

19.635 

7 

130.9 

166.6 

38.485 

A 

68.44 

87.14 

20.129 

A 

133.2 

169.6 

39.175 

| 

70.13 

89.30 

20.629 

1 

135.6 

172.6 

39.871 

ft 

71.86 

91.49 

21.135 

A 

137.9 

175.6 

40.574 

i 

73.60 

93.72 

21.648 

i 

140.4 

178.7 

41.282 

A 

75.37 

95.96 

22.166 

A 

142.8 

181.8 

41.997 

¥ 

77.15 

98.22 

22.691 

A 

145.2 

184.9 

42.718 

A 

78.95 

100.5 

23.221 

147.7 

188.1 

43.445 

i 

80.77 

102.8 

23.758 

} 

150.2 

191.3 

44.179 

A 

82.62 

105.2 

24.301 

A 

152.7 

194.4 

44.918 

1 

84.48 

107.6 

24.850 

I 

155.2 

197.7 

45.664 

ft 

86.38 

110.0 

25.406 

ft 

157.8 

200.9 

46.415 

? 

88.29 

112.4 

25.967 

i 

160.3 

204.2 

47.173 

8 

90.22 

114.9 

26.535 

if 

163.0 

207.6 

47.937 

1 

92.16 

117.4 

27.109 

i 

165.6 

210.8 

48.707 

ft 

94.14 

119.9 

27.688 

it 

168.2 

214.2 

49.483 

Steel  Weights 


213 


WEIGHTS.  —  Half-Round,  Hollow  Half-Round, 
Edge,  and  Convex. 


Feather 


SiziT'- 

Weight 

Size. 

Weight 

DESCRIP- 
TION. 

per 
Lineal 
Foot. 

Descrip- 
tion. 

per 
Lineal 
Foot. 

Breadth. 

Thick- 
ness. 

Breadth. 

Thick- 
ness. 

6 

3 

48.07 

%\ 

1 

7.17 

6} 

5 
4i 

2f 

40.39 
33.38 
27.04 

if 
I 

6.64 
6.11 

4 

2 

21.36 

2J 

it 

5.58 

8i 

lj 

18.78 

21 

f 

5.05 

ft          ^. 

3i 

If 

16.36 
14.11 
12.02 

2J 
2* 

1 

4.52 
3.98 

i  im%> 

2| 

i| 

10.10 

2 

f 

4.30 

%  ^H 

2i 

if 

8.34 

2 

f 

3.45 

w 

2i 
2 

« 

6.75 
5.34 

2 

A 

3.03 

If 

2 

4.09 

H 

2 

i 

2.60 

ii 

f 

3.00 

If 

f 

3.76 

if 

f 

2.09 

w 

If 

1 

3.02 

i 

| 

1.34 

If 

A 

2.65 

4 

H 

18.36 

H    l§§ 

If 

} 

2.28 

«     .— 

8f 
8§ 

l 

15.78 
13.36 

n 

f 

3.25 

8* 

A 

8.83 

05      \g 

n 

i 

2.62 

j  ph  fa 

3* 

} 

8.01 

i* 

A 

2.30 

J2  A  \L 

H 

I 

7.35 

ii 

§ 

1.98 

W  J  ^s, 

3 

1 
| 

6.68 

t» 

2| 

5.34 

O 

ii 

f 

2.99 

2 

I 

3.26 

O 

ii 

ii 

2.70 

H 

| 

2.25 

ii 
if 

1 

A 

2.41 
2.12 

2* 

I 

3.73 

2* 

i 

2.98 

if 

1.82 

« 

2i 
2 

1 

§ 

2.69 
2.39 

1.72 

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2 

A 

2.09 

n 

tV 

1.46 

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2 

1 

1.79 

ij 

§ 

1.19 

1 

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if 

I 

i 
i 

1.57 
1.34 
1.23 

i 
A 

1.56 
1.32 

if 

B 

.93 

l 

1 

1.09 

i| 

A 

.85 

214 


The  Naval  Constructor 


WEIGHT    OF    SHEET   STEEL. 


0000 

Birmingham  Wibk 
Gauge  and  Englihh 

American  (B.  &  S.) 

New  U.S.  Stand- 

Standard Gauge. 

Wire  Gauge. 

ard  Gauge,  1873. 

Thickness 

Weight 

Thickness 

\v«iuht 

Thickness 

WoiRht 

in  Inches. 

per  Sq.  Ft. 

in  Inches. 

per  Sq.  Ft. 

in  Inches. 

per  Sq.  Ft. 

.454 

18.62 

.460 

18.76 

.406 

16.58 

000 

.425 

17.34 

.410 

16.72 

.375 

15.30 

00 

.380 

15.50 

.365 

14.88 

.344 

14.03 

0 

.340 

13.87 

.325 

13.26 

.313 

12.75 

1 

.300 

12.2-4 

.289 

11.80 

.281 

11.48 

2 

.284 

11.59 

.258 

10.52 

.266 

10.84 

3 

.259 

10.56 

.229 

9.36 

.250 

10.20 

4 

.238 

9.71 

.204 

8.33 

.234 

9.56 

5 

.220 

8.98 

.182 

7.42 

.219 

8.93 

6 

.203 

8.28 

.162 

6.61 

.203 

8.29 

7 

.180 

7.34 

.144 

5.88 

.188 

7.65 

8 

.165 

6.73 

.129 

5.24 

.172 

7.01 

9 

.148 

6.04 

.114 

4.66 

.156 

6.38 

10 

.134 

5.47 

.102 

4.15 

.141 

5.74 

11 

.120 

4.89 

.091 

3.70 

.125 

6.10 

12 

.109 

4.44 

.081 

3.29 

.109 

4.46 

13 

.095 

3.87 

.072 

2.93 

.094 

3.83 

14 

.083 

3.38 

.064 

2.61 

.078 

3.19 

15 

.072 

2.94 

.057 

2.32 

.070 

2.87 

16 

.065 

2.65 

.051 

2.07 

.063 

2.55 

17 

.058 

2.37 

.045 

1.84 

.056 

2.30 

18 

.049 

1.99 

.040 

1.64 

.050 

2.04 

19 

.042 

1.71 

.036 

1.46 

.044 

1.79 

20 

.035 

1.42 

.032 

1.30 

.038 

1.53 

21 

.032 

1.30 

.028 

1.16 

.034 

1.40 

22 

.028 

1.14 

.025 

1.03 

.031 

1.28 

23 

.025 

1.02 

.023 

0.921 

.028 

1.15 

24 

.022 

0.898 

.020 

0.821 

.025 

1.02 

25 

.020 

0.816 

.018 

0.729 

.022 

0.89 

26 

.018 

0.734 

.016 

0.651 

.019 

0.77 

27 

.016 

0.653 

.014 

0.581 

.017 

0.70 

28 

.014 

0.571 

.013 

0.515 

.016 

0.64 

29 

.013 

0.531 

.011 

0.459 

.014 

0.57 

30 

.012 

0.489 

.010 

0.409 

.013 

0.51 

31 

.010 

0.408 

.009 

0.364 

.011 

0.45 

32 

.009 

0.367 

.008 

0.324 

.010 

0.41 

33 

.008 

0.326 

.007 

0.288 

.009 

0.38 

34 

.007 

0.286 

.006 

0.257 

.009 

0.35 

35 

.005 

0.204 

.006 

0.228 

.008 

0.32 

36 

.004 

0.162 

.005 

0.204 

.007 

0.29 

Weight  of  Bulb-angle 


l 


215 


aia 


sis 


218 


518 


l-tl  • 


SIS 


218 


118 


518 


SI8 


b-    O) 

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•  COO  N  h  i(5  00  ^HiOOCO  qcot^.r-4 
•iO«D      iO   CO   CO   CO      CO   CO   CO   N      N   S  S  00 


»I8 


-<*  -^  -#  U5   ^  -t  1(5  lO   K5  K5  1(5  (O   CO  lO  CO  CO 


■18 


N  IN  N  N   !00(OU5   ^  CO  05  «   0)0)0)0   U5  lO  ■* 

n  o  M  (o    qncq  a    t^  o  cq  cq    occcdo)    n  q  m 

CO   ^   ■*   tJH      tJ?^-*-"*      t)5io»0«5      K5  io   iO  i(j      lO   CO  CO 


CO    CO   CO    -tf 


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216 


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The  Naval  Constructor 


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ft 
H 

P 
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s 

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218 

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13.64 

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CN    CO   CO    'f 

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9.74 
10.21 
10.67 
11.14 

10.27 
10.73 
11.20 
11.67 

11.28 
11.75 
12.22 
12.68 

11.84 
12.31 
12.77 
13.24 

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Tf    N   OS 
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00  00  00  OS 

9.03 

9.45 

9.88 

10.30 

9.51 

9.94 

10.36 

10.79 

10.44 
10.87 
11.29 
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t^   t^  00   00 

8.29 
8.68 
9.06 
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8.74 
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9.58 

9.96 

10.36 

10.73 

10.05 
10.44 
10.82 
11.20 

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7.95 
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4.72 
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5.47 
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Weight  of  Bulb-angle 


217 


w 

o 

CO 

tn 

H 

a 

H 

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W 

M 

3 

818 

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5;I8 

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818 

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h  «  m  co 

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19.38 
20.02 
20.66 
21.29 

NOtIOO 
N   ^J   O    O 
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IN    IN    (N    CN 

5518 

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CO   IN    00   "^ 

»0    »0    ■*    •* 
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©   ON    00 

CN     IN     -I     r-H 

tfi    N    00   ■* 

N  oo  oo  oi 

18.31 
18.90 
19.50 
20.09 

19.61 
20.20 
20.80 
21.39 

sis 

14.73 
15.28 
15.84 
16.39 

ffl    A    O   "5 

co  q  »o  © 

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16.58 
17.13 
17.68 
18.24 

«    NM    00 
CN    N   CO   00 
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18.44 
18.99 
19.54 
20.09 

218 

O   h   N   M 
00   CO    00   CO 

co  ■*  tj5  io 

^  os  t^  os 
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15.52 
16.03 
16.54 
17.05 

CN    CO    Tji    IO 

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d  d  t^  t^ 

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sis 

■*   H   00   U5 
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CN    CO   CO    -t 

13.42 
13.89 
14.36 
14.82 

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218 

11.88 
12.30 
12.73 
13.15 

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13.86 
14.28 
14.71 
15.13 

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L1.27 
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3.57 
3.96 
4.34 
4.72 

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218 


The   Naval  Constructor 


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218 

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22.67 
23.35 
24.03 
24.71 

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CN   CN    CN    CN 

25.02 
25.70 
26.38 
27.06 

26.58 
27.26 
27.94 
28.62 

28.20 
28.88 
29.56 
30.24 

SIS 

21.49 
22.13 
22.77 
23.41 

22.24 
22.88 
23.52 
24.15 

23.72 
24.35 
24.99 
25.63 

25.19 
25.83 
26.47 
27.10 

26.73 
27.36 
28.00 
28.64 

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21.59 
22.19 
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23.78 
24.37 
24.97 
25.56 

25.23 
25.82 
26.42 
27.01 

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20.29 
20.85 
21.40 

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22.35 
22.90 
23.46 
24.01 

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17.85 
18.36 
18.87 
19.38 

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19.69 
20.20 
20.71 
21.22 

20.91 
21.42 
21.93 
22.44 

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11.88 
12.13 
12.39 
12.64 

12.65 
12.90 
13.16 
13.41 

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8.74 
8.96 
9.17 
9.38 

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Weight  of  Bulb-angle  TJ219 


H 
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to 

to 

h 

0 

02 

H 

H 

9 

H 
to 

S 

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to 
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39.74 
40.55 
42.16 

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41.62 
42.43 
44.05 

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37.97 

38.74 
40.26 

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39.77 
40.53 
42.07 

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9 

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co 

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36.19 
36.91 
38.35 

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37.90 
38.62 
40.07 

5 

00 
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co  oq 
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34.38 
35.06 
36.42 

CO 
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id 

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36.01 
36.69 
38.05 

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52.32 
53.17 
54.02 
55.72 

54.36 
55.21 
56.06 
57.76 

56.42 
57.27 
58.12 
59.82 

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44.62 
45.42 
46.23 
47.85 

48.16 
48.96 
49.77 
51.39 

50.10 
50.91 
51.72 
53.33 

52.06 
52.86 
53.67 
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49.07 

47.87 
48.63 
49.40 
50.93 

49.74 
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51.27 
52.80 

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48.50 

47.40 
48.12 
48.84 
50.29 

49.20 
49.93 
50.65 
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38.62 
39.30 
39.98 
41.34 

41.65 
42.33 
43.01 
44.37 

43.34 
44.02 
44.70 
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45.04 
45.72 
46.40 
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30.40 
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28.30 
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30.48 
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26.18 
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28.42 
30.52 
32.05 
34.25 

35.78 
37.96 
39.49 
41.78 

43.31 
45.63 
47.16 
49.55 

51.08 
53.54 
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59.10 
61.71 
63.24 
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26.97 
28.99 
30.43 
32.55 

33.99 
36.09 
37.53 
39.74 

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43.42 
44.86 
47.18 

48.62 
50.99 
52.44 
54.85 

56.30 
58.82 
60.27 
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25.53 
27.46 
28.82 
30.85 

32.21 
34.22 
35.58 
37.70 

39.06 
41.21 
42.57 
44.80 

46.16 
48.45 
49.81 
52.13 

53.49 
55.93 
57.29 
59.76 

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30.42 
32.35 
33.62 
35.66 

36.93 
39.00 
40.27 
42.42 

43.69 
45.90 
47.17 
49.42 

50.69 
53.04 
54.32 
56.70 

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22.64 
24.40 
25.59 
27.45 

28.64 
30.48 
31.67 
33.62 

34.81 
36.79 
37.98 
40.04 

41.23 
43.35 
44.54 
46.70 

47.89 
50.16 
51.35 
53.64 

SIS 

21.19 
22.87 
23.97 
25.75 

26.85 
28.61 
29.71 
31.58 

32.68 
34.58 
35.68 
37.66 

38.76 
40.80 
41.90 
43.98 

45.08 
47.27 
48.37 
50.59 

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19.75 
21.34 
22.36 
24.05 

25.07 
26.74 
27.76 
29.54 

30.54 
32.37 
33.39 
35.28 

36.24 
38.25 
39.27 
41.26 

42.28 
44.38 
45.40 
47.53 

SIS 

18.30 
19.81 
20.74 
22.35 

23.28 
24.87 
25.80 
27.50 

28.43 
30.16 
31.09 
32.90 

33.83 
35.70 
36.63 
38.54 

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16.86 
18.28 
19.13 
20.65 

21.50 
23.00 
23.85 
25.46 

26.31 
27.95 
28.80 
30.52 

31.37 
33.15 
34.00 

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15.41 
16.75 
17.51 
18.95 

19.71 
21.13 
21.89 
23.42 

24.18 
25.74 
26.50 
28.14 

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18.95 
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CN    CN 

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CO    ■* 
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id 

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CN    CO    O   iO 

q  cn  q  ■* 
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CN    CN    CN    <N 

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CN     CN     rH     rH 

CD   O)   N    00 

oo  oo  a  d 

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CO   CO 
CN    iO 

CN    CN 

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CN    CN 

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CN    CN 

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ci 

CI 

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re 
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ci 

OS 

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01 

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OS 

ci 

CI 

X 
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CO 
CI 

M   M    M   N 

H^N^ 

CO    CO   CO    Tj" 
CN    CN    CN    CN 

»IS 

CO    q    CO   CO 

cco'c'n 

IQ 

b-  CN 
N  q 

N    00 

CO 
X 

*I8 

<*IS 

(•bhi) 

•aSuBU  jo 

hX>  «x>  •*»  -*o 
W5   iO  "O   CO 

LO 

iO   iO 

2 

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to 

IO 

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OS 

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OS 

:    : 

: 

:    : 

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a 

: 

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- 

o   -      -      - 

228 


T 


The  Naval  Constructor 


I 

y 

< 

h 
O 

00 

9 

H 

H 

B 
n 
a 
is 

H 

i 

u 

3 

818 

62.10 
62.95 
63.80 
66.35 

64.65 
65.50 
66.35 
68.05 

67.11 
67.96 
68.81 
70.51 

68.81 
69.66 
70.51 
72.21 

71.29 
72.14 
72.99 
74.69 

SIS 

59.21 

60.02 
60.82 
63.24 

61.63 
62.43 
63.24 
64.85 

64.01 
64.81 
65.62 
67.23 

65.62 
66.42 
67.23 
68.84 

68.03 
68.83 
69.64 
71.25 

SIS 

56.32 
57.08 
57.85 
60.14 

58.61 
59.38 
60.14 
61.67 

60.90 
61.67 
62.43 
63.96 

62.43 
63.20 
63.96 
65.49 

64.75 
65.52 
66.28 
67.81 

1518 

53.43 
54.15 
54.87 
57.04 

55.59 
56.31 
57.04 
58.48 

58.80 
58.52 
59.25 
60.69 

59.24 
59.96 
60.69 
62.13 

61.48 
62.20 
62.93 
64.37 

sis 

50.54 
51.22 
51.90 
53.94 

52.58 
53.26 
53.94 
55.30 

54.70 
55.38 
56.06 
57.42 

56.06 
56.74 
57.42 

58.78 

58.21 
58.89 
59.57 
60.93 

SIS 

47.65 
48.29 
48.92 
50.84 

49.56 
50.19 
50.83 
52.11 

51.60 
52.23 
52.87 
54.15 

52.87 
53.50 
54.14 
55.42 

54.94 
55.57 
56.21 
57.49 

218 

CO    to    lO   CO 

t>.  co  q  t>- 

•ji    tfj   to   N 

46.54 
47.14 
47.73 
48.92 

48.49 
49.09 
49.68 
50.87 

49.68 
50.28 
50.87 
52.06 

51.66 
52.26 
52.85 
54.04 

SIS 

NCI    NM 
X  ■*  OS  CO 
i-5   tN   <N   rji 

■>t     •*     •*     HI 

43.52 
44.07 
44.63 
45.73 

45.39 
45.94 
46.50 
47.60 

46.49 
47.04 
47.60 
48.70 

48.39 
48.94 
49.50 
50.60 

SIS 

38.98 
39.49 
40.00 
41.53 

rH    (N     CO    lO 

to  q  to  to 

O    rH    rH    (N 

T«     -HH     Tf     T* 

42.29 
42.80 
43.31 
44.33 

43.29 
43.80 
44.31 
45.33 

CN    CO    ■*    CO 

rH    q    rH     rH 

lOilifON 

^1     *^1    ^1    ^4 

SIS 

36.09 
36.56 
37.02 
38.43 

37.49 
37.95 
38.42 
39.36 

39.19 
39.65 
40.12 
41.06 

40.12 
40.58 
41.05 
41.99 

tO     rH     X     CN 

OOtCNN 
r-I   IN    IN    CO 

^       "^       ^       ^* 

SIS 

O   <N    to    <N 

<n  q  q  co 
CO  CO  -^  to" 

CO    CO   CO    CO 

34.47 
34.90 
35.32 
36.17 

36.08 
36.51 
36.93 

37.78 

36.93 
37.36 
37.78 
38.63 

38.57 
39.00 
39.42 
40.27 

«I8 

30.31 
30.69 
31.07 
32.22 

31.45 
31.83 
32.22 
32.98 

32.98 
33.36 
33.75 
34.51 

33.74 
34.12 
34.51 
35.27 

35.30 
35.68 
36.07 
36.83 

•IS 

27.42 
27.76 
28.10 
29.12 

t«   X  <N    O 

■*     t>.    rH     X 

x  oo  d  d 

IN    <N    (N    IN 

H8 

•18 

■a  18 

"IS 

'     (-8UI) 

CO   CD   CO   t» 

CO   CO   CO   t^ 

CO   CD    CD   t» 

CO    CO    CO   b- 

CD    CO    CD   b- 

(•sny) 

2:    :   : 

rfr 

CN    .      .      . 

r* 

tN    -      .      . 

CO   .      .      . 

Weight  of  Bulb-Tee 


-T229 


to 

o 

02 
ft 

H 
W 
H 
W 

H 

30 

as 

W 
K 
M 
p 

ft 
H 

SIS 

OS    ^    OS    OS 

q  oo  q  co 
CN   CO  ■*   d 
t*.  t.  t^  t^ 

CO   i-H    CO   CD 
iq  -tf  IN  q 
uj   ON    00 
N   l>   N   N 

©  rH   ©   © 

N  h  q  © 

NCCOOO 

b-  n  t^  oo 

©  ^  ©  © 

00   t>   lO   IN 

oo  ©  rH  co 

l>    00    00    00 

©     ■"*!     ©     © 

iq  -<*  cn  © 

h  ci  »  ^i 

00    00    00    00 

SIS 

■<t  •*  io  co 
q  •*  <n  oo 

«  6  ri  ci 

CO   N   N    S 

<N    CN    CO    tJ4 
i-i    OS    l>   CO 
CN    <N    CO    IO 
t^    |>    t^   t^ 

■*   -^   lO   © 

NiO   «  O 

co  ■<*'  »d  © 
i>  t^  t^  t^ 

00    00   ©   © 

CN  ©  oo  iq 
d  n  N  © 
t-  N  N.  J> 

77.90 
78.70 
79.51 
81.12 

SIS 

66.28 
67.05 
67.81 
69.34 

N^    OCC 
*il«N 
OOftOH 
CO   CO   N   N 

©   t>.   CO    © 
CN    ©   N   CN 

©    ©    i-i    CO 

N  N  N  t> 

©    CO    ©    CN 

q  ■*  ih  i> 

CN   CO   Tt<   »d 
N  N  N  N 

74.19 
74.96 
75.72 
77.25 

fcIS 

IN    ■*    N    i-H 

q  q  co  oo 

<N    CO    tj5    id 

CO    CO    CD    CD 

65.24 
65.96 
66.69 
68.13 

00   O   M   N 

q  -^  tH  iq 

©  i>  oo  © 

©  ©  ©  © 

iO   N  O  iji 
©  t>  iq  © 

©  d  ©  i-h 
©  ©  N  t» 

©    IN    lO   © 
IO    CN    ©   CO 

d  ^  i-l  co 
N  I>  N  N 

SIS 

N   »C   «   OS 
lO   N   »   N 

d  d  d  <n" 

iO   CD   CD   CO 

61.80 
62.48 
63.16 
64.52 

63.16 
63.84 
64.52 
65.88 

65.45 
66.13 
66.81 
68.17 

HO)   NM 
00   r)J    rH    iq 

©   t^   00   © 

©   ©    ©   © 

SIS 

56.21 
56.84 
57.48 
58.76 

CO   OS   M    H 

cq  q  q  q 
oo  oo  d  d 
iO  io  iO  CO 

59.63 
60.26 
60.90 
62.18 

61.84 
62.47 
63.11 
64.39 

63.11 
63.74 
64.38 
65.66 

SIS 

io  m  -#  co 

0C*   ON 
CN    CO    ■<*    id 
iO   «5   "5   lO 

rH     I-H     O    OS 

O)   lO   rt   CN 

«:  io  io  >o 

56.10 
56.70 
57.29 
58.48 

58.22 
58.82 
59.41 
60.60 

59.41 
60.01 
60.60 
61.79 

SIS 

49.49 
50.04 
50.60 
51.70 

51.47 
52.02 
52.58 
53.68 

NO    00   00 

»q  r-j  q  n 

IN    CO    CO    tJH 

w  iO  >o  >o 

54.61 
55.16 
55.72 
56.82 

rt    ©   CN    CN 
N    CN    00   © 

>0   d    (O   N 

lO    lO   lO    lO 

SIS 

■*    iO    CO   00 

rH    ©    i-H    i-H 

CO    ■<*    iO    N 
©  iq  ©  © 

oo  oo  d  © 
■*  ^  ■*  >o 

48.99 
49.50 
50.01 
51.03 

51.00 
51.51 
52.02 
53.04 

CN    CO    ■*    © 
©    iO    ©    © 
CN    CN    CO   Tj5 
lO    iO    lO   lO 

SIS 

00    "*     rH     IO 

t>-  <N   J>  CO 

CN    CO    CO    -tf 
^    ^    ^    ^ 

©   IO    <N    © 

iO  ©  «o  -* 
■*  io  d  d 

<N    00   lO   © 
iq   ©   ■>*   CO 

id  id  ©  t>^ 

©    iO   <N    © 
CO    00   CO    <N 
N   N    00O) 

48.32 
48.78 
49.25 
50.19 

SIS 

39.42 
39.85 
40.27 
41.12 

41.14 
41.57 
41.99 
42.84 

©    <N    ■*    © 
©   ^   00   © 
H    <N    CN    CO 

43.77 
44.20 
44.62 
45.47 

N    115    NO 

©   ©    •*    CO 

■>*  id  id  © 

•IS 

co  ■*  co  os 
q  >t  oq  kj 

CO    CO    CO    CO 

ooosw 

N   ©    ■>*<    <N 
S   00  00  oi 

CO    CO    CO    CO 

•IS 

HS 

•IS 

•IS 

*IS 

(•sui) 
•eSuBU  jo 

*+»  H*>  mr«  -+• 
CD    CD    CO   t^ 

H«  -+>  <+«  -+• 

©  ©  ©  t~ 

r+,    Ht.    <+.    r+t 
©     ©     ©     I> 

H>  Hn  c*«  -+• 
©    ©    ©    N 

-+*  He*  «H  H-« 
©    ©    ©    t> 

(•8UI) 

«  :    :    : 

"*  :    :    : 

P+1 

■*  :    :    : 

lO  -     :     - 

•  :    :    : 

t-H 

230' 


The  Naval  Constructor 


to 

to 

-< 

fa 
0 

05 

s 

H 
H 
H 

to 

fa 

H 

>5 

as 
cc 
H 
to 

H 

SIS 

84.26 
85.11 
85.96 
87.66 

85.96 
86.81 
87.66 
89.36 

88.74 
89.59 
90.44 
92.14 

89.44 
90.29 
91.14 
92.84 

93.25 
94.60 
94.95 

96.65 

SIS 

80.48 
81.28 
82.09 
83.70 

82.10 
82.90 
83.71 
85.32 

84.79 
85.59 
86.40 
88.01 

86.41 
87.21 
88.02 
89.63 

89.13 
89.93 
90.74 
92.35 

SIS 

OS    CO   <N    lO 

q  •«*  <n  t» 

(OSXO) 

h-  t-  b-  I» 

78.22 
78.99 
79.75 
81.28 

80.83 
81.60 
82.36 
83.89 

82.36 
83.13 
83.89 
85.42 

85.00 
85.77 
86.53 
88.06 

SIS 

72.91 
73.63 
74.36 
75.80 

74.36 
75.08 
75.81 
77.25 

76.88 
77.60 
78.33 
79.77 

CO   «5   X   <N 

M   ONN 

o6  oi  a>  ** 

t-  t-   t-  X 

80.88 
81.60 
82.33 
83.77 

SIS 

69.13 
69.81 
70.49 
71.85 

70.49 
71.17 
71.85 
73.21 

eo  -i  os  io 
q  q  <n  q 
cn  eo  ■*  »o 
t»  r>-  t^.  t» 

OS   h-   iG   i-h 

<n  q  q  q 

■^   tj"   io   j>I 

r>.  r^  ^  t- 

CO  ^f   CN    X 

*1  "*  ■"!  ** 

C9N00O 

t-  t-  t»  h- 

SIS 

65.36 
65.99 
66.63 
67.91 

66.63 
67.26 
67.90 
69.18 

68.98 
69.61 
70.25 
71.53 

70.26 
70.89 
71.53 
72.81 

72.64 
73.27 
73.91 
75.19 

SIS 

l»  b-   CO   >0 

«3HNO> 
H   fi   N   M 
CO   CO   CO    CO 

CO   CO   iO   ■* 

N   CO   CS   rt 

<N    CO   CO    1C 

CO   CO  CO   CO 

65.03 
65.63 
66.22 
67.41 

66.22 
66.82 
67.41 
68.60 

68.51 
69.11 
69.70 
70.89 

SIS 

57.79 
58.34 
58.90 
60.00 

58.89 
59.44 
60.00 
61.10 

61.08 
61.63 
62.19 
63.29 

X   CO    OS   OS 
H    1^   IN    CO 
CN    CN    CO    ^ 

CO  CO  CO  CO 

©   lO   <-"    " 

Tf»ioe 

•«t    Tj<    ic"    d 

CO  CO   CO   CO 

SIS 

54.01 
54.52 
55.03 
56.05 

55.03 
55.54 
56.05 
57.07 

M    ^   "ON 

rt     O     rH     fH 

i^  t^l  oo  d 

IQ    1Q    IC    1Q 

58.15 
58.66 
59.17 
60.19 

60.28 
60.79 
61.30 
62.32 

SIS 

50.23 
50.69 
51.16 
52.10 

51.16 
51.62 
52.09 
53.03 

SIS 

•fa 

«I8 

'-IS 

«I8 

*ia 

•*is 

(•sui) 

•93UBU  JO 

CO    CO    CO    t» 

co  co  co  r^ 

CO    CO    CO    t^ 

CO   CO    CD   Is- 

co  co  co  t> 

(•8UI) 

•itfdaci 

CO      ;.            ;.             j 

•4i 

**S    -8   > 

t^  3     »     - 

*-'•: 

Weight  of  Steel   Hollow  Pillars         231 


Outside  Diameter. 

Thickness. 

Weight 

in  Lbs. 

per  Lin. 

Foot. 

Inches. 

Millimetres. 

Parts  of 
an  Inch. 

Decimals  of 
an  Inch. 

Millimetres. 

U 

64 

1 

0.25 

6.34 

6.01 

24 

64 

ft 

0.3125 

7.93 

7.30 

21 

70 

1 

0.25 

6.34 

6.68 

2} 

70 

6 
IB 

0.3125 

7.93 

8.14 

3 

77 

1 

0.25 

6.34 

7.34 

3 

77 

A 

0.28125 

7.14 

8.17 

3 

77 

r 

0.3125 

7.93 

8.97 

3 

77 

0.375 

9.52 

10.51 

H 

83 

f 

0.28125 

7.14 

8.93 

1 

83 

0.375 

9.52 

11.52 

89 

t 

0.28125 

7.14 

9.68 

34 

89 

0.375 

9.52 

12.52 

3f 

95 

f 

0.28125 

7.14 

10.43 

3| 

95 

0  375 

9.52 

13.52 

4 

102 

A 

0.3125 

7.93 

12.31 

4 

102 

fB 

0.4375 

11.11 

16.65 

41 

108 

ft 

0.3125 

7.93 

13.14 

41 

108 

ft 

0.4375 

11.11 

17.82 

44 

115 

ft 

0  3125 

7.93 

13.98 

44 

115 

ft 

0.4375 

11.11 

18.98 

4f 

121 

0.3125 

7.93 

14.01 

4| 

121 

ft 

0.4375 

11.11 

20.15 

5 

127 

ft 

0.3125 

7.93 

15.65 

5 

127 

ft 

0.4375 

11.11 

21.32 

5* 

140 

ft 

0.3125 

7.93 

17.32 

54 

140 

p 

0.4375 

11.11 

23.66 

51 

146 

i 

0.375 

9.52 

21.53 

5| 

146 

4 

0.5 

12.69 

28.04 

6 

153 

1 

0.375 

9.52 

22.53 

6 

153 

f 

0.40625 

10.31 

24.29 

6 

153 

0.5 

12.69 

29.37 

6 

153 

ft 

0.5625 

14.28 

32.67 

61 

159 

y 

0.40625 

10.31 

25.37 

i 

159 

ft 

0.5625 

14.28 

34.17 

166 

y 

0.40625 

10.31 

26.46 

64 

166 

a 

0.5625 

14.28 

35.67 

6! 

171 

0.40625 

10.31 

27.54 

61 

171 

ft 

0.5625 

14.28 

37.18 

7 

178 

4i 

'0.40625 

10.31 

28.63 

7 

178 

41 

0.46875 

11.90 

32.72 

7 

178 

32 

0.5625 

14.28 

38.68 

7 

178 

0.625 

15.87 

.42.56 

74 

191 

0.46875 

11.90 

35.22 

74 

191 

f 

0.625 

15.87 

45.90 

71 

197 

J 

0.46875 

11.90 

36.47 

71 

197 

0.625 

15.87 

47.57 

8 

203 

f 

0.46875 

11.90 

37.73 

8 

203 

0.625 

15.87 

49.23 

84 

216 

1 

0.46875 

11.90 

40.23 

84 

216 

0.5 

12.69 

42.73 

84 

216 

! 

0.625 

15.87 

52.57 

1 

216 

I* 

0.6875 

8.73 

57.38 

222 

0.5 

12.69 

44.06 

81 

222 

h 

0.6875 

8.73 

59.21 

9 

229 

0.5 

12.69 

45.40 

9 

229 

ii 

0.6875 

8.73 

1     61.04 

232 


The  Naval   Constructor 

WEIGHT   OF   STEEL  ANGLES 


Thickness  in 

Deci- 

Sum  of 

Flanges. 

0 

.10 

0.12 

0.14 

0.16 

0.18 

0.20 

0.22 

0.24 

0.26 

0.28 

Thickness  in 

Inches. 

Milli- 

metres. 

2 

.78 

3.18 

3.57 

3.97 

4.76 

5.16 

5.56 

5.95 

6.75 

7.14 

2 

51       ( 

l  .65 

0.77 

0.89 

1.00 

1.11 

122 

1.33 

1.44 

1.54 

1.64 

2 

54       ( 

).6<> 

0.82 

0.94 

1.07 

1.19 

1.31 

1.42 

1.54 

1.65 

1.76 

2 

57       < 

J. 73 

0.87 

1.00 

1.14 

1.27 

1.39 

1.52 

1.64 

1.76 

1.88 

2 

60       < 

).77 

0.92 

1.06 

1.20 

1.34 

1.48 

1.61 

1.74 

1.87 

1.99 

2 

64       ( 

>.S2 

0.97 

1.12 

1.27 

1.42 

1.56 

1.71 

1.84 

1.98 

2.11 

2 

67       ( 

1.86 

1.02 

1.18 

1.34 

1.50 

1.65 

1.80 

1.95 

2.09 

2.23 

2 

70       ( 

1.90 

1.07 

1.24 

1.41 

1.57 

1.73 

1.89 

2.05 

2.20 

2.35 

2 

73 

1.94 

1.12 

1.30 

1.48 

1.65 

1.82 

1.99 

2.15 

2.31 

2.47 

3 

77 

1.18 

1.36 

1.54 

1.73 

1.90 

2.08 

2.25 

2.42 

2.59 

3i 

79 

1.23 

1.42 

1.61 

1.80 

1.99 

2.17 

2.35 

2.53 

2.71 

3i 

83 

1.28 

1.48 

1.68 

1.88 

2.07 

2.27 

2.46 

2.64 

2.83 

3} 

86 

1.33 

1.54 

1.75 

1.96 

2.16 

2.36 

2.56 

2.75 

2.95 

ti 

89 

1.38 

1.60 

1.82 

2.03 

2.24 

2.45 

2.66 

2.86 

3.07 

3 

92 

1.43 

1.66 

1.88 

2.11 

2.33 

2.55 

2.76 

2.97 

3.18 

3} 

95 

1.48 

1.72 

1.95 

2.18 

2.41 

2.64 

2.86 

3.09 

3.30 

9 

98 

1.53 

1.78 

2.02 

2.26 

2.50 

2.73 

2.97 

3.20 

3.43 

4 

102 

1.84 

2.09 

2.34 

2.58 

2.83 

3.07 

3.31 

3.54 

ft 

108 

1.96 

2.22 

2.49 

2.75 

3.01 

3.27 

3.53 

3.68 

4§ 

115 

2.08 

2.36 

2.64 

2.92 

3.20 

3.48 

3.75 

4.02 

4} 

121 

2.19 

2.50 

2.80 

3.09 

3.39 

3.68 

3.97 

4.26 

5 

127 

2.31 

2.63 

2.95 

3.26 

3.58 

3.88 

4.19 

4.49 

.8 

133 

2.77 

3.10 

3.43 

3.76 

4.09 

4.41 

4.73 

140 

2.90 

3.26 

3.60 

3.95 

4.29 

4.63 

4.97 

5i 

146 

3.04 

3.41 

3.77 

4.14 

4.50 

4.85 

5.21 

6 

153 

3.56 

3.94 

4.32 

4.70 

5.07 

5.45 

6i 

159 

3.71 

4.11 

4.51 

4.90 

5.30 

5.68 

a 

166 

3.87 

4.28 

4.70 

5.11 

5.52 

5.92 

6} 

171 

4.45 

4.88 

5.31 

5.74 

6.16 

7 

178 

4.62 

5.07 

5.52 

5.96 

6.40 

7i 

184 

4.79 

5.26 

5.72 

6.18 

6.64 

a 

191 

4.96 

5.45 

5.92 

6.40 

6.87 

7} 

197 

5.13 

5.63 

6.13 

6.62 

7.11 

8 

203 

5.82 

6.33 

6.84 

7.35 

8i 

209 

6.01 

6.54 

7.06 

7.59 

l\ 

216 

6.74 

7.28 

7.83 

222 

6.94 

7.51 

8.06 

9 

229 

7.73 

8.30 

9* 

242 

8.17 

8.78 

10 

254 

9.25 

10i 

267 

11 

280 

m 

293 

12 

305 

12* 

318 

Weight  of  Steel  Angles 

PER  FOOT   RUN. 


L 


233 


MALS  OF  AN  INCH. 

0.30 

0.32 

0.34 

0.36 

0.38 

0.40 

0.42 

0.44 

0.46 

0.48 

0.50 

0.52 

Millimetres. 

7.74 

8.14 

8.73 

9.32 

9.72 

10.32 

10.71 

11.31 

11.70 

12.30 

12.70 

13.29 

1.73 

1.83 

1.86 

1.96 

1.99 

2.10 

2.12 

2.24  , 

2^35 

2.24 

2.37 

2.50 

2.37 

2.51 

2.64 

2^77 

2.50 

2.64 

2.79 

2.93 

2.63 

2.78 

2.93 

3.08 

3  '.22 

2.75 

2.92 

3.07 

3.23 

3.39 

2.88 

3.05 

3.22 

3.38 

3.55 

3.7i 

3.01 

3.19 

3.36 

3.54 

3.71 

3.88 

3.14 

3.32 

3.51 

3.69 

3.87 

4.05 

4^22 

3.26 

3.46 

3.65 

3.84 

4.03 

4.22' 

4.40 

3.39 

3.60 

3.80 

4.00 

4.19 

4.39 

4.58 

4!  76 

3.52 

3.73 

3.94 

4.15 

4.35 

4.56 

4.76 

4.95 

3.65 

3.87 

4.09 

4.30 

4.52 

4.73 

4.93 

5.14 

5^34 

3.77 

4.00 

4.23 

4.46 

4.68 

4.90 

5.11 

5.33 

5.54 

4.03 

4.28 

4.52 

4.76 

5.00 

5.24 

5.47 

5.70 

5.93 

6.i5 

4.28 

4.55 

4.81 

5.07 

5.32 

5.58 

5.83 

6.07 

6.32 

6.56 

6!80 

7!64 

4.54 

4.82 

5.10 

5.37 

5.65 

5.92 

6.18 

6.45 

6.71 

6.97 

7.23 

7.48 

4.79 

5.09 

5.39 

5.68 

5.97 

6.26 

6.54 

6.82 

7.10 

7.38 

7.65 

7.92 

5.05 

5.36 

5.68 

5.99 

6.20 

6.60 

6.90 

7.20 

7.49 

7.78 

8.08 

8.36 

5.30 

5.64 

5.96 

6.29 

6.62 

6.94 

7.25 

7.57 

7.88 

8.19 

8.50 

9.80 

5.56 

5.91 

6.25 

6.60 

6.94 

7.28 

7.61 

7.94 

8.27 

8.60 

8.93 

9.25 

5.81 

6.18 

6.54 

6.90 

7.26 

7.62 

7.97 

8.32 

8.66 

9.01 

9.35 

9.69 

6.07 

6.45 

6.83 

7.21 

7.58 

7.96 

8.33 

8.69 

9.06 

9.42 

9.78 

10.13 

6.32 

6.72 

7.12 

7.52 

7.91 

8.30 

8.68 

9.07 

9.45 

9.82 

10.20 

10.57 

6.58 

7.00 

7.41 

7.82 

8.23 

8.64 

9.04 

9.44 

9.84 

10.23 

10.63 

11.01 

6.83 

7.27 

7.70 

8.13 

8.55 

8.98 

9.40 

9.81 

10.23 

10.64 

11.05 

11.46 

7.09 

7.54 

7.99 

8.43 

8.88 

9.32 

9.75 

10.19 

10.62 

11.05 

11.48 

11.90 

7.34 

7.81 

8.28 

8.74 

9.20 

9.66 

10.11 

10.59 

11.01 

11.46 

11.90 

12.34 

7.60 

8.08 

8.57 

9.05 

9.52 

10.00 

10.47 

10.94 

11.40 

11.86 

12.33 

12.78 

7.85 

8.36 

8.85 

9.35 

9.85 

10.34 

10.82 

11.31 

11.79 

12.27 

12.75 

13.22 

8.11 

8.63 

9.14 

9.66 

10.17 

10.68 

11.18 

11.68 

12.18 

12.68 

13.18 

13.67 

8.36 

8.90 

9.43 

9.96 

10.49 

11.02 

11.54 

12.06 

12.57 

13.09 

13.60 

14.11 

8.62 

9.17 

9.72 

10.27 

10.81 

11.36 

11.90 

12.43 

12.97 

13.50 

14.03 

14.55 

8.87 

9.44 

10.01 

10.58 

11.14 

11.70 

12.25 

12.81 

13.36 

13.90 

14.45 

14.99 

9.38 

9.99 

10.59 

11.19 

11.78 

12.38 

12.97 

13.55 

14.14 

14.72 

15.30 

15.88 

9.89 

10.53 

11.17 

11.80 

12.43 

13.06 

13.68 

14.30 

14.92 

15.54 

16.15 

16.76 

10.40 

11.08 

11.74 

12.41 

13.08 

13.74 

14.39 

15.05 

15.70 

16.35 

17.00 

17  64 

11.62 

12.32 

13.02 

13.72 

14.42 

15.11 

15.80 

16.48 

17.17 

17.85 

18.53 

12.90 

13.64 

14.37 

15.10 

15.82 

16.55 

17.27 

17.98 

18.70 

19.41 

14.25 

15.01 

15.78 

16.54  117.29 

18.05 

18.80 

19.55 

20.30 

15.66 

16.46 

17.25    18.04 

18.83 

19.62 

20.40 

21.18 

!>:;  I 


J 


The   Naval  Constructor 

WEIGHT   OF   STEEL   ANGLES 


Thickness  in  Deci- 

Sum  of 
Flanges. 

0.54 

0.56 

0.58 

0.60 

0.62 

0.64 

0.66 

0.68 

0.70 

0.72 

Thickness  in 

Inches. 

Milli- 

metres. 

13.89 

14.28 

14.88 

15.27 

15.87 

16.2 

7    16.86 

17.46 

17.85 

18.45 

5 

127 

8.19 

I 

133 
140 
146 

8.65 
9.11 
9.57 

9.41 
9.88 

9^70 
10.20 

6 

153 

10.02 

10.36 

10.69 

li".02 

| 

159 

10.48 

10.83 

11.18 

11.53 

166 

10.94 

11.31 

11.67 

12.04 

i2!io 

\2.'t 

5    '.'.'.'. 

61 

171 

11.40 

11.79 

12.17 

12.55 

12.92 

13.  C 

10    .... 

7 

178 

11.86  12.26 

12.66 

13.06 

13.45 

13. 1 

14    14.23 

1 

184 

12.32 

12.74 

13.15 

13.57 

13.98 

14.; 

8    14.79 

191 

12.78 

13.21 

13.65 

14.08 

14.50 

14. < 

3    15.35 

i5i77 

i(U8 

7J 

197 

13.24 

13.69 

14.14 

14.59 

15.03 

15.4 

7    15.91 

16.35 

16.78 

8 

203 

13.70 

14.17 

14.63 

15.10 

15.56 

16. ( 

12    16.47 

16.92 

17.37 

17.82 

« 

209 

14.16 

14.64 

15.13 

15.61 

16.08 

16. ', 

6    17.03 

17.50 

17.97 

18.43 

8* 

216 

14.61 

15.12 

15.62 

16.12 

16.61 

17.1 

0    17.59 

18.08 

18.56 

19.05 

81 

222 

15.07 

16.59 

16.11 

16.63 

17.14 

17. ( 

5    18.15 

18.66 

19.16 

19.66 

9 

229 

15.53 

16.07 

16.60 

17.14 

17.67 

18.1 

9    18.71 

19.24 

19.75 

20.27 

9} 

242 

16.45 

17.02 

17.59 

18.16 

18.72 

19.5 

8    19.84 

20.39 

20.94 

21.49 

10 

254 

17.37 

17.97 

18.58 

19.18 

19.77 

20.C 

7    20.96 

21.55 

22.13 

22.72 

10* 

267 

18.29 

18.93 

19.56 

20.20 

20.83 

21.4 

6    22.08 

22.70 

23.32 

23.94 

11 

280 

19.20 

19.88 

20.55 

21.22 

21.88 

22.1 

4    23.20 

23.86 

24.51 

25.17 

iii 

293 

20.12  20.83 

21.53  22.24 

22.94 

23. ( 

>3    24.32 

25.02 

25.70 

26.39 

12 

305 

21.0421.78 

22.52 

23.26 

23.49 

24.' 

2    25.45 

26.17 

26.89 

27.61 

12* 

318 

21.96  22.73 

23.51 

24.48 

25  04 

25.  i 

il    26.57 

27.33 

28.08 

28.84 

13 

331 

22.88  23.69 

24.49 

25.30 

26.10 

26. { 

0    27.69 

28.48 

29.27 

30.06 

13| 

343 

23.79124.64 

25.48 

26.32 

27.15 

27. < 

8    28.81 

29.64 

30.46 

31.29 

14 

356 

24.7125.59 

26.46 

27.34 

28.21 

29. ( 

7    29.93 

30.80 

31.65 

32.51 

14* 

369 

25.63  26.54 

27.45 

28.36 

29.26 

30.1 

6    31.06 

31.95 

32.84 

33.73 

15 

381 

26. 55127.49 

28.44 

29.38 

30.31 

31.S 

5    32.18 

33.11 

34.03 

34.96 

15* 

394 

27.4728.45 

29.42 

30.40 

31.37 

32.1 

4    33.30 

34.26 

35.22 

36.18 

16 

407 

28.38  29.40 

30.41 

31.42 

32.42 

33.4 

2    34.42 

35.42 

36.41 

37.41 

0.10 

0.12 

0.14 

0.16 

0.18 

0.2( 

)     0.22 

0.24 

0.26 

0.28 

13 

331 

13| 

343 

14 

356 

14* 

369 

15 

381 

15} 

394 

16 

407 

.... 

! 

Weight  of  Steel  Angles 


PER  FOOT   RUN. 


235 


mals  or  an  Inch. 


0.74     0.76     0.78     0.80     0.82     0.84     0.86     0.88     0.90     0.92      0.94      0.96 


Millimetres. 


18.85  19.44    19.84    20.43    20.83    21.43    22.02    22.42    23.01    23.41    24.01    24.40 


19.52 
20.15 
20.78 
22.04 
23.30 
24.56 
25.81 
27.07 
28.33 
29.59 
30.85 
32.10 
33.36 
34.62 
35.88 
37.14 
38.39 


20.00 
20.65 
21.29 
22.58 
23.88 
25.17 
26.46 
27.75 
29.04 
30.34 
31.63 
32.92 
34.21 
35.51 
36.81 
38.10 
39.38 


21.80 
23.13 
24.45 
25.78 
27.10 
28.43 
29.76 
31.08 
32.41 
33.73 
35.06 
36.39 
37.71 
39.04 
40.36 


22.30 
23.66 
25.02 
26.38 
27.74 
29.10 
30.46 
31.82 
33.18 
34.54 
35.90 
37.26 
38.62 
39.98 
41.34 


25.59 
26.99 
28.38 
29.78 
31.17 
32.56 
33.96 
35.35 
36.75 
38.14 
39.53 
40.93 
42.32 


29.02 
30.44 
31.87 
33.30 
34.73 
36.16 
37.58 
39.01 
40.44 
41.87 
43.30 


33.27 
34.77 
36.26 
37.76 
39.26 
40.75 
42.25 
43.74 
45.24 


37.03 
38.56 
40.09 
41.62 
43.15 
44.68 
46.21 


40.91 
42.48 
44.04 
45.61 
47.17 


0.30     0.32     0.34      0 


0.38     0.40     0.42     0.44 


0.46     0.48 


0.50     0.52 


17.14 


17.96 
18.68 


18.79 
19.54 
20.29 


19.61 
20.39 
21.18 
21.96 


20.43 
21.25 

22.06 
22.88 
23.70 


21.25 
22.10 
22.95 
23.80 
24.65 
25.50 


236 


The  Naval  Constructor 


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12.66 
13.52 
14.47 
15.35 
16.18 
16.43 
17.25 
17.53 
18.28 
18.48 
19.32 
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20.38 
20.71 
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Weight  of  Steel   Bulb  Angles 


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29.18 
29.55 
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33.57 
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23.20 
24,39 
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27.32 
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238 


The  Naval  Constructor 


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20.73 
19.74 
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216X  77X  77 
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229  X  89  X  89 
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267X  89X  89 
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Weight  of  Steel  Channels 


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39.21 
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42.97 
42.21 
43.51 
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240 


The  Naval  Constructor 


WEIGHT  IN  LBS.    OF   STEEL   BULB   TEES   PER 
FT.   RUN. 


Size. 

Thickness  in  Decimals  of  an  Inch. 

0.30 

0.32 

0.34 

0.36 

0.38 

0.40 

0.42 

0.44 

Inches. 

Millimetres. 

Thickness  in  Millimetres. 

7.74 

8.14 

8.73 

9.32 

9.72 

10.32 

10.71 

11.31 

7X5 
8X5* 
9X5* 
10X6 
11X6J 
12X6* 

178X127 
203X140 
229X140 
254X153 
~280X166 
305X166 

16 

U 

16.00 
19.36 

17.08 
19.90 
22.79 

17.55 
20.44 
23.40 
27.01 

18.03 
20.99 
24.01 
27.69 
31.71 

18.51 
21.53 
24.62 
28.37 
32.46 
35.58 

18.98 
22.08 
25.24 
29.05 
33.20 
36.40 

19.46 
22.62 
25.85 
29.73 
33.95 
37.22 

Size. 

Thickness  in  Decimals  of  an  Inch. 

0.46 

0.48 

0.50 

0.52 

0.54 

0.56 

0.58 

0.60 

Inches. 

Millimetres. 

Thickness  in  Millimetres. 

11.70 

12.30 

12.70 

13.29 

13.89 

14.28 

14.88 

15.27 

7X5 
8X5* 
9X5* 
10X6 
11X6* 
12X6* 

178X127 
203X140 
229X140 
254X153 
280X166 
305X166 

19.93 
23.16 
26.46 
30.41 
34.70 
38.03 

20.41 
23.71 
27.07 
31.09 
35.45 
38.85 

20.89 
24.25 
27.68 
31.77 
36.20 
39.66 

21.36 
24.80 
28.30 
32.45 
36.94 
40.48 

21.84 
25.34 
28.91 
33.13 
37.69 
41.30 

22.31 
25.88 
29.52 
33.81 
38.44 
42.11 

26!  43 
30.13 
34.49 
39.19 
42.93 

26!  97 
30.74 
35.17 
39.94 
43.74 

Size. 

Thickness  in  Decimals  of  an  Inch. 

0.62 

0.64 

0.66 

0.68 

0.70 

0.72 

0.74 

0.76 

Inches. 

Millimetres. 

Thickness  in  Millimetres. 

15.87 

16.27 

16.86 

17.46 

17.85 

18.45 

18.85 

19.44 

7X5 

8X5* 
9X5* 
10X6 
11X6* 
12X6* 

178X127 
203X140 
229X140 
254X153 
280X166 
305X166 

SIM 
35.85 
40.68 
44.56 

3L97 
36.53 
41.43 
45  48 

37^21 
42.18 
46.29 

37.89 
42.93 
47.11 

43.68 
47  92 

44!  42 

48.74 

49 .56 

56!37 

Weight  of  Steel  Bulb   Plates        I   241 


1 


WEIGHT  IN  LBS.    OP   STEEL   BULB    PLATES    PER 
FT.   RUN. 


Thickness  in  Decimals  of  an  Inch. 

Depth. 

0. 16    0.18  1  0.20  |  0.22  j  0.24  j  0.26  |  0.28  |  0.30    0.32    0.34    0.36 

Thickness  in  Millimetres. 

Inches. 

Milli- 
metres. 

3.97 

4.76 

5.15 

5.56 

5.95 

6.75 

7.14 

7.74 

8.14 

8.73 

9.32 
7.19 

5 

127 

3.79 

4.13 

4,47 

4.81 

5.15 

5.49 

5.83 

6.17 

6.51 

6.85 

6 

153 

5.54 

5.95 

6.36 

6.77 

7 

17 

7.58 

7.99 

8.40 

8.81 

7 

178 

7.15 

7.62 

8.10 

8 

58 

9  05 

9  55 

10.00 

10.48 

8 

204 

9 

05 

10.50 

11  04 

11.58 

12.13 

9 

229 

12.29 

12.90 

13.52 

14.13 

10 

254 

14.48 

15.16 

15.48 

11 

280 

12 

304 

Thickness  in  Decimals  op  an  Inch. 

Di 

0.38  1  0.40    0.42  1  0.44  1  0.46  |  0.48  |  0.50  1  0.52  1  0.54  1  0.56  1  0.58 

Thickness  in  Millimetres. 

Milli- 

Inches. 

metres. 

9.72 

10.32 

10.71 

11.31 

11.70 

12.30 

12.70 

13.29 

13.89 

14.28 

14.88 

5 

127 

7.53 

7.87 

6 

153 

9.21 

9.62 

10.03 

10.44 

7 

178 

10.96  11.43 

11.91 

12.38 

12.86 

13.93 

13.81 

8 

204 

12.67  13.22 

13.76 

14.30 

14.85 

15.39 

15.94 

16.48 

17.02 

17.57 

18.11 

9 

229 

14.74  15.35 

15.96 

16.58 

17.19 

17.80 

18.41 

19.02 

19.64 

20.25 

20.86 

10 

254 

16.52  17.20 

17.88 

18.56 

19.24 

19.92 

20.60 

21.28 

21.96 

22.64 

23.32 

11 

280 

18. 521 19. 27 

20.02 

20.76 

21.51 

22.26 

23.01 

23.76 

24.50 

25.25 

26.00 

12 

304 

...   [21.26 

22.07 

22.89 

23.71  24.52 

25.34 

26.15 

26.97 

27.79 

28.60 

Thickness  in  Decimals  of  an  Inch. 

PTH. 

0.60  |  0.62  |  0.64    0.66    0.68  |  0.70  |  0.72  |  0.74  |  0.76  |  0.78  | 

Thickness  in  Millimetres. 

Inches. 

Milli- 
metres. 

15.27 

15.87 

16.27 

16.86 

17.46 

17.85 

18.45 

18.85 

19.44 

19:84 

5 

127 

6 

153 

7 

178 

8 

204 

9 

229 

21.47 

22.08 

10 

254 

24  00 

24  68 

25.36 

26.04 

26  72 

11 

280 

26  75 

27.50 

28.24 

28.99 

29.74 

30.49 

31.24 

31.98 

12 

304 

29.42 

30.23 

31.05 

31.87 

32.68 

33.50 

34.31 

35.13 

35.95 

36.76 

242 


The  Naval   Constructor 


WEIGHTS 

OF  STEEL   ZEE  BARS 

PER  FOOT  RUN. 

Size  of  Web  and 
Flanges. 

Thickness  in  Decimals  or  an  Inch. 

0.30 

0.32 

0.34 

0.36 

0.38 

0.40 

0.42 

Inches. 

Millimetres. 

Thickness  in  Millimetres. 

7.74 

8.14 

8.73 

9.32 

9.72 

10.32 

10.71 

5X3  X3 
6X3*  X3J 
7X3JX3J 
8X3JX3J 
9X3iX3i 
10X3JX3| 

127X77X77 
153X89X89 
178X89X89 
204X89X89 
229X89X89 
254X89X89 

12.71 

u 

15 

80 
89 

13.88 
16.68 
18.08 

14.47 
17.36 
18.80 
20.24 

15.05 
18.05 
19.51 
20.99 
22.54 

15.64 
18.74 
20.22 
21.74 
23.34 
24.99 

16.22 
19.42 
20.94 
22.50 
24.14 
25.84 

Size  of  Web  and 
Flanges. 

Thickness  in  Decimals  of  an  Inch. 

0.44 

0.46 

0.48 

0.50 

0.52 

0.54 

0.56 

Inches. 

Millimetres. 

Thickness  in  Millimetres. 

11.31 

11.70 

12.30 

12.70 

13.29 

13.89 

14.28 

5X3  X3 
6X3iX3£ 
7X3*  X3J 
8X3JX3J 
9X3JX3J 
10X3J  X3i 

127X77X77 
153X89X89 
178X89X89 
204X89X89 
229X89X89 
254X89X89 

16.81 
20.11 
21.65 
23.25 
24.93 
26.88 

17.39 
20.79 
22.37 
24.00 
25.73 
27.53 

17.98 
21.48 
23.08 
24.75 
26.53 
28.38 

18.56 
22.16 
23.79 
25.50 
27.33 
29.22 

19.15 
22.85 
24.51 
26.26 
28.12 
30.07 

19.73 
23.54 
25.22 
27.01 
28.92 
30.92 

20.32 
24.22 
25.94 
27.76 
29.72 
31.76 

Size  of  Web  and 
Flanges. 

Thickness  in  Decimals  of  an  Inch. 

0.58 

0.60 

0.62 

0.64 

0.66 

0.68 

Inches. 

Millimetres. 

Thickness  in  Millimetres. 

14.88 

15.27 

15.87 

16.27 

16.89 

17.46 

5X3  X3 
6X3*  X3* 
7X3£X3* 
8X3iX3§ 
9X3|  X3J 
10X3*  X3£ 

127X77X77 
153X89X89 
178X89X89 
204X89X89 
229X89X89 
254X89X89 

20.90 
24.91 
26.65 
28.51 
30.51 
32.61 

21.49 
25.59 
27.36 
29.26 
31.31 
33.46 

26!  28 
28.08 
30.02 
32.11 
34.30 

28^79 
30.77 
32.90 
35.15 

3i!52 
33.70 
35.09 

34!50 
36.84 

Weight  of  Steel  Plating  in   Pounds 


WEIGHT   OF  A    SQUARE   FOOT   IN   LBS,   AND 
AREA   IN   FEET   PER    TON   OF    STEEL    PLATING. 


Thickness. 

Weight  per 

Square 

Foot  in 

Lbs. 

Number  of 

Square 

Feet  per 

Ton. 

Fractions  of 
an  Inch. 

Decimals  of 
an  Inch. 

Millimetres. 

A 

0.02 

0.50799 

0.816 

2745.098 

A 

0.04 

1.01598 

1.632 

1372.549 

A 

0.06 

1.52397 

2.448 

915.033 

A 

0.08 

2.03196 

3.264 

686.275 

A 

0.10 

2.53995 

4.08 

549.02 

5*0 

0.12 

3.04794 

4.896 

457.516 

A 

0.14 

3.55594 

5.712 

392.157 

A 

0.16 

4.06393 

6.528 

343.137 

A 

II 

0.18 

4.57192 

7.344 

305.011 

0.20 

5.07991 

8.16 

274.51 

0.22 

5.58790 

8.976 

249.554 

0.24 

6.09589 

9.792 

228.758 

u 

0.26 

6.60388 

10.608 

211.161 

u 

0.28 

7.11187 

11.424 

196.078 

H 

0.30 

7.61986 

12.24 

183.007 

i% 

0.32 

8.12785 

13.056 

171.569 

If 

0.34 

8.63584 

13.872 

161.476 

H 

0.36 

9.14383 

14.688 

152.505 

8 

0.38 

9.65183 

15.504 

144.479 

§8 

0.40 

10.15982 

16.32 

137.255 

IS 

0.42 

10.66781 

17.136 

130.719 

ii 

0.44 

11.17580 

17.952 

124.777 

So 

0.46 

11.68379 

18.768 

119.352 

ii 

0.48 

12.19178 

19.584 

114.379 

ii 

0.50 

12.69977 

20.4 

109.804 

n 

0.52 

13.20776 

21.216 

105.581 

§5 

Ii 

0.54 

13.71575 

22.032 

101.670 

0.56 

14.22374 

22.848 

98.039 

ii 

0.58 

14.73173 

23.664 

96.659 

if 

0.60 

15.23972 

24.48 

91.503 

it 

0.62 

15.74772 

25.296 

88.552 

n 

0.64 

16.25571 

26.112 

85.784 

I! 

0.66 

16.76370 

26.928 

83.185 

0.68 

17.27169 

27.744 

80.738 

fl 

0.70 

17.77968 

28.56 

78.431 

0.72 

18.28767 

29.376 

76.253 

IS 

0.74 

18.79566 

30.192 

74.192 

y 

0.76 

19.30365 

31.008 

72.239 

n 

0.78 

19.81164 

31.824 

70.387 

H 

0.80 

20.31903 

32.64 

68.627 

y 

0.82 

20.82762 

33.456 

66.954 

H 

0.84 

21.33561 

34.272 

65.359 

H 

0.86 

21.84361 

35.088 

63.839 

i$ 

0.88 

22.35160 

35.904 

62  389 

n 

BO 

0.90 

22.85959 

36.72 

61.002 

0.92 

23.36758 

37.536 

59.676 

K 

0.94 

23.87557 

38.352 

58.406 

H 

0.96 

24.38356 

39.168 

57.190 

H 

0.98 

24.89155 

39.984 

56.022 

i 

1.00 

25.39954 

40.8 

54.902 

244 


The   Naval   Constructor 


"WEIGHTS    OF   BUILT   STEEL   TUBULAR   PILLARS. 


Otjtside  Diameter. 

Thickness. 

Weight  per 
Foot  Run, 

Inches. 

Millimetres. 

Inches. 

Millimetres. 

Lbs. 

6 

153 

0.40 

10.32 

23.93 

8) 

166 

0.40 

10.32 

26.06 

7 

178 

0.40 

10.32 

28  20 

7* 

191 

0.40 

10  32 

30.34 

8 

203 

0.40 

10.32 

32.47 

8 

203 

0.44 

11.31 

35.53 

6ft 

216 

0.40 

10.32 

34.61 

8ft 

216 

0.44 

11,31 

37.88 

9 

229 

0.40 

10.32 

36.74 

9 

229 

0.44 

11.31 

40.23 

10 

254 

0.40 

.   10.32 

41.02 

10 

254 

0.44 

11.31 

44.93 

10 

254 

0.50 

12.70 

50.74 

11 

280 

0.44 

11.31 

49.63 

11 

280 

0.50 

12.70 

56.08 

12 

305 

0.50 

12.70 

61.42 

12 

305 

0.54 

13.89 

66  10 

13 

331 

0.54 

13.89 

71.87 

13 

331 

0.60 

15.27 

79.47 

14 

356 

0.54 

13.89 

77.64 

14 

356 

0.60 

15.27 

85.88 

15 

381 

0.60 

15.27 

92.29 

16 

407 

0.60 

15.27 

98.70 

17 

432 

0.60 

15.27 

105.11 

18 

458 

0.60 

15.27 

111.51 

18 

458 

0.64 

16.27 

118.68 

18 

458 

0.70 

17.85 

129.35 

18 

458 

0.74 

18.85 

136.43 

Weight  of  Armor  in   Pounds  245 


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246 


The  Naval   Constructor 


WEIGHTS    AND    AREAS    OF    PUNCHINGS   OF   CHl- 

CULAR  LIGHTENING  AND  OTHER  HOLES  FROM 

STEEL  PLATHtfG  OF  VARIOUS  THICKNESSES. 


Thickness  in  Decimals  of  an  Inch. 

Diameter  of 

Punchings. 

Area, 

0.24 

0.26 

0.28 

0.30 

0.32 

0.34 

0.36 

0.38 

0.40 

Square 
Inches. 

Thickness  in  Millimetres. 

Inches. 

Milli- 
metres. 

5.95 

6.75 

0.52 

7.14 
0.56 

7.74 
0.60 

8.14  |  8.73 
0.64!"0~68 

9.32 
0.72 

9.72 
0.76 

10.32 
0.80 

3 

77 

7.07 

0.48 

4 

102 

12.57 

0.85 

0.93 

1.00 

1.07 

1.14 

1.21 

1.28 

1.35 

1.42 

5 

127 

19.64 

1.31 

1.45 

1.56 

1.67 

1.78 

1.89 

2.00 

2.11 

2.23 

6 

153 

28.27 

1.92 

2.08 

2.24 

2.40 

2.56 

2.72 

2.88 

3.04 

3.20 

7 

178 

38.48 

2.62 

2.83 

3.05 

3.27 

3.49 

3.71 

3.93 

4.14 

4.36 

8 

203 

50.27 

3.42 

3.70 

3.99 

4.27 

4.56 

4.84 

5.13 

5.41 

5.70 

9 

229 

63.62 

4.33 

4.69 

5.05 

5.41 

5.77 

6.13 

6.49 

6.85 

7.21 

10 

254 

78.54 

5.34 

5.79 

6.23 

6.68 

7.12 

7.57 

8.01 

8.46 

8  90 

11 

280 

95.03 

6.46 

7.00 

7.54 

8.08 

8.62 

9.15 

9.69 

10  23 

10.77 

12 

305 

113.10 

7.69 

8.33 

8.97 

9.61 

10.25 

10.89 

11  54 

12.18 

12.82 

13 

331 

132.73 

9.03 

9.78 

10.53 

11.28 

12.03 

12.79 

13.54 

14.29 

15.04 

14 

356 

153.94 

10.47 

11.34 

12.21 

13.08 

13.96 

14.83 

15.70 

16.57 

17.45 

15 

381 

176.71 

12.02 

13.02 

14.02 

15.02 

16.02 

17.02 

18.03 

19.03 

20.03 

16 

407 

201.06 

13.67 

14.81 

15.95 

17.09 

18.23 

19.37 

20.51 

21.65 

22.79 

17 

432 

226.98 

15.44 

16.72 

18.01 

19.29 

20. 5S 

21.87 

23.15 

24.44 

25.72 

18 

457 

254.47 

17.30 

18.75 

20.19  21.63 

23.07 

24.51 

25.96 

27.40 

28.84 

Thickness  in  Decimals  of  an  Inch. 

DlAME 

HER  OF 

PUNCI 

UN  OS. 

Area, 

Square 
Inches. 

0.42 

0.44 

0.46 

0.48 

0.50 

0.52 

0.54 

0.56 

0.58 

Thickness  in  Millimetres. 

Inches. 

Milli- 
metres. 

10.71 

11.31 

0.88 

11.70 
0.92 

12.30 
0.96 

12.70 
1.00 

13.29 
1.04 

13.89 
1.08 

14.28 
1.12 

14.88 
1.16 

3 

77 

7.07 

0.84 

4 

102 

12.57 

1.50    1.57 

1.64 

1.71 

1.78 

1.85 

1.92 

1.99 

2.06 

5 

127 

19.64 

2.34,  2.45 

2.56 

2.67 

2.78 

2.89 

3.00 

3.12 

3.23 

6 

153 

28.27 

3.36    3.52 

3.69 

3.85 

4.01 

4.17 

4.33 

4.49 

4.55 

7 

178 

38.48 

4.58 

4.80 

5.02 

5.23 

5.45 

5.67 

5.89 

6.11 

6.32 

8 

203 

50.27 

5.98 

6.27 

6.55 

6.84 

7.12 

7.41 

7.69 

7.97 

8.26 

9 

229 

63.62 

7.57 

7.93 

8.29 

8.65 

9.01 

9.37 

9.73 

10.09 

10.45 

10 

254 

78.54 

9.35 

9.79 

10.24 

10.68 

11.13 

11.57 

11.02 

11.46 

11.91 

11 

280 

95.03 

11.31  11.85 

12.39 

12.92 

13.46 

14.00 

14.54 

15.08 

15.62 

12 

305 

113.10 

13.46  14.10 

14.72 

15.38 

16.02 

16.66 

17.30 

17.94 

18.58 

13 

331 

132.73 

15.79  16.55 

17.30 

18.05 

18.80 

19.55 

20.31 

21.06 

21.81 

14 

356 

153.94 

18.32  19.19 

20.06 

20.93 

21.81 

22.68 

23.55 

24.42 

25.30 

15 

381 

176.71 

21.03  22.03 

23.03 

24.03 

25.04 

26.04 

27.04 

28.04 

29.04 

16 

407 

201.06 

23.92(25.06 

26.20 

27.34 

28.48 

29.62 

30.76 

31.90 

33.04 

17 

432 

226.98 

27.01  28.30 

29.38 

30.87 

32.15 

33.44 

34.73 

36.01 

37.30 

18 

457 

254.47 

30.2831.72 

33.16 

34.61 

36.05 

37.49 

38.93 

40.37 

41.81 

C.G.  by  Experiment  247 


Lloyd's  Bulb  Sections. 

The  depth  in  inches  JD  of  the  section  to  be  the  base  from  which 
to  deduce  the  other  dimensions. 
The  width  of  the  btubs  to  be  2±C  for  bulb  angles,  and  S\G  for 

2)  +  3 

bulb  plates  and  tees,  when  C  is  in  the  case  of  bulb  angles, 

and  for  bulb  plates  and  tees.     The  form  of  the  bulbs  to  be 

in  accordance  with  the  sketches. 

L D 


S3  ^" 


\ 


f 


Fig.  44. 

The  standard  thickness  for  regulating  the  widths  of  bulb  of 
beams  and  bars  whose  depth  is  not  an  exact  number  of  inches, 
should  correspond  to  the  depth  in  inches  next  below  the  actual 
depth,  thus  —  for  tee  beams  and  bulb  plates  10^  inches  depth,  the 
standard  thickness  to  be  used  in  determining  the  dimensions  of 

the  bulb  should  be  -^—  or  —  .   See  figures  44  and  45. 

C.G.  BY  EXPERIMENT. 

All  finished  vessels  should  be  inclined  before  leaving  the  build- 
er's hands  and  their  exact  centre  of  gravity  found  experimentally. 
The  value  of  this  information  cannot  be  over-estimated,  although 
in  many  cases  where  possessed  it  does  not  seem  to  be  applied  with 
the  care  its  importance  demands,  as  evidenced  by  the  proportions 
of  many  ships  of  the  merchant  marine. 


IMS 


The  Naval  Constructor 


Fig.  45. 

The  principle  on  which  the  experiment  is  based  will  be  under- 
stood from  a  reference  to  Fig.  46,  where  p  is  a  small  weight  placed 
on  deck  at  centre  line,  and  afterwards  shifted  to  either  side 
through  a  distance  a.  The  centre  of  gravity  before  the  movement 
was  made  is  shown  at  G.  It  will  be  evident  that  this  centre  after 
the  weight  has  been  shifted,  will  move  to  a  new  location  parallel  to 
the  line  of  shift,  and  that  the  weight  multiplied  by  the  distance 
through  which  it  has  been  moved,  will  give  a  moment  equal  to 
the  weight  of  the  whole  ship  by  the  distance  the  common  centre 
of  gravity  G  has  been  moved  to  (?i,  so  that  we  get :  — 

Before  attempting  to  carry  out  the  inclining  experiment,  the 


C.G.  by  Experiment 


249 


Fio.  46. 


following  preparations  should  be  made,  observing  that  although 

not  imperative  that  the  vessel  be  completely  finished,  it  is  well  to 

have  her  in  that  condition  if  possible.     The   bilges  should  be 

carefully  examined  to  see 

that  they  are   perfectly 

free  from  loose  water,  and 

the  boilers,    condenser, 

fresh    water    and    ballast 

tanks  must  be  either  empty 

or  pumped  up  "chock 

full,"  as  any  free  water  in 

the  ship  will  destroy  the 

value  of  the  experiment. 

All  workmen,  unless  those 

assisting,    must  be   sent 

ashore,  and  when  the  shift 

is  being  measured  the 

assistants  and   laborers 

should  be  lined  up  on  centre  line  of  ship,  a  position  they  shall 

have  occupied  before  beginning.     The  weather  should  be  perfectly 

calm,  and  an  enclosed  space  of  water  as  a  basin,  or  dock,  selected, 

and  the  mooring  lines  eased  off  slack  to  permit  the  vessel  to  move 

freely. 

The  inclining  weights  should  aggregate  .5  to  one  per  cent  of 
the  displacement,  and  two  parallel  lines  should  be  marked  off  on 
deck  amidships,  representing  the  distance  through  which  the  centres 
of  gravity  of  the  weights  shall  be  moved.  A  suitable  position 
must  be  obtained,  say  in  the  engine  or  boiler  hatch,  in  which  to  fix 
a  large  tee  square  with  the  cross  head  placed  downwards,  and  a 
plumb  line  and  bob  attached  at  the  end  of  the  blade,  care  being 
taken  that  the  bob  swings  clear  of  the  square.  When  these  prep- 
arations have  been  made  and  the  inclining  weights  placed  on  deck, 
an  accurate  draught  should  be  taken  and  the  men  ranged  up  on 
centre  line,  when  a  plumb  line  may  be  marked  off  on  the  edge  of 
square  as  a  starting  point,  the  weights  being  thereafter  transferred 
from  the  centre  line  to  port  or  starboard  and  an  observation  made. 
The  weights  should  then  be  moved  right  over  to  the  opposite  side, 
and  the  inclination  noted.  As  a  final  check  on  the  total  shift  the 
weights  may  be  shifted  back  to  their  original  position,  when  of 
course  the  plumb  line  should  cover  the  point  originally  marked  on 
starting.  From  the  following  data  procured  we  shall  be  enabled 
to  calculate  the  centre  of  gravity  on  the  principle  previously  re- 
ferred to,  viz.: — 

(1)  Draught  of  water. 

(2)  Displacement  from  the  foregoing. 


250 


The  Naval  Constructor 


(3)  Weights  shifted. 

(4)  Distance  between  the  two  lines  representing  the  space 
through  which  weights  were  shifted. 

(5)  Length  of  plumb  line  from  point  of  suspension  to  edge  of 
square. 

(6)  Travel  of  plumb  line  from  port  to  starboard,  and  starboard 
to  port.     Take  mean. 

(7)  Condition  of  the  ship  as  regards  state  of  completion  and 
what  weights  as  cargo,  coal,  fresh  water,  water  in  boilers, 
ballast  tanks  and  dunnage  are  on  board. 

As  the  vessel  has  been  previously  slacked  off,  on  shifting  the 
weights,  it  will  be  apparent  that  the  ship  will  heel  over  so  that  the 
centre  of  gravity  G,  and  the  centre  of  buoyancy  B\  (Fig.  47),  will 
be  in  the  same  vertical  line  and  M  will  be  the  metacentre.  Let 
a  represent  the  angle  of  heel,  then  :  — 


Fig.  47. 


The  tangent  of  a  is  found  by  taking  the  length  of  plumb  line 
"-42?"  and  the  mean  shift  of  bob  "BE"  on  tee  square,  from 
which  we  get :  — 

BE 

tana=ZlJ* 

The  triangle  GMG  and  BAE  are  similar,  then 

GGi_BE 

GM  ~  AB1 

__        GMXBE      Pxa 


and 


GM: 


AB 

j)Xq     AB 

'    D        BE 


D    ' 

px  a 

D  x  tan  a 


Centre  of  Gravity. 


251 


The  height  of  M  may  be  calculated  for  the  draught  with  which 
we  are  dealing  or  directly  measured  from  the  metacentric  diagram, 
and  the  GM  as  obtained  above  deducted  from  this  height  will  give 
the  centre  of  gravity  above  base  at  the  time  of  the  experiment. 
This  height  of  course  will  require  correction  by  deducting  the 
inclining  weights  and  the  excess  water  in  boilers,  if  these  have 
been  pumped  chock  full  for  the  experiment. 

Centre  of  Gravity. 

The  vertical  centre  of  gravity  of  a  ship  is  probably  the  most  im- 
portant point  which  the  naval  architect  has  to  determine,  as  well 
as  the  most  difficult  to  calculate  with  accuracy.  Therefore  it  is 
that  the  calculation  of  this  centre  in  detail  is  only  resorted  to 
when  insufficient  data  derived  from  a  somewhat  similar  type  is 
wanting,  as  the  most  reliable  method  is  that  computed  from  actual 
centres  obtained  from  experiments.  However,  where  this  is  not 
obtainable,  the  calculation  in  detail  by  careful  working  out  and 
good  judgment  should  give  equally  accurate  results.  Where  the 
former  method  is  resorted  to,  the  table  of  coefficients  given  in  the 
chapter  on  Design  will  be  found  of  service,  observing  that  these 
are  for  the  finished  vessel  loaded  with  a  homogeneous  cargo. 

When,  however,  it  is  imperative  to  go  into  the  calculation  in 
detail,  the  simplest  method  will  be  to  treat  the  hull  proper  as  a 
shell  of  uniform  thickness,  and  when 
the  centre  of  gravity  as  such  is  as- 
certained, to  make  the  necessary  ad- 
ditions for  excesses  on  particular  6 
strakes,  keelsons,  beams,  deck  plat- 
ing, superstructure  and  wood,  outfit 
and  equipment  weights.  The  centre 
of  gravity  of  the  machinery  with  steam 
up  will  be  furnished  by  the  engineers. 

On  a  body  plan  of  ten  sections 
with  half-end  ordinates,  mark  off 
around  the  half  girths  of  each  section 
a  spot  every  two  feet  apart,  as  shown 
on  Fig.  48,  dropping  a  perpendicular 
line  from  these  locations  to  the  base. 
Measure  these  heights  above  the  base 
and  tabulate  them  for  each  section, 
calling  the  centre  line  "  O  "  as  in  the 
table.  One  side  only  need  be  dealt 
with,  as  the  ship  is  symmetrical  about  the  middle  line. 

Each  of  the  ten  sections  having  been  treated  in  a  like  manner  to 
the  foregoing,  and  the  individual  centres  of  gravity  of  all  deter- 


FlG.  48. 


252 


The  Naval  Constructor 


Station. 

Skction  No.  5. 

Heights. 

Multipliers. 

Functions. 

0 
1 
2 
3 
4 
5 
6 

AV 
1 .3' 
2.4' 
4.1' 
6.1' 
8.2' 

h 
2 
1 

2 

1 
2 

* 
9 

L2* 
1.3 

4.8 

4.1 

12.2 

4.1 

)27.7 
3.07' 

3.07' =  C.G.  of  No.  6  above  base. 

mined,  these  centres  are  then  tabulated  and  the  common  centre  oi 
gravity  found  by  a  similar  operation  to  the  above,  i.e.,  they  are  in- 
tegrated by  Simpson's  multipliers,  and  the  sum  of  the  functions  so 
obtained  divided  by  the  sum  of  the  multipliers,  when  the  resulting 
quotient  will  be  the  perpendicular  height  of  the  common  centre  of 
gravity  of  all  the  sections  or  of  a  shell  of  uniform  thickness. 


Vertical  Centre 

of  Gravity  of  Shell. 

Sections. 

C.G.  of  Sec- 
tions 
above  Base. 

Simpson's 
Multipliers. 

Functions. 

0 

6.00 

1 

1.50 

i 

5.21 

1 

5.21 

1 

4.16 

| 

3.12 

2 

3.50 

2 

7.00 

3 

3.36 

1 

3.36 

4 

3.20 

2 

6.40 

5 

3.07 

1 

3.07 

6 

3.56 

2 

7:12 

7 

3.93 

1 

3.93 

8 

4.20 

2 

8.40 

9 

4.66 

3 

3.49 

»* 

5.00 

1 

6.00 

10 

5.74 

i 

1.43 

.  .  . 

15 

)  59.03 
3.94' 

3.94'=  Mean 

C.G.  above  hi 

ise. 

Centre  of  Gravity 


253 


Another  method  to  obtain  the  vertical  height  of  C.G.  due  to 
form  for  a  shell  of  uniform  thickness  is  to  take  the  sum  of  the 
functions  of  water  line  half-breadths  of  all  sections  from  base  to 
gunwale,  and  divide  them  by  the 
sum  of  the  multipliers  used,  which 
will  give  a  mean  half-breadth  for 
each  water  plane.  By  plotting  off 
these  mean  dimensions,  a  mean 
section  of  the  ship  may  be  drawn 
on  stout  paper,  cut  out  with  a 
penknife,  then  pinned  to  port  and 
starboard  alternately  and  swung 
on  a  board  having  a  plumb  line 
scribed  on  as  shown  in  Fig.  49. 

The  intersection  of  the  mark 
points  A  and  B  with  the  plumb 
line,  should  be  joined  with  the  pin 
holes  C  and  D,  and  where  they 
cross  each  other  on  centre  line  will 
be  the  mean  height  of  centre  of  gravity.  Carefully  done,  this 
will  give  a  very  close  approximation  to  the  calculation.  Of  course 
the  usual  additions  as  mentioned  in  the  preceding  method  will  be 
required  to  calculate  the  actual  C.G.  of  vessel. 

Outfit  in  detail,  stores,  fresh  water,  coal,  etc.,  will  be  set  down, 
giving  the  weight  and  estimated  height  of  their  respective  centres 
of  gravity  from  base,  when  the  sum  of  the  moments  produced 
divided  by  the  total  weight  will  give  a  resulting  quotient  equal  to 
the  mean  height  of  C.G.  of  ship  from  base  without  cargo,  the 
centre  of  gravity  of  which  may  be  found  by  a  similar  experiment,  as 
it  is  customary  to  treat  this  as  being  of  a  homogeneous  character. 


254  The  Naval  Constructor 

CHAPTER  VII. 
STRENGTH    OF   SHIPS. 

It  is  not  generally  considered  necessary  to  make  strength  calcu- 
lations for  an  ordinary  merchant  vessel  when  the  scantlings  are  in 
accordance  with  any  of  the  classification  societies'  rules,  but  in  the 
case  of  a  special  design,  and  also  in  warships,  it  is  advisable  to  do  so. 

In  these  calculations,  the  ship  is  considered  as  a  girder  and  the 
principle  is  the  same  as  that  of  a  beam  supported  at  both  ends,  or 
only  at  the  middle,  as  may  be  the  case  for  "  sagging  "  or  "  hog- 
ging" respectively,  uniformly  loaded  but  unevenly  distributed. 
As  it  is  practically  impossible  to  determine  accurately  the  amount 
of  stress  that  a  ship  will  be  subjected  to  wheu  laboring  in  a  sea- 
way, it  would  seem  quite  legitimate  to  arrive  at  the  necessary 
conclusions  on  the  basis  of  comparison  with  other  ships,  which 
have  proved  to  be  sufficiently  strong,  and  this  is  what  is  usually 
done  in  practice.  In  order  that  this  information  may  be  of  use 
for  comparative  purposes,  it  is  advisable  to  lay  off  the  curves  of 
weight,  buoyancy,  bending  moments,  etc.,  to  some  standard 
length  and  the  mean  weight  or  buoyancy  ordinate  to  some  stand- 
ard height,  so  as  to  make  the  diagram  as  convenient  as  possible. 

Curve  of  Weights. 

The  mean  weight  per  foot  of  length  of  the  total  hull  is  calcu- 
lated at  convenient  distances  apart  and  these  set  up  as  ordinates 
from  the  base  line  of  the  diagram,  at  their  corresponding  stations, 
taking  care  to  use  the  proper  scale  as  previously  determined  on  ; 
the  other  heavy  weights,  as  guns,  armor,  machinery,  coal,  homo- 
geneous cargo,  etc.,  are  calculated  separately  and  added  as  rect- 
angles above  the  curve  of  hull  weights.  A  mean  curve  is  then 
run  through  these  points,  taking  care  that  its  centre  of  gravity 
comes  over  the  centre  of  buoyancy  and  that  the  area  circumscribed 
by  the  curve  equals  the  displacement  of  the  ship. 

Curve  of  Buoyancy. 

The  displacement  in  tons  per  foot  of  length  is  then  calculated  at 
suitable  intervals  apart  and  set  up  as  ordinates  in  the  same  man- 
ner as  for  the  weight  curve.  The  area  enclosed  by  a  curve  pass- 
ing through  these  spots  should  also  equal  the  displacement  of  the 
vessel  and  will  show  the  distribution  of  the  support  given  by  the 
fluid  pressures  in  relation  to  the  curve  of  weights  at  any  point  in 
the  ship's  length. 


Strength  of  Ships 


255 


256 


The  Naval  Constructor 


Calculation  Table  for 


Moment  of  Inertia  of  Section 


Item. 


Bar  keel  ($) 

Flat  plate  keel  ($)  .  .  .  . 
Garboard  strake  A  .  .  .  . 
Strakes  B,  C,  D,  and  E    .     . 

Strake  F 

Strake  G 

Strake  H 

Strake  J 

Strake  K 

Strakes  M,  N,  O,  P,  and  R  . 
Strakes  S  and  T 

Strake  U  (sheer) ....      j 

Strake  W 

Strake  X  (sheer) ....      J 

Strakes  Y  and  Z 

f  Keelson  (£) 

f  Keelson,  bottom  angle  .  . 
$  Keelson,  top  angle  .  .  . 
First  longitudinal  .... 
Second  longitudinal  .  .  . 
Third  longitudinal    .... 

Margin  plate 

Margin  angle 

Inner  bottom  strake  A  (£) 
Inner  bottom  strakes,  B,  C,  D. 
E,F  .     .     .     .     .     .     .     . 

Tie  plate 

Bilge  keel  angles 

Bilge  keel  plate 

Lower  hold  stringer 


Size. 


6"  x  3" 

27"  x  W' 
48"- §  J" 

4-51"xH" 

48"  x  U" 

60"  XU" 

54"  xM" 

60"  x  W 

54"  xW' 

5(54"xH") 

2  (44"  x  W) 

51"xfr 

37. 5"  x  fg" 

5H"xf#" 

51"  x  U" 

37.5"  x  H" 

2-51" x  W 

58"  x  W' 

5"  x  5"  x  i§" 

4"x4"xM" 

47"  x  \%" 

44"  x  \%" 

40£"  x  ffi' 

58"  xH" 

4"X4"x  £&" 

30"x^" 

279. 6"  x  ft" 

33"  xH" 
2-6"  x  4"  x^' 

10"  xH" 
2  [  10"x3£"x48' 

10"  xM" 


Gross 
Area. 


Sq.  In. 
18.0 
31.1 
48.0 

173.4 

432 

540 
48.6 
54.0 
48.6 

229.5 
97.2 
51.0) 
37.5) 
51.7 
51.0) 
37.5) 
51.0 
21.7 
7.4 
4.8 
23.5 
22.0 
20.2 
40.6 
4.8 
19.5 

153.7 

19.8 

9.5 

9.0 

121.6 


Table  for  Moment  of  Inertia 


257 


Moment  of  Inertia. 


at  Frame  M  and  at  Frame  N. 

Arm 

—  d. 

Moment 
—  dA. 

Moment 

of  Inertia 

=  d*A. 

Depth 
of  Web 

— Ft.' 

Square  of 
Depth  =  ft2. 

A  Net 

Area  =. 

A 

&Ah\ 

Ft. 

Ft.   Sq.  In. 

Ft.2  Sq.In. 

Ft.2 

Sq.  In. 

Ft.2Sq.In. 

-26.71 

-382 

10,202 

-  2659 

-588 

15,625 

.   .    . 

.... 

-  26.30 

-499 

26,285 

.    .    . 

.... 

-25.55 

-3,562 

91,000 

.... 

-  24.60 

-863 

21,241 

.    •   • 

.... 

-  24.00 

-1,087 

24,883 

.... 

-  22.05 

-853 

18,816 

y ' 

9 

8.V 

29 

-  18.65 

-806 

15,026 

4.50 

20.3 

3.6 

73 

-  14.45 

-559 

8,081 

4.50 

20.3 

3.2 

65 

-    2.75 

-503 

1,383 

20.50 

420.25 

15.25 

6,409 

11.30 

875 

9,883 

8.5 

72.25 

6.45 

466 

17.10 

1,188 

20,322 

(4.25 
(3.12 

18.06 
9.73 

3.3} 
2.5) 

84 

20.75 

845 

17,524 

4.30 

18.49 

3.4 

63 

24.50 

1,703 

41,717 

(4.25 
(3.12 

18.06 
9.73 

3.8} 
2.5) 

84 

30.10 

1,222 

36,784 

8.00 

64.00 

3.4 

218 

-24.10 

-434 

10,454 

4.83 

28.33 

1.5 

35 

-  2^.35 

-148 

3,888 

-21.75 

-76 

1,656 

-23.70 

-107 

2,528 

3.92 

'  15.37 

'  .V 

'  6 

-  23.25 

-105 

2,433 

3.67 

13.47 

.4 

6 

-  22.80 

-103 

2,339 

3.37 

11.36 

.4 

5 

-22.00 

-662 

14,568 

3.67 

13.47 

2.5 

3.4 

-24.10 

-84 

2,033 

.  .  . 

-21.55 

-347 

7,477 

-21.05 

-2,762 

58,135 

-  20.33 

-317 

6,447 

-  22.60 

-172 

3,882 

-  23.00 

-196 

4,496 

-  15.60 

-306 

4,771 

_ 

258 


The  Naval  Constructor 


Calculation  Table  for  Moment 


Moment  of  Inertia  of  Section 

Item. 

Size. 

Gross 
Area. 

Net 

Area  = 

A. 

Upper  hold  stringer .     .     . 
Orlop  deck  stringer  .     .     . 
Orlop  deck  stringer  angle  . 
Orlop  deck  plating   .     .     . 
Lower  deck  stringer      .    . 
Lower  deck  stringer  angle 
Lower  deck  plating  .     .     . 
Lower  deck  ridge  bar    .     . 
Middle  deck  stringer     .     . 
Middle  deck  stringer  angle 
Middle  deck  plating      .     . 
Middle  deck  ridge  bar  .     . 

Upper  deck  stringer      .     . 

Upper  deck  stringer  angle 

Upper  deck  plating  .     .     . 

Upper  deck  ridge  bar    .     . 

Shelter  deck  stringer    .     . 

Shelter  deck  stringer  angle 

Shelter  deck  plating      .     . 

Shelter  deck  ridge  bar  .     . 
Bridge  deck  stringer     .     . 

Bridge  deck  stringer  angles 

Bridge  deck  plating  .     .     . 

1 
i 
i 
! 

I 

2  [  10"x3£"x48" 
10"XW" 

49"  x  «" 

4"x4"xH" 
229"  x  A" 

49"X*r 

4"x4"x-l|" 

229"  X-&" 
9"x3.85"x|#"[ 

49"  xM" 

4"x4"xH" 

233"  X  A" 

9"x3.85"xH"[ 

41" x  f £" 

60"x»" 

5"x6"xif 

139"  xii"    | 

60"  xH"    ' 

8"  x  3£"  x  \$"  [ 

50"  xH" 

wxji" 

2-6"x6"x£#" 
135"  x  M" 

58"  XM" 

8"x81"xir  [ 

62"  x&" 

7"x3*"xH" 

3i"x8J"x^" 

246"  x^" 

)  Sq.  In. 
|  21.6 

31.9 

4.1 
80.2 
31.9 

4.1 
91.6 

7.9 
39.2 

4.1 
104.9 
7.9 
41.0) 
45.01 

6.6 

115.5 

7.0 
45.0  ) 
76.2  i 
16.4 

j  131.3 

7.0 
23.4 

j    8.6 

61.5 

Sq.  In. 
19.6 

27.9 

3.1 
69.7 
27.9 

3.1 
79.6 

7.0 
33.6 

3.1 
91.4 

7.0 

72.9 

4.3 

101.1 

6.1 

102.7 

12.4 

114.3 

6.1 
20.0 

7.3 

50.5 

2,515.3 

2,036.9 

2,370.8 

1,918.5 

Moment  of  Inertia  of  Section  at  Frame  M. 
Assumed  neutral  axis  2G.5'  above  base. 
Actual  neutral  axis  :=  %%$  =  1.28'  above  assumed  neutral  axis  =  27.78' 


above  base  line 
Moment  of  inertia  about  correct  neutral  axis 

=  1,629,112  Ft.*  Sq.  In. 
Note.  —  Rivets  neglected  both  in  compression  and  tension. 


2  (810,320  +  7,577  —  3,341) 


Table  for  Moment  of  Inertia 


259 


of  Inertia.  —  (Continued.) 


at  Frame  M  and  at  Frame  N. 


Arm 
=zd. 


Ft. 
11.35 

6.40 
6.35 
6.00 
1.00 
1.70 
2.00 
1.25 
9.67 
9.75 
10.00 
9.25 

17.70 

17.70 

18.10 

17.15 

25.,  5 

25.60 

26.10 
25.15 

33.65 

33.75 

34.05 


Moment 
—  dA. 


Ft.  Sq.  In 

-222 

-179 

-20 

-418 

45 

5 

159 

9 

325 

30 

914 

65 

1,290 

76 

1,830 

105 
2,645 

317 

2,983 
153 

673 

246 

1,720 


( +19,423 1 
|  —16,010  | 

2,613 

( +15,562  1 
\  —16,810 

-1,248 


Moment 

of  Inertia 

=  d*A. 


flts    II 


Ft.2Sq.In 
2,524 

1,144 

125 

2,509 

71 

9 

318 

11 

3,142 

295 

9,140 

599 

22,840 
1,347 

33,120 
1,794 

68,096 

8,127 

77,861 
38.58 

22,646 

8,315 

58,550 


810,320 


684,025 


037 


1,919 x 


Square  of 
Depth  =  A2. 


Ft.2 


1.282=3,341 
.652  =  806 


A  Net 

Area  = 

A 

TIT 


Sq.  In. 


&Ah*. 


Ft.2Sq.In 


5 

359 


Moment  of  Inertia  of  Section  at  Frame  If. 
Assumed  neutral  axis  r=  26.5'  above  base. 
Actual  neutral  axis  =  ||f§  =  .65'  below  assumed  neutral  axis  =s  25.85' 

above  base  line. 
Moment  of  inertia  about  correct  neutral  axis  =  2  (684,025  +  7,-359  —  806, 

=  1,381,156  Ft.2  Sq.  In. 


260  The  Naval  Constructor 


Curve  of  Load. 

The  curve  of  loads  is  obtained  by  measuring  the  difference 
between  the  curves  of  weight  and  buoyancy  at  the  various  ordi- 
nates  and  spotting  off  the  excess  buoyancy  above  the  base  ;  and  the 
excess  weight  below  their  points  of  intersection  with  this  line  will 
show  the  waterborne  sections,  which  for  calculating  purposes  are 
taken  as  the  points  of  support. 

Curve  of  Shearing  Stresses. 

This  curve  is  calculated  from  the  foregoing  curve  of  load  by 
faking  its  area  at  various  ordinates  measured  from  forward  aft 
and  plotting  these  areas  off  above  or  below  the  base  line  as  in  the 
case  of  the  curve  of  loads,  observing  that  the  greatest  stresses 
will  be  opposite  the  points  of  support  (or  waterborne  sections). 
A  curve  run  through  the  foregoing  spots  will  show  the  shearing 
stresses  graphically. 

Curve  of  Bending  Moments. 

As  the  bending  moment  at  any  section  in  the  length  of  a  ship 
is  equal  to  the  algebraic  sum  of  the  shearing  stresses  in  relation  to 
either  end,  it  is  evident  that  a  curve  of  bending  moments  may  be 
obtained  from  these  stresses  and  plotted  off  as  was  done  for  the 
shearing  curve  from  the  curve  of  loads,  observing  that  the  maxi- 
mum and  minimum  bending  moments  will  be  coincident  with  the 
points  of  support. 

To  apply  similar  curves  and  the  data  constituting  them  to  the 
determination  of  the  stresses  experienced  by  a  ship  amongst 
waves,  it  is  usual  to  take  the  two  extreme  bending  moments  to 
which  a  vessel  is  subjected,  viz.:  (1)  hogging  on  the  crest  of  a 
wave,  and  (2)  sagging  in  the  trough,  and  to  construct  a  trochoid 
wave  of  such  form  as  will  give  the  same  displacement  of  immersed 
body  (in  both  cases)  as  obtained  in  smooth  water.  The  curves 
are  then  calculated  as  explained  in  the  foregoing,  taking  the 
height  of  wave  as  being  ^  of  the  length. 

The  subjoined  table  shows  a  specimen  calculation  of  the  moment 
of  inertia  of  the  sections,  observing  that  although  the  rivets  in  this 
case  are  neglected  for  compression,  it  would  probably  be  some- 
what more  accurate  to  include  them. 

Unless  in  exceptional  cases  it  will  be  found  sufficiently  approxi- 
mative for  comparative  purposes  to  multiply  the  displacement  of 
the  proposed  vessel  by  one-thirtieth  to  one  thirty -fifth  of  the  length 
when  the  product  will  equal  the  maximum  bending  moment,  as 


Strength  of  Ships  261 

lxd  .    '     ,     ,. 

■ — — —  =  maximum  bending  moment, 
oO 
and  the  minimum  tension  on  sheerstrake  equals 
Maximum  bending  moment  x  Neutral  axis  below  sheerstrake  _ 

Total  moment  of  inertia 
Tension  stress  per  square  inch.     The  compression  on  the  bottom 
plating  is  similarly  computed,  substituting  the  distance  of  neutral 
axis  above  keel  for  "  below  sheerstrake." 

The  value  of  the  maximum  tensile  strength  per  square  inch  of 
section  varies  of  course  with  the  size  and  proportions  of  vessels. 
A  suitable  value  for  vessels  of  wholesome  proportions  built  to  any 
of  the  great  classification  societies'  rules  is  about  2  tons  per  square 
inch  in  small  vessels  to  about  9  in  the  largest  liners,  taking  the 
comparative  method  of  calculating  the  bending  moment  given 
above. 

It  will  be  evident  from  an  examination  of  the  table  showing  a 
specimen  calculation  of  the  moment  of  inertia  of  a  ship's  cross 
section,  that  the  further  the  sectional  area  of  the  ship  is  arranged 
from  the  neutral  axis,  the  greater  will  be  the  moment  of  resistance 
to  bending.  It  is  in  recognition  of  this  geometrical  quality  that 
the  upper  deck  in  3-deck  and  other  ships  is  made  the  strength 
deck,  and  that  the  keel  plate  and  garboards  are  thickened  as  well 
as  the  sheerstrake  and  stringer  being  increased  at  that  level,  in 
addition  to  reinforcing  the  bilge  ;  for,  with  a  ship  rolling  and 
pitching,  'tmust  often  happen  that  the  greatest  bending  moments 
will  frequently  be  exerted  at  the  bilge  and  upper  deck  gunwale. 
By  making  the  shelter  deck  in  3-deck  vessels  the  "strength 
deck, ' '  a  great  increase  in  the  strength  of  these  ships  has  been  made 
in  recent  years,  as  demonstrated  by  actual  practice,  steamers  of 
this  class  being  now  practically  "  4-deckers  "  from  a  strength  point 
of  view. 


262  The  Naval  Constructor 

CHAPTER  VIII. 

RESISTANCE  OF  SHIPS. 
The  Admiralty  Coefficient. 

The  amount  of  power  required  to  propel  a  vessel  at  a  given 
speed  is  generally  computed  by  (1)  the  Admiralty  Coefficient  for- 
mula, or  (2)  a  formula  based  on  the  ship's  actual  resistance,  the 
former  being  purely  empirical  and  requiring  great  judgment  and 
practice  in  the  selection  of  the  coefficient,  and  the  other  founded  on 
scientific  experimental  data  and  theories  which  have  acquired  con- 
firmatory proof  amounting  to  law,  since  they  were  first  enunciated 
by  William  Froude.  The  following  notes  on  resistance  are  taken 
principally  from  the  papers  by  this  eminent  investigator,  and  from 
the  later  work  of  Middendorf ,  Taylor,  and  others. 

The  Admiralty  Coefficient  (C)  is  calculated  from  the  results  of 
actual  trials,  and  is  based  on  the  false  assumptions  that  the  area 
of  wetted  surface  (S)  for  similar  ships  is  proportional  to  the  § 
power  of  the  displacement  (Z$),  and  that  the  resistance  (R)  plus 

(If    IT    B     \ 
'    *    ' )  varies  as  the  cube  of  the 

speed  ( Vs).    From  this  we  get  the  well-known  formula : 

and  for  the  speed  with  a  stated  I.H.P., 
CxI.H.P. 


2? 

Therefore  the  coefficient : 

I.H.P.  * 


C  = 


It  will  be  obvious  that  these  coefficients  must  cover  a  wide  range 
of  values,  hence  the  difficulty  of  their  application  by  the  inex- 
perienced. For  this  reason  we  append  a  table  of  values  in  vessels 
of  greatly  divergent  types.  It  should,  however,  be  noted  that  for 
vessels  of  similar  form  but  different  lengths,  the  coefficient  will 
show  great  disparity,  and  for  vessels  of  similar  form  and  length 
but  different  draught,  there  will  likewise  be  much  dissimilarity  in 
the  coefficient.     In  the  selection  of  this  coefficient  it  should  also 


Froude's  Law  of  Comparison 


263 


be  remembered  that  the  class  of  steamer  to  which  it  is  applied 
must  be  similar  not  only  in  form,  but  in  type  of  engine  as  well, 
and  of  corresponding  speed.  This  does  not  necessarily  mean  the 
same  speed,  as  will  be  explained  later. 


Table  of  Admiralty  Coefficients. 


Type  of  Vessel. 


Launches  (yachts)  .... 
Launches (navy)  .... 
Vedettes  (high  speed)  .  .  . 
Speed  launches  and  yachts  . 
Steam  yachts  (large)     .     .     . 

Torpedo  boats 

Torpedo  boat  destroyers    .     . 

Cruisers 

Harbor  and  revenue  steamers 
River  steamers  (shallow  dr.)  . 
River  .  teamers  (paddle)  .  . 
River  steamers  (stern  wheel). 
Channel  steamers 
Freighters  (small) 
Freighters  (large) 
Intermediate  liners 
Ocean  liners    .     . 


Length 
L. 


Feet. 

18-30 

27-45 

50-60 

70-100 

130-250 

100-150 

170-235 

500 

55-75 

60-100 

100-250 

75-150 

250-300 

100-250 

300-500 

500-600 

500-750 


Block 
Coeffi- 
cient, 
5. 


28-.  38 
30-.  40 
35-.  42 
41-.43 
40-.  48 
40-.  44 
40-.  43 

.54 
45-.  50 
50-. 55 
50-.  60 
6S-.75 
58-.  65 
.73-.  78 
.78-.78 
.70-.  72 
.60-.  65 


Knots 
7   -10 
7  -12 

14  -20 

16  -22 

12  -20 
20  -25 
27  -33 

22 
9  -10 
8f-13 

13  -20 
8|-13 

17  -21 

8H1 
11  -13 

14  -16 
20  -25 


Ad- 
miralty 
Coeffi- 
cient, 
C. 


65-70 
50-70 
75-130 
135-165 
165-175 
140-170 
175-210 

275 
110-120 
85-120 
100-180 
65-120 
240-270 
100-230 
240-280 
270-310 
265-285 


FROUDE'S  LAW  OF  COMPARISON. 


As  the  result  of  experiments  with  models  and  full  sized  ships 
Froude  discovered  that  there  was  great  resemblance  between 
their  "curves  of  resistance,1'  i.e.,  a  curve  plotted  off  withascaleof 
knots  as  abscissae,  and  the  pounds  resistance  to  towing  as  ordi- 
nates.     See  Fig.  51. 

To  test  this,  however,  it  is  necessary  to  apply  the  Law  of 
Comparison,  which  he  thus  states  :  — 

11  If  the  ship  be  D  times  the  dimension  of  the  model  and  at  the 
speeds  Vi,  V%,  Vs  .  .  .  the  measured  resistances  of  the  model 


204 


The  Naval  Constructor 


are  Rh  R2,  R8  .  .  .,  then  for  speed  \ll)Vv   yDVv   \ID 
of  the  ship,  the  resistance  will  be  D8^,  -D8^,  IPRs-  • 

To  the  speeds  of  model  and  ship  thus  related,  he  applied  the 
term  "corresponding  speeds."  This  law  expresses  the  resistance 
due  to  surface  friction,  plus  wavemaking  resistance,  the  former 
being  commonly  referred  to  as  skin  resistance  and  the  other  as 
residuary  resistance,  embracing  as  it  does,  the  resistance  caused 


20,000 


10,000  g 


5,000 


13 


n 

& 

l*^ 

I' 

C^> 

II 

Speed  in  Knots 
Fig.  51. 


by  the  motion  of  the  waves  and  the  drag  of  dead  water  eddies, 
such  as  are  formed  at  abrupt  endings  to  bossings,  the  siding  of 
stern  posts  and  in  the  wake  of  propeller  struts.  The  skin 
resistance  is  proportional  to  the  area  of  wetted  surface,  and  is  re- 
sponsible for  almost  the  total  resistance  up  to  about  8  knots  speed. 
Beyond  this  speed  the  total  resistance  increases  rapidly,  showing 
the  effect  of  the  residuary  resistance.  This  will  be  more  readily 
understood,  when  we  recollect  that  the  wave  undulations  progres- 
sively increase  in  height  with  increases  in  speed,  and  that  the  crests 
of  these  waves  are  accountable  for  about  95  per  cent  of  the  total 
residuary  resistance,  the  remaining  5  per  cent,  as  already  stated, 
being  due  to  eddies,  etc.  Referring  to  the  diagram  here  reproduced, 
showing  curves  of  residuary  and  skin  resistances,  ' '  the  graduated 
undulations  in  the  residuary  resistance  curve  are  due  to  quasi- 
hydrostatic  pressure  against  the  after-body,  corresponding  with 
the  variations  in  its  position  with  reference  to  the  phases  of  the 
train  of  waves  comprising  the  wave  line  profile,  there  being  a  com- 
parative excess  of  pressure  (causing  a  forward  force  or  diminution 


Froude's  Law  of  Comparison 


265 


of  resistance)  when  the  after-body  is  opposite  a  crest,  and  the 
reverse  when  it  is  opposite  a  trough.  Their  spacing  is  uniform 
at  a  uniform  speed,  because  waves  of  given  speed  have  always  the 
same  length  ;  it  is  more  open  at  the  higher  speeds,  because  waves 
are  longer  the  higher  their  speed;  their  amplitude  is  greater  at 


RESISTANCE  IN  TONS. 


RESISTANCE  IN  TON8. 
o>            00            o 
I     .1      I.I      I    ,1      1,1 L 


RESISTANCE  IN  TONS. 


Fig.  52. 


1   i,  i    L  i    I'   I  '    II 

O  K>  * 

RESISTANCE  IN  TONS. 


the  higher  speeds,  because  the  waves  made  by  the  ship  are  higher ; 
and  their  amplitude  diminishes  with  increased  length  of  middle 
body,  because  the  Wave  system  by  diffusing  itself  transversely 
loses  its  height." 


266  The  Naval  Constructor 


1  i  <md e  found  that,  at  the  lower  speeds,  two  ships,  one  200  ft. 
and  the  other  240  ft.  in  length,  had  the  same  residuary  resistance  ; 
the  difference  in  the  larger  vessel  was  simply  due  to  its  increase  of 
skin  friction  due  to  the  greater  wetted  surface.  At  13. 16  knots,  how- 
ever, the  240-foot  vessel  had  the  lesser  total  resistance  of  the  two, 
owing  to  her  position  on  the  residuary  resistance  curve  coming  in 
a  hollow  ;  the  consequent  diminution  in  this  resistance  was  greater 
than  her  increase  of  skin  friction. 

The  resistance  depends  on  the  relative  placing  of  the  after-body 
and  the  wave  system,  and  the  length  spacing  of  the  wave  system 
depends  on  the  speed,  therefore  the  position  of  after-bodies, 
which  is  specially  favorable  at  some  given  speed,  may  be  specially 
unfavorable  at  a  higher  speed,  and  at  a  higher  speed  still  may  be 
favorable  again. 

This  it  is  which  explains  the  economy  with  which  some  vessels 
attain  certain  speed  whilst  others  of  almost  identical  form,  but 
slight  variation  in  length,  fall  short  of  the  others'  performance. 

To  apply  the  investigations  of  Froude  to  actual  ships,  it  is  usual 
to  make  a  model  of  the  proposed  ship  and  run  it  in  a  tank,  and 
from  the  data  obtained  apply  the  law  of  comparison.  For  ex- 
ample, if  a  model  be  made  of  a  liner  700  feet  long  on  a  scale  of 
\  inch  to  the  foot,  and  the  required  speed  of  the  ship  be  24  knots, 
at  what  speed  will  the  model  require  to  be  run  to  correspond  with 
the  desired  velocity  ?  "  In  comparing  similar  ships,  or  ships  with 
models,  the  speed  must  be  proportional  to  the  square  root  of  their 
linear  dimensions. ' ' 

Therefore  the  model  will  be 

700  feet     __,  .     . 
-— — —  =  87  A  inches, 
£  inch  J  ' 

or  7  feet  3J  inches,  and  the  ratio  of  linear  dimensions, 

700  feet 

-T29-  =  96' 

and  speed  corresponding  to  24  knots, 

24  -r  V96  =  2.45  knots. 

In  like  manner,  if  we  are  working  from  the  known  speed  of 

another  ship,  say,  of  600  feet  length,  then : 

£#$=  1.16  ratio  of  linear  dimensions, 

and  24  -f  V06  =  25.8  knots, 

corresponding  speed  of  the  600-foot  boat. 

APPLICATION  OF  FROUDE'S  LAW. 

It  is,  however,  in  dealing  with  data  derived  from  trial  perform- 
ances that  the  law  of  comparison  is  invaluable  to  those  having  the 


Application  of  Froude's  Law 


267 


responsibility  of  powering  ships.  For,  given  the  trial  data  of  the 
ships,  we  may  apply  this  to  other  vessels  of  similar  form  to  obtain 
the  I.H.P.  necessary  to  drive  them  at  a  stated  speed.  Of  course, 
we  assume  that  the  efficiency  of  the  engines,  boilers  and  propellers 
are  equal  in  both  cases,  otherwise  that  their  coefficients  of  efficiency 
are  the  same.  So  that  when  we  know  the  displacement,  power, 
and  speed  of  a  given  ship  represented  .by  D,  P,  and  V,  and  it  is 
required  to  estimate  the  I.H.P.  from  a  proposed  vessel  of  like 
form  of  Di,  Pi,  and  Fi,  then, 


POWER  CURVE 


(1) 

and  (2) 

Substituting  values, 
(1) 

(2) 


Vi 


8peed  in  knot8 
Fig.  53. 

=  /32, 
1 17, 


58,000  I.H.P. 
=  24.4  knots. 


We  may  also  run  a  speed  curve  of  the  known  vessel,  where 
progressive  runs  have  been  made,  as  shown  in  Fig.  53,  and  from 
this  deduce  the  proposed  vessel's  corresponding  curve  with  the  aid 
of  the  formula  given. 


268  The  Naval  Constructor 

The  curve  illustrated  is  that  of  a  66-ft.  vedette  pinnace,  and  it  is 
proposed  to  deduce  the  power  curve  of  a  21  knot  speed  launch  from 
it,  being  a  type  of  similar  form. 

Displacement  of  vedette 13.75  tons. 

Displacement  of  speed  launch    .     .     22.50  tons. 

The  corresponding  length  L\  of  the  speed  launch  would  be 
obtained  from  the  length  of  the  vedette  and  the  ratio  of  the  dis- 
placements. 

Corresponding  speed, 

Corresponding  power, 

So  that  after  the  derived  curve  has  been  plotted  from  the  spots 
calculated  as  above  for  various  speeds,  it  must  be  continued  in  the 
same  contour  until  it  is  opposite  the  21-knot  ordinate,  when  the 
required  power  may  be  read  off. 

STANDARD  CURVES  OF  POWERS. 

Taylor  in  his  "  Resistance  of  Ships  "  advocates  the  adoption  of 
a  "standard"  displacement  in  applying  the  Law  of  Comparison, 
to  which  all  trial  particulars  should  be  reduced,  and  for  this  pur- 
pose takes  10,000  tons  as  a  basis,  giving  tables  of  factors  to 
facilitate  the  reduction  of  the  speed  and  power  data  possessed,  to 
this  standard  displacement. 

He  makes  each  curve  cover  a  range  of  one  knot,  after  the 
manner  shown  on  Fig.  54.  As  an  example  of  the  method 
employed  in  estimating  the  indicated  horse  power  by  the  aid  of 
these  standard  curves  and  tables,  let  us  postulate  that  the  power 
is  required  for  a  proposed  ship  of : 

Length 440  feet. 

Breadth 48  feet. 

Draught 19.5  feet. 

Displacement 7,000  tons. 

Coefficient,  5 .595. 

Speed         18^  knots. 

Then  to  reduce  10,000  tons  displacement,  dimension,  speed,  and 
power  factors  are  calculated. 


Standard  Curves  of  Powers 


269 


In  the  above  case  these  are  1.126,  1.061,  and  1.017  respectively, 
which  work  out  : 

Length   x  1.126  =  495.44  feet. 
Breadth  x  1.126  =  54.04  feet. 
Draught  X  1.126  =  21.96  feet. 
Speed      x  1.061  =  19.63  knots. 

SPEED  AND  POWER  CURVE 
(STANDARDIZED) 
20,000 

19,000 

18,000 

J  7,000 

16,000 

±  15,000 

14,000 

13.000 

12,000 

11,000 

10,000 


\£® 

rU^ 

19 


.4  .5  .8 

KNOTS 
Fig.  54. 


20 


From  the  diagram  shown  we  find  that  the  "Umbria"  at  19.63 
knots  took  13,000  I.H.P.  at  10,000  tons  standard  displacement, 
and  this  divided  by  the  power  factor  1.517,  will  give  the  I.H.P. 
required,  viz.: 

H^°  =  8,570  I.H.P. 
1.517 

Any  one  may  prepare  a  set  of  these  standard  curves,  making 
each  one  cover  a  range  of  one  knot,  from  his  own  trial  data. 
These  will  be  found  very    useful,    as  of  the    many    methods 


270  The  Naval  Constructor 


employed  to  estimate  horse  power,  this  is  probably  one  of  the 
most  reliable,  besides  being  easy  of  application.  Of  course,  to  do 
this  one  must  be  possessed  of  the  requisite  data  and  the  judgment 
to  know  how  to  apply  it. 

In  conjunction  with  the  curves,  tables  should  also  be  calculated 
for  the  dimension,  speed,  and  power  factors  for  graduated  dis- 
placements as  follows  : 

The  dimension  factor  is  the  ratio  of  the  linear  dimensions,  as: 

Ratio  of  displacement,  '       =  1.43 ; 

therefore,  dimension  factor 

J=-\/L43=  1.126 
for  7,000  tons  displacement. 


Speed  factor  =  (1^°]i=  1.061, 


and  Power  factor  =  ^j?  X  1.061  =  1.517. 

I.H.P.  by  Independent  Method. 

Where  the  type  of  vessel  is  abnormal,  the  speed  excessive,  or 
sufficient  data  to  which  to  apply  the  comparative  method  is  not 
possessed,  the  effective  horse  power  should  be  calculated  in  detail 
from  the  skin  and  wave  resistances,  and  by  the  selection  of  a 
suitable  efficiency  coefficient  for  the  machinery,  the  Indicated 
Horse  Power  may  be  computed  with  great  accuracy.  For  this 
purpose  it  is  necessary  to  know  the  wetted  surface,  and  this  may 
be  figured  with  the  aid  of  either  of  the  tables  given  on  p.  98. 

The  wetted  surface  determined,  this  area  must  be  multiplied  by 
the  coefficient  of  friction  due  to  the  particular  surface  which  will 
give  the  skin  friction,  and  this  in  turn  multiplied  by  the  power  ne- 
cessary to  overcome  one  pound  resistance  at  one  knot  (.0030707  V) 
by  the  1.83  power  of  the  velocity  required,  will  give  the  E.H.P. 
for  skin  resistance.     Otherwise  stated, 

Skin  resistance  power  =f.S.  .00307 V2-63  =  Et. 

To  this  must  be  added  the  power  for  residuary  or  wave-making 
resistance  E„. 

Wave  resistance  power  =  .00307  &P~5  =  Ew. 

Then  these  two  combined  give  us  the  E.H.P.  for  the  total 
resistance,  from  which  the  I.H.P.  may  be  determined  by  taking  a 
suitable  coefficient  of  efficiency. 

It  should  be  stated  that  "&'"  ranges  from  .35  in  swift,  narrow 
vessels,  to  .55  in  full,  slow  vessels. 


Least  Resistance  by  MiddendorPs  Method    271 

Substituting  values  and  applying  them  to  the  determination  of 
the  I.H.P.  required  for  the  440-ft.  steamer  dealt  with  on  p.  189, 
we  have, 

Wetted  surface  =  26,600  sq.  ft.  =  8. 
Coefficient  of  friction  "/"  =  .009. 
Power  per  pound  of  resistance  at  one  knot  =  .00307  V. 
Percentage  of  efficiency  =  60%  of  I.H.P. 
Speed  in  knots  V  —  18.5. 
Coefficient  b=  .35. 
Then,  Et  =  .009  x  26,600  X  .00307  F2.83 

=  2,830  E.H. P. 
And,  •  Ew=. 00307  x.  35 V5 

=  2,330  E.H. P. 
The  addition  of  the  skin  and  wave  resistance  powers  gives  us 
the  total'  effective  horse  power. 

E.H.P.  =  2,830  +  2,330  =  5,160 
and  the  indicated  horse  power  at  60%  efficiency  =  8,600  I.H.P., 
being  a  similar  result  to  that  obtained  by  the  comparative  method. 

Froude's  Frictional  Constants  for  Salt  Water  or 
Smoothly  Painted  Surfaces. 


Length 

Coefficient 

Length 

Coefficient 

of 

of 

of 

of 

Vessel. 

Friction. 

Vessel. 

Friction. 

50 

.00963 

200 

.00902 

60 

.00950 

250 

.00897 

70 

.00940 

300 

.00892 

80 

.00933 

350 

.00889 

90 

.00928 

400 

.00886 

100 

.00923 

450 

.00883 

120 

.00916 

500 

.00880 

140 

.00911 

550 

.00877 

160 

.00907 

600 

.00874 

180 

.00904 

.  .  . 

FORM  OF  LEAST  RESISTANCE, 
MIDDENDORF'S  METHOD. 


BY 


Herr  Middendorf  gives  the  following  method  of  obtaining  the 
angles  of  entrance  and  run  to  give  the  form  of  least  resistance,  and 


272 


The  Naval  Constructor 


Table  Giving  Angles  of  Entrance  and  Run 

Lengtlit 


26  Ft. 

40  Ft. 

65  Ft. 

90  Ft. 

125  FT. 

165  Ft. 

Speed 

in 
Knots. 

TO 

40  Ft. 

TO 

65  Ft. 

to" 
90  Ft. 

TO 

125  Ft. 

TO 
165  FT. 

TO 

200  Ft. 

a 
and 

d 

9 

a 

and 

0 

9 

a 

and 
0 

9 

a 

and 

0 

9 

a 
and 

9 

a 

and 

0 

9 

5 

o 
18.0 

0 

30.5 

o 
18.5 

31.5 

0 

20.0 

o 
33.0 

21.0 

0 

35.0 

9 

22.5 

o 
37.0 

o 
24.0 

o 
39.5 

6 

17.0 

29.0 

17.5 

30.0 

185 

31.5 

20.0 

33.0 

21.5 

35.0 

23.0 

37.5 

7 

16.0 

27.5 

16.5 

28.5 

17.5 

29.5 

18.5 

31.0 

20.0 

33.0 

21.5 

35.0 

8 

15.0 

2f>.5 

15.5 

26.5 

16.5 

27.5 

17.5 

29.0 

19.0 

31.0 

20.0 

33.0 

9 

14.5 

24.0 

14.5 

25.0 

15.5 

26.0 

16.5 

27.5 

17.5 

29.0 

18.5 

30.5 

10 

13.5 

22.5 

14.0 

23.0 

14.5 

24.0 

15.5 

25.5 

16.5 

27.0 

17.5 

28.5 

11 

12.5 

21.0 

13.0 

21.5 

13.5 

22.0 

14.5 

23.5 

15.0 

25.0 

16.0 

26.5 

12 

11.5 

19.5 

12.0 

20.0 

12.5 

20.5 

13.0 

21.5 

14.0 

23.0 

15.0 

24.5 

13 

10.5 

18.0 

11.0 

18.5 

11.5 

19.0 

12.0 

20.0 

13.0 

21.0 

13.5 

22.5 

14 

10.0 

16.5 

10.5 

17.0 

10.5 

17.5 

11.0 

18.5 

12.0 

19.5 

12.5 

21.0 

15 

9.0 

15.5 

9.5 

16.0 

10.0 

16.5 

10.5 

17.0 

110 

18.0 

11.5 

19.0 

16 

8.5 

14.5 

8.5 

14.5 

9.0 

15.0 

9.5 

16.0 

10.0 

16.5 

10.5 

17.5 

17 

8.0 

13.5 

8.0 

13.5 

8.5 

14.0 

9.0 

14.5 

9.0 

15.5 

9.5 

16.5 

18 

7.5 

12.5 

7.5 

12.5 

7.5 

13.0 

8.0 

13.5 

8.5 

14.5 

9.0 

15.0 

19 

7.0 

11..". 

7.0 

12.0 

7.0 

12.5 

7.5 

13.0 

8.0 

13.5 

8.5 

14.0 

20 

6.5 

11.0 

6.5 

11.0 

7.0 

11.5 

7.0 

12.0 

1   7.5 

12.5 

8.0 

13.0 

21 

6.0 

10.5 

6.5 

11.0 

6.5 

10.5 

7.0 

11.5 

7.5 

12.0 

22 

6.0 

10.5 

6.0 

10.5 

6.5 

11.0 

7.0 

11.5 

23 

6.0 

10.0 

6.0 

10.5 

6.5 

10.5 

24 

6.0 

10.0 

6.0 

10.0 

25 
26 

6.0 

9.5 

Angles  of  Entrance  and   Run 


273 


for  Ships  of  Various  Lengths  and  Speeds. 
in  Feet. 


200  Ft. 

260  Ft. 

320  Ft. 

390  Ft. 

460  Ft. 

540  Ft. 

620  Ft. 

to 

TO 

TO 

TO 

to 

to 

TO 

260  Ft. 

320  Ft. 

390  Ft. 

460  Ft. 

540  Ft. 

620  Ft. 

720  Ft. 

a 

and 

0 

a 

and 

/3 

0 

a 

and 

/3 

0 

a 

and 

/3 

0 

a 
and 

/3 

0 

a 

and 

/3 

0 

a 
and 

/3 

9 

o 

0~~ 

o 

5 

0 

o 

o 

o 

0 

0 

o 

o 

~~  o 

o 

26.0 

42.0 

27.5 

44.5 

24.5 
23.0 
21.5 

39.5 
37.0 
35.0 

26.5 
24.5 
23.0 

42.0 
39.5 
37.0 

28.0 
26.5 
25.0 

44.5 
42.0 
39.5 

28.0 
26.5 

44.5 
41.5 

28.0 

44.0 

20.0 

32.5 

21.5 

34.5 

23.0 

36.5 

24.5 

39.0 

26.5 

41.0 

28.5 

44.0 

19.0 

30.5 

20.0 

32.0 

21.5 

34.0 

23.0 

36.0 

24.5 

38.5 

26.5 

41.0 

28.5 

44.0 

17.5 

28.0 

18.5 

30.0 

20.0 

32.0 

21.5 

34.0 

23.0 

36.0 

25.0 

38.0 

26.5 

41.0 

16.0 

26.0 

17.0 

27.5 

18.5 

29.5 

20.0 

31.5 

21.5 

33.5 

23.0 

35.5 

25.0 

38.0 

14.5 

24.0 

15.5 

25.5 

17.0 

27.5 

18.5 

29.0 

20.0 

31.0 

21.5 

33.0 

23.0 

35.0 

13.5 

22.0 

14.5 

23.5 

15.5 

25.0 

17.0 

27.0 

18.5 

28.5 

20.0 

30.5 

21.0 

32.5 

12.5 

20.0 

13.0 

21.5 

14.5 

23.0 

15.5 

25.0 

17.0 

26.5 

18.0 

28.0 

19.5 

30.0 

11.5 

19.0 

12.0 

20.0 

13.0 

21.5 

14.0 

23.0 

15.5 

24.5 

16.5 

26.0 

18.0 

27.5 

10.5 

17.5 

11.0 

18.5 

12.0 

19.5 

13.0 

21.0 

14.0 

22.5 

15.0 

23.5 

16.5 

25.0 

9.5 

16.0 

10.0 

17.0 

11.0 

18.0 

12.0 

19.5 

13.0 

20.5 

13.5 

21.5 

15.0 

22.5 

9.0 

14.5 

9.5 

15.5 

10.0 

16.5 

11.0 

17.5 

11.5 

18.5 

12.5 

19.5 

8.0 

13.5 

8.5 

14.5 

9.0 

15.0 

10.0 

16.0 

10.5 

17.0 

11.0 

17.5 

12.0 

18.5 

7.5 

12.5 

8.0 

13.0 

8.5 

13.5 

9.0 

14.5 

9.5 

15.0 

10.0 

16.0 

11.0 

16.5 

7.0 

11.5 

7.5 

12.0 

8.0 

12.5 

8.5 

13.0 

9.0 

13.5 

9.5 

14.0 

9.5 

15.0 

6.5 

11.0 

7.0 

11.5 

7.5 

11.5 

7.5 

12.0 

8.0 

12.5 

8.5 

13.0 

8.0 

13.5 

6.0 

10.0 

6.5 

10.5 

7.0 

10.5 

7.0 

11.0 

7.5 

11.0 

7.5 

11.5 

9.0 

12.0 

6.0 

9.0 

6.0 

10.0 

6.0 

10.0 

6.0 

10.0 

65 

10.5 

7.0 

10.5 

7.0 

11.0 

6.0 

9.0 

6.0 

9.0 

6.0 

10.0 

6.0 

10.0 

6.0 

10.5 

6.5 

10.5 

7.0 

10.5 

274 


The   Nav,al   Constructor 


Form  of  Least  Resistance  275 

appended  is  a  table  giving  the  value  of  these  angles  for  various 
speeds  and  lengths  of  vessels  obtained  from  actual  well-known 
ships  of  the  best  form. 

On  the  construction  lines  of  the  body  plan  and  profile,  a  mean 
water  line  is  drawn  half  way  between  keel  and  load  line,  as  shown 

atf- 

By  referring  to  the  table  of  angles,  a  is  selected  for  the  length 
of  vessel  being  designed  and  the  tangent  of  the  same  spotted  on 
the  half-breadth  plan.  This  will  give  the  outline  of  the  mean 
water  plane. 

Two  diagonals,  D  and  Dlf  are  struck  in  on  the  after  body  plan, 
the  former  intersecting  the  centre  line  at  half  the  draught,  as  well 
as  the  base  line  at  a  distance  equal  to  the  half-breadth  of  the  ship, 
and  Di  intersecting  the  load  water  plane  at  centre  line  as  well 
as  the  half  moulded  breadth  construction  line  at  the  mean  water 
line  height,  as  shown  in  Fig.  55. 

The  angles  /3  and  6  are  obtained  from  the  table  and  transferred 
to  the  half-breadth  plan  representing  the  half  planes  of  D  and  D\ 
respectively. 


276 


The  Naval  Constructor 


ELEMENTS    OF 


Moulded 

i  *° 

ki, 

km. 

Name. 

Description. 

Dimensions. 

1 
1 
1 
C 

•< 

A 

M 

3h 

•3  ~ 

'it 

| 

4 

i 

1 

- 

— 

q 

E 

2« 

3  a 

Campania  . 

1st  Class  Ocean 

/ 

/  // 

/  // 

/    // 

Liner,  T.S.     .    . 

600 

65  0 

41    6 

2610 

19,336 

.644 

.667 

.976 

Manchuria 

1st  Class  Interme- 

diate Liner,  T.S. 

GOO 

650 

43   3 

33  2 

26,514 

.715 

.762 

.942 

Normannia 

1st  Class  Ocean 

Liner,  T.S.     .    . 

500 

57  3 

38   0 

24  0 

11,588 

.59 

.625 

.94 

Tantallon 

1st    Class   Cape 

Castle     . 

Liner      .... 

440 

505 

3411 

24   6 

10,100 

.647 

.695 

.932 

Kiev  .    .    . 

Russian  Volunteer 

Fleet 

419 

49  6 

32   0 

23 11J 

10,640 

.738 

.769 

.959 

Texan    .    . 

1st  Class  Ocean 

Freighter,  T.S.  . 

471 

57  0 

35   0 

27  0 

16,236 

.784 

.820 

.958 

Nevadan    . 

1st  Class  Ocean 

Freighter,  T.S.  . 

360 

46  0 

27   2 

23  0 

8,217 

.758 

.788 

.961 

M.  S.  Dol- 

Ocean Freighter, 

lar  .    .    . 

S.S 

300 

40  0 

26   0 

22  0 

5,960 

.79 

.801 

.986 

Victoria     . 

Channel,  T.S.    .    . 

220 

28  0 

17   0 

10  0 

860 

.502 

.569 

.822 

Jupiter  .    . 

Sound,  P.S.  .    .    . 

230 

28  0 

9   6 

6  n 

699 

.578 

.621 

.930 

Greyhound 

Channel,  P.S.    .    . 

230 

27  0 

10  0 

610* 

690 

.568 

.622 

.913' 

Tynwald*  . 

Channel,  T.S.    .    . 

265 

344 

14   6 

10  0 

1,508 

.58 

.594 

.976 

Sandy  Hook 

Sound,  T.S.  .    .    . 

260 

37  0 

15   0 

10  2 

1,165 

.417 

.5 

.82 

Mayflower . 

Yacht,  T.S.  .    .    . 

275 

36  6 

21   0 

15  6 

2,414 

.535 

.612 

.874 

Giralda.    . 

Yacht,  T.S.   .    .    . 

275 

350 

19   0 

13  6 

1,862 

.505 

.498 

.904 

Ophelie*     . 

Yacht,  Auxiliary 

Composite      .    . 

160 

26  6 

17   0 

11   6 

568 

.407 

.59 

.682 

Lady  Tor- 
frida*.    . 

Yacht,  Auxiliary 

Steel 

157 

27  0 

17   0 

11   6 

552 

.3968 

.6 

.664 

Zaida*    .    . 

Yacht,  T.S.   .    .    . 

136| 

22  6 

13   9 

8  9 

332 

.428 

.59 

.73 

Pizzaro  .    . 

Guard  Boat,  S.S.  . 

155 

21  6 

11   0 

6  6* 

303 

.482 

.626 

.773 

Ponce  de 

Leon  .    . 

Guard  Boat,  S.S.  . 

135 

19  0 

10   6 

6   6J 

202 

.439 

.594 

.74 

Sandoval    . 

Guard  Boat,  S.S.  . 

110 

15  6 

8   9 

5  0 

100 

.407 

.610 

.667 

Fradera*    . 

Guard  Boat,  S.S.  . 

74 

11  9 

7   3 

4   0 

41 

.412 

.662 

.622 

Scud*     .    . 

Speed  Launch,  S.S. 

86 

10  7 

5  10 

2  9 

30 

.43 

.625 

.687 

Neuquen*  . 

Revenue  Steamer, 

S.S 

65 

12  0 

7   0 

4  3 

41* 

.437 

.585 

.757 

Princess 

Customs  Launch, 

Maud*     . 

S.S 

55 

12  0 

6   8 

4   6 

37 

.435 

.56 

.776 

Designed  by  the  Author. 


Elements  of  Typical  Steamers  277 


TYPICAL   STEAMERS. 


Si? 

fa  fa 
fafa 
<J  O 

fa 
fa  m 

teg 
hH 
H 

H 

s 

o 

s 

fa 
O 

fc  o 

>  ft 

o 

M 

fa 

fa 
fa 

o 
O 

OB 

8 

£ 
W 

H 
K 

fa 

3 
fa 

fa 
o 
O 

SI 

§5S 

H  0 

txj 

OS 

H 
O 
ft 

m  ; 
fa 

GO 

H 

—  r. 

ft  o 

.726 

7,610 

.4702 

2,960 

.1829 

10,570 

.6531 

4,665 

17,878 

29,246 

79 

22.09 

252 

.826 

7,987 

.474 

1,844 

.1092 

9,831 

.583 

2,100 

12,000 

75 

14 

.718 

4,525 

.416 

1,677 

.154 

6,202 

.57 

2,525 

10,535 

16,300 

94 

20.75 

263 

.777 
.837 

7,161 
9,065 

8,379 
3,844 

79 

17.23 

227 

2,827 

.426 

1,167 

.1758 

3,995 

.6019 

627 

98 

13.93 

306 

.875 

3,891 

.463 

637 

.0764 

4,528 

.539 

731 

8,390 

3,535 

75 

12.8 

245 

.847 

2,125 

.472 

531 

.118 

2,656 

.59 

528 

3,000 

75 

.868 

1,210 

.388 

328 

.105 

1,538 

.493 

447 

2,522 

1,302 

88 

11.25 

207 

.667 

272 

.26 

172 

.1641 

444 

.424 

203 

736 

1,400 

201 

16.5 

260 

.693 

196 

.320 

98 

.1602 

394 

.48 

221 

550 

2,425 

56 

18.18 

116 

.698 

195 

.314 

88.5 

.1425 

283.5 

.4565 

195.5 

524 

2,022 

58 

18.49 

203 

.67 

446 

.338 

236 

.179 

682 

.517 

590 

1,130 

5,200 
2,800 

161 
128 

18.92 
17.0 

190 

.721 

994 

.4716 

672 

.3186 

1,666 

.7902 

484 

2,365 

4,604 

167 

16.36 

169 

.668 

700 

.3823 

347 

.1895 

1,047 

.5718 

500 

1,661 

7,223 

218 

20.64 

172 

.692 

115 

.164 

221 

.3150 

336 

.4790 

83 

532 

646 

110 

11.73 

164 

.656 

200 

.2775 

140 

.1945 

340 

.4720 

85 

598 

720 

134 

11.62 

155 

.683 

132 

.312 

70 

.1653 

202 

.4773 

92 

353 

620 

150 

12.8 

169 

.684 

91 

.248 

39 

.1073 

130 

.3555 

55 

257 

504 

242 

13.4 

193 

.652 

59 

.2193 

37 

.136 

96 

.3554 

38 

167 

338 

270 

13.14 

203 

.666 

31 

.2088 

24 

.1618 

55 

.3706 

29 

101 

229 

294 

12.09 

167 

.67 

14 

.219 

8 

.125 

22 

.344 

8| 

41 

180 

295 

11.5 

100 

.686 

9 

.17 

4.4 

.083 

13.4 

.253 

14.6 

31£ 

531 

430 

20.34 

155 

.695 

12 

.22 

5 

.092 

17 

.312 

12.5 

39} 

97 

318 

10.1 

119 

.68 

16 

.364 

4.5 

.102 

20.5 

.466 

10.5 

37 

81 

228 

9.27 

108 

Section  II. 

STRENGTH   OF   MATERIALS. 


CHAPTER  I. 
STRESSES. 

It  is  by  the  application  of  the  known  strengths,  as  derived  by 
experiment,  of  the  various  materials  used  in  shipbuilding  to  the 
physical  properties  possessed  by  their  geometrical  sections  that  we 
are  enabled  to  calculate  with  accuracy  the  loads  they  will  bear 
with  a  predetermined  margin  of  safety  when  subjected  to  either 
of  the  four  simple  stresses  of  tension,  compression,  shearing  and 
torsion. 

Ultimate  Strength  is  the  direct  stress  producing  rupture  of 
the  material. 

"Working  Load  is  the  stress  applied  in  practice,  and  its  ratio  to 
the  ultimate  strength  varies  with  the  nature  of  the  stresses  applied, 
viz. :  (1)  tension  with  a  dead  load ;  (2)  tension  with  a  live  load, 
or  (3)  a  live  load  working  alternately  in  opposite  directions  (see 
Table).  '    H 

Many  of  the  fittings  in  shipwork  come  under  the  third  category, 
as  in  rudders,  derricks,  etc.  In  derricks  the  inertia  of  the  load 
has  not  only  to  be  overcome,  but  also  the  jarring  and  surging.  For 
this  reason  a  very  common  factor  of  safety  for  these  details  is  ten 
times  the  ultimate  strength. 

Proof  Strength  is  the  test  load  to  which  cranes,  davits,  der- 
ricks, chains,  cables,  etc.  are  subjected,  and  is  usually  a  multiple 
of  the  working  load  or  ultimate  strength.  Careful  measurements 
should  be  taken  before  applying  this  load,  and  these  checked  after 
the  load  has  been  removed,  to  discover,  if  any,  the  amount  of 
permanent  set. 

Stress  and  Strain. —  Stress  is  the  measure  of  the  internal  force 
or  resistance  in  a  bar  due  to  the  load  applied  tending  to  produce 

279 


280  The  Naval  Constructor 


deformation,  and  strain  is  the  alteration  of  form  due  to  the  stress. 
So  that  the  relationship  between  these  two  terms  really  is  one  of 
cause  and  effect,  although  in  general  the  terms  are  erroneously 
used  synonymously. 

Stress  is  measured  by  weight  and  strain  in  inches,  or  as  a  per- 
centage of  the  length  of  the  bar  or  member  strained.  Thus,  we 
say  that  a  6-foot  bar  is  subjected  to  a  tensile  stress  of  20  tons,  pro- 
ducing a  strain  of  J  inch  per  foot  (elongation  being  §  inch)  or  1.04 
per  cent  of  the  bar's  length. 

Tensile  Stress.  — If  two  equal  forces  acting  in  opposite  direc- 
tions, away  from  each  other,  be  applied  to  a  bar,  they  will  tend 
to  stretch  it,  thus  producing  a  tensile  strain. 

Compressive  Stress. —  Should,  however,  the  forces  act 
towards  one  another  they  will  produce  a  compressive  strain. 

Shearing  Stress. — When  two  forces  acting  in  opposite  direc- 
tions are  exerted  through  the  cross  section  of  a  pin  or  rivet  con- 
necting two  flat  bars,  the  pin  is  subjected  to  single  shear.  If, 
however,  another  similar  bar  be  connected  enclosing  either  of 
the  other  bars,  then  the  pin  or  rivet  will  be  in  double  shear,  and 
may  be  reduced  by  half  its  original  sectional  area. 

Bending  or  Transverse  Stress.  —  Bending  stresses  are  im- 
posed on  beams  when  they  are  loaded  or  forces  exerted  on  them, 
although  more  correctly,  tensile,  compressive  and  shearing  stresses 
are  at  work  simultaneously  on  the  top,  bottom  and  abutments 
respectively. 

Torsional  Stress  is  encountered  mostly  in  shafting  and  in  the 
rudder  stocks  of  ships.  In  the  latter  case  it  consists  of  twisting 
stresses  acting  alternately  in  opposite  directions,  requiring  a  much 
larger  margin  of  «afety  than  necessary  with  any  of  the  other 
stresses  named. 

Resilience.  —  This  term  is  applied  to  the  amount  of  work  done 
by  compressing  or  extending  a  bar  and  multiplying  the  length  of 
such  compression  or  extension  by  the  load  which  produced  it. 

Elasticity  is  the  property  which  substances  possess  of  return- 
ing to  their  original  size  and  shape  after  straining.  In  tension 
materials  increase  in  length  and  decrease  under  compressive 
stresses,  and  within  certain  limits  this  lengthening  or  shortening 
is  proportional  to  the  stress  applied.  From  this  it  is  evident 
that  this  quality  is  more  important  than  even  the  strength  of  the 
material  in  tension  or  compression. 

Modulus  of  Elasticity.  —  The  amount  of  this  proportional 
variation  of  the  weight  applied  and  the  alteration  in  length  of  the 


Stresses 


281 


bar  is  known  as  the  modulus  of  elasticity,  and  may  also  be  expressed 
as  the  tensile  force,  which,  when  applied,  will  double  the  bar's 
length,  and  of  course  may  be  different  in  the  same  material  when 
subjected  to  tension,  compression  or  shear. 

Permanent  Set.  —  If  a  bar  be  extended  or  contracted  by  the 
application  of  a  load  jeyond  its  elastic  limit,  it  is  said  to  have 
permanent  set.  This  would  take  place  in  mild  steel  if  a  load  of 
17  tons  per  square  inch  of  section  were  exceeded. 


Fig.  56. 


Distance*.  Akea.       Moments. 

Si     =     4.40      X     2.04  =  39.49 

82     =     1.75     X      1.48  =  4.73 

6*3     -     2.00     x      1.64  =  6.56 

Si     =     3.75     X     2.44  =  34.30 

Moment  of  Inertia  J  =  85.08 

Section  Modulus       Z  =  -=-=-=■  =  16.5. 
5.15 

The  Moment  of  Inertia  of  a  section  or  body  is  a  mathematical 
quantity  used  to  calculate  the  strength  of  materials,  and  is  taken 
relatively  to  the  neutral  axis  or  centre  of  gravity  of  the  section. 
If  the  section  of  a  bulb  tee  beam,  as  shown  in  Fig.  66,  be  cen- 
trally loaded  on  top,  the  fibres  above  the  line  xy  (neutral  axis)  will 
be  compressed,  and  those  below  extended,  and  consequently  the 
arc  formed  by  the  table  of  the  beam  will  be  shorter,  and  that 
formed  by  the  bulb  longer,  than  the  arc  through  the  line  NSt 


282  The  Naval  Constructor 

which  will  be  exactly  the  same  length  as  the  original  dimension 
of  the  beam  before  the  application  of  the  load,  the  lamina 
through  this  axis  being  neither  in  compression  nor  tension,  and 
are  therefore  known  as  the  neutral  surface  of  the  beam.  Hence, 
if  we  take  very  small  areas  at  known  distances  from  the  neutral 
axis  to  their  centres  of  gravity  and  multiply  these  areas  by  the 
square  of  their  distances  above  or  below  this  line,  we  shall  have 
by  adding  the  products  together  the  moments  of  inertia  (I)  of  the 
section  ;  and  again  by  dividing  this  moment  by  the  distance  of  the 
most  extreme  fibre  we  shall  get  the  quantity  known  as  the  section 
modulus. 

In  the  example  given  the  result  is  fairly  accurate,  although  a 
more  absolute  result  may  be  obtained  by  greater  subdivision  of 
the  areas.  This,  however,  is  not  necessary  for  ordinary  calcula- 
tions. 

The  value  of  the  section  modulus  depends  entirely  on  the  geo- 
metrical form  of  the  section.  The  material  of  which  the  beam  is 
made  and  its  ultimate  strength  known  and  divided  by  the  factor 
of  safety  selected,  gives  us  the  safe  limiting  stress.  This  stress 
multiplied  by  the  section  modulus  produces  the  moment  of  resis- 
tance of  the  beam.  In  the  example  given  let  the  beam  be  of  steel 
of  60,000  lbs.  ultimate  strength  and  the  factor  of  safety  5,  we 
then  have  £&£&a  =  12,000  lbs.  safe  limiting  stress,  and  section 
modulus  =  16.5  X  12,000  lbs.  =  198,000  lbs.  moment  of  resistance. 
Suppose  then  that  this  were  a  12-foot  boat  skid  beam  fixed  at 
both  ends  and  loaded  at  centre,  what  weight  of  steam  pinnace 
would  it  safely  support  ?  The  maximum  bending  moment  on  a 
beam  so  loaded  would  be  £  WL  where  W  is  the  weight  and  L  the 
length  between  points  of  support.  Equating  this  bending  moment 
with  the  moment  of  resistance,  we  have 

SZ  _  WL. 

then  W  =  11,000  lbs. 

Where  the  figure  or  section  is  symmetrical  about  its  centre  of 
gravity  the  /  and  other  elements  may  be  readily  Figured  from  the 
appended  Table  of  Elements  of  Usual  Sections. 

Radius  of  Gyration.  —  The  radius  of  gyration  is  that  funda- 
mental property  of  a  section  used  in  determining  the  strength  of 
pillars  and  struts,  and  its  square  or  r2  about  a  given  axis  is  equal 
to  the  moment  of  inertia  of  the  surface  about  the  axis  divided  by 
the  area,  therefore  the  radius  of  gyration 


V 


inertia 


Stresses 


283 


-KI1Q 


aoHj 

-SOHJ 


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284 


The  Naval  Constructor 


ELEMENTS    OF    SECTIONS. 


Moment  of 
Inektia. 


i*-6— J. 


_ ,j, 


V 


- 

>-- 

r— i 

^- 

■* 

Z3 


0.0491  (I)*  -d*) 


16 


0.1098  r4 


0.7854  6a3 


W 

12 
12 


12 


6ft3 
36 


Section 
Modulus. 


0.0982 


ZH-d* 


Wi=  0.1098r8 
ir2=  0.2587  r8 


0.7854  6a2 


bh* 


0.1178  h* 


1  i?4-6* 


6      B 


24 


Base 

FROM 
C.G. 


0.4244 


\h 


\a   \-r  I;  \ 
DIUS  OF 

Gyration 


iV^2"^2 


0.0699  r2 


Least  side 


3.46 

h 
3.46 


/  7*2+  62 


]2 


The  lesser. 


—  or  - 
4.24      4.9 


Figs.  57  to  64. 


Elements  of  Sections 


ELEMENTS    OF   SECTIONS.—  (Continued.) 


Section. 


=* 


m 

S — b — *\ 


Moment  of 
Inertia. 


662+6661+612 


36(2&  +  &i) 


Ah2 
9.9 


^2 
10.4 


19 


AM 
10.9 


^2 
6.1 


AM 
6.73 


Section 
Modulus. 


662+6&61+612 


12(3  6  +  2&i) 


Ah 
6.7 


7.4 


Ah 
9.5 


7.6 


ft2 


Ah 
3.0 


-4  ft 
3^3 


Base 
from 
C.G. 


1  3H-&1 
3  26  +  6^ 


h_ 
3.1 


A- 
3.5 


A 
3.3 


Figs.  65  to  71. 


28G  The  Naval  Constructor 

BEAM    BENDING    MOMENTS.  ETC. 

■W— LOAD.       t— LENGTH  OF  BEAM  BETWEEN  8UPPORT8.       K  — FIBRE  STRESS. 
I— MOMENT  OF  INERTIA.      E  —  MODULUS  OF  ELASTICITY.      R— -5—  SECTION  MODULUS. 
C—  DISTANCE  OF  EXTREME  FIBRES  FROM  NEUTRAL  AXIS. 


HOW  LOADED  A  SUPPORTED 


STRESS  DIAGRAM 
ORDINATE6  GIVE  BENDING  MOMENTS 


Draw  Triangle 


Draw  Triangle 


ifM>^Tifrx.,G| 


L  © 


Draw  ED-Wt  &  AF=^ 


Figs.  72  to  83. 


Beam   Bending  Moments 


287 


BEAM   BENDING    MOMENTS,    ETC. 


W=Load. 

K  =  Fibre  Stress. 


L  =  Length  of  Beam  between  Supports. 
/  =  Moment  of  Inertia. 

R  =  -  =  Section  Modulus. 


E  =  Modulus  of  Elasticity 

C  =  Distance  of  Extreme  Fibres  from  Neutral  Axis. 


Bending 
Moment,  M. 

Deflection,  /. 

Reaction 

AT  A  AND  B. 

Safe  Load  JF 

Elastic  Curve 
Equation. 

M=  Wx    ' 

Mmax  =   WL 

W    L* 
J~  3     EI 

B=  W 

w=*¥ 

WW 
y  ~  2EI 

Vx       la;3] 
\_L      3  Z3  J 

,f      Wx 

M                WL 

Mmaz  —  —3 — 

4 

W    L* 
f~  48    EI 

W  =  4™ 

JFZ3 
y  ~~  16  EI 

Vx       4  a;3"] 
\L      3  i3j 

t^            ,n     1/          Wd\X 

For  AD,  M=.  — =A- 
Ld 

For  BD,M=^p 
Wdd\ 

Mmax=:  f — 

Li 

A~    L 

Jj 

W=KR~ 
ddt 

_  fFd2^2 
V~  6LEI 
[    xl,xl        x*    1 
L    d  ^rf,      ^dj 

[2^       xt        arx3-1 
L  rft    ^d        d^d] 

For  AD, 

M=  ft  Wx 
For  BD, 

Mmax=&  WL 

Md=&WL 

7  WL* 

J  ~  768  EI 

5     48^7 
For 

A  =  ft  W 
B=\hW 
W_UKR 
3   L 

VWL*Yx       5x3] 
32  #/  \_L      3  Z3J 
JF  X3 
Vl~  32  £7  X 
[la?!     5ar,»    11  a;,3] 
Ul  +  2  L*     3    Z3J 

..      WL  (x       1\ 

'M=-Y-\l-1) 

M                 WL 

fT     Z3 

7       192  £/ 

w  =  sKTR- 

Li 

JF  Z3 
V~  16  EI  X 

[a-2      4  a?3  "I 
U2      3Z3J 

For  A  and  B, 

TFZ'   /> 
/—     16    EI 

W 

A  =  B  =  l 

W=2™ 
P 

y=/-p+ 

*J  p*-X>+L(x-\) 

2EI 

P  =  TT^-^Constant 

288 


The  Naval  Constructor 

BEAM    BENDING   MOMENTS,  ETC. 


W— LOAD.      L— LENGTH  OF  BEAM  BETWEEN  SUPPORTS.      K— FIBRE  8TRE88. 

I      MOMENT  OF  INF.BTIA.       E  — MODULUS  OF  ELASTICITY.       R—-g—  SECTION  MODULUS. 

C— DISTANCE  OF  EXTREME  FIBRES  FROM  NEUTRAL  AXIS. 


HOW  LOADED  4  8UPPORTED 


STRE88  DIAGRAM 
ORDINATE8  GIVE  BENDING  MOMENTS 


Draw  Parabola 
A- 


Draw  Parabola 
A-^ 


X 


>4qq6666 


3)QOQQQQ)% 


b  ,  xrnrrriv^B 


OOlQO 


QOQnOQQO 


Draw  A-^  &  BC-^ 


t^fc&.^-J 


Figs.  84  to  95. 


Beam  Bending  Moments 


289 


BEAM   BEND.NG   MOMENTS, 
JF=Load. 


ETC.  —  (Continued.) 


L  —  Length  of  Beam  between  Supports. 

E  =  Modulus  of  Elasticity.       R  =  -  =  Section  Modulus. 

K  =  Fibre  Stress.  7=  Moment  of  Inertia. 

C  =  Distance  of  Extreme  Fibres  from  Neutral  Axis. 


Bending 
Moment,  AT. 

Deflec- 
tion, /. 

Reaction  at 

A  AND  B. 

Safe  Load,  W. 

Elastic  Cubve 
Equation. 

..      Wx* 

AT                  WL 

Mmax  =  — ^— 

W   L* 

J  ~   8    El 

Ll 
B  z=W 

_  W  L* 

y '  ~  24  El 

Mmax  r=  — s — 
o 

5  WL* 
J  ~  384,  El 

W  =  8^ 
It 

W  L* 
V  ~  24  El  X 

__      Wx  /3      a;\ 

1/==-2-(i-x) 
*r            WL 

Mmax  —  — x— 
o 

M^mWL 

T  ~  192  El 
Max.  deflec- 
tion, 
x  =  0.4215  L 

A-iW 
B  =%W 

W  =  8*fi 

Li 

v        48  El* 

WL/l      x      x*\ 

J  ~Z8AEl 

TFZ» 
V  ~2AEl 

Tx*      2x*.x*>-\ 

^  =  1-13 

Mmax  =  ^ 

f~  15  El 

B  =W 

Li 

y  ~~  12  El 
rx       lar5"] 
IL      5  Z5J 

MK  =  A(a  +  ±L) 

A       W(2d  +  b) 
A~         2L 

W(2a  +  b) 

290  The  Naval  Constructor 

USE    OF    THE    TABLE    OF    ELEMENTS   OF 
CIRCULAR    SECTIONS. 

In  calculating  the  scantlings  of  masts,  derricks,  kingposts,  rud- 
ders, shafting,  and  details  generally,  where  circular  sections  are 
employed,  the  Table  of  Elements  will  be  found  very  convenient 
and  time-saving,  as,  having  determined  on  a  thickness  or  a  diam- 
eter to  which  it  is  decided  to  work,  the  appropriate  formulae  for 
the  various  elements  may  be  read  off  with  facility. 

In  the  first  column  is  given  the  ratio  of  internal  to  external  di- 
ameter. It  is  required  to  find  the  elements  of  a  hollow  section 
with  an  outside  diameter  D  =  5  inches  and  an  internal  diameter 
d=  .8  D=4  inches,  or  5"  x  \"  thick. 

Column  2  gives  the  sectional  area  coefficient  of  the  pipe,  viz., 
.2826  x  D2  —7.065  square  inches. 

Similarly  the  coefficient  for  the  moment  of  inertia,  I,  is  found 
in  the  third  column  to  be  .02899  by  the  fourth  power  of  the  diam- 
eter D,  or  .02899  X  625  =  18.118  =  1. 

By  the  fourth  column  we  get  the  coefficient  for  the  square  of 
the  least  radius  of  gyration  as  .1026  D2  =  .1026  X  25  =  2.565, 
and  in  the  following  or  fifth  column  the  radius  of  gyration  =  .32 
D  =  .32  x  5" =  1.6. 

For  the  modulus  of  resistance  of  the  section,  or  I/y,the  coefficient 
for  the  pipe  with  a  ratio  of  .8  D  is 

.05798  D*  =  .05798  X  125  =  7.247. 

The  torsional  modulus  of  resistance  is 

.11595  2)3  -  J1595  x  125  =  14493. 

If  it  be  required  to  select  a  diameter  of  hollow  or  solid  circular 
section  for  a  given  moment  of  inertia,  or,  having  obtained  a  diam- 
eter, it  is  found  advisable  to  amend  the  same  to  another  diameter 
giving  the  same  J,  then  the  increase  or  decrease  of  thickness  may 
be  readily  computed  with  the  aid  of  column  8,  and  in  a  like  man- 
ner the  sectional  area  for  a  constant  moment  of  inertia  is  calcu- 
lated by  the  coefficients  in  the  following  column. 

The  last  two  columns  give,  similarly,  the  diameters  and  areas 
for  a  constant  moment  of  resistance. 

Inversely  we  may  calculate  the  diameter  of  a  bar  or  tube  equal 
to  a  given  moment  of  inertia,  or  moment  of  resistance,  or  radius 
of  gyration,  etc.  For  example,  the  diameter  is  required  of  a  tubu- 
lar section  which  shall  equal  a  moment  of  inertia  of  12.  It  is 
proposed  to  make  the  pipe  relatively  thin  ;  therefore  we  select  a 
ratio  of  d/D  =  .90  per  column  one,  from  which  we  get  an  I  co- 
efficient =  .01689 ;  therefore, 

V  .01689      V  .01689 
=  5. 14  inches  outside  diameter  x  £  inch  thick  (fully). 


Moduli  of  Circular  Sections 


291 


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292 


The   Naval   Constructor 


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Moduli  of  Circular  Sections  293 

MODULI   OF   CIRCULAR   SECTIONS 


o 

INERTIA  OP  CIRCULAR  SECTIONS. 

TO 

/=  Mom.  of  Inertia.    Z=  Section  Modulus. 

M 

_      irdT 

nd3 

nd* 

_      nd3 

r     nd* 

_    wd> 

D 

64 

Z=M 

/> 

/_64~ 

z=lv 

D 

/=154 

Z=-& 

1 

0.0491 

0.0982 

34 

65,597 

3,859 

67 

989,166 

29,527 

2 

0.7854 

0.7854 

85 

73,662 

4,209 

68 

1,049,556 

30,869 

3 

3.976 

2.651 

36 

82,448 

4,580 

69 

1,112,660 

32,251 

4 

12.57 

6.283 

37 

91,998 

4,973 

70 

1,178,588 

33,674 

5 

30.68 

12.27 

38 

102,354 

5,387 

71 

1,247,393 

35,138 

6 

63.62 

21.21 

89 

113,561 

5,824 

72 

1,319,167 

36,644 

7 

117.9 

33.67 

40 

125,664 

6,283 

73 

1,393,995 

38,192 

8 

201.1 

50.27 

41 

138,709 

6.766 

74 

1,471,963 

39,783 

9 

322.1 

71.57 

42 

152,745 

7,274 

75 

1,553,156 

41,417 

10 

490.9 

98.17 

43 

167,820 

7,806 

76 

1,637,662 

43,096 

11 

718.7 

130.7 

44 

183,984 

8,363 

77 

1,725,571 

44,820 

12 

1,018 

169.6 

45 

201,289 

8,946 

78 

1,816,972 

46,589 

13 

1,402 

215.7 

46 

219,787 

9,556 

79 

1,911,967 

48,404 

14 

1,886 

269.4 

47 

239,531 

10,193 

80 

2,010,619 

50,265 

15 

2,485 

331.3 

48 

260,576 

10,857 

81 

2,113,051 

52,174 

16 

3,217 

402.1 

4!) 

282,979 

11,550 

82 

2,219,347 

54,130 

17 

4,100 

482.3 

50 

306,796 

12,272 

83 

2,329,605 

56,135 

18 

5,153 

572.6 

r,l 

332,086 

13,023 

84 

2,443,920 

58,189 

19 

6,397 

673.4 

r,2 

358,908 

13,804 

85 

2,562,392 

60,292 

20 

7,854 

785.4 

63 

387,323 

14,616 

86 

2,685,120 

62,445 

21 

9,547 

909.2 

54 

417,393 

15,459 

87 

2,812,205 

64,648 

22 

11,499 

1,045 

55 

449,180 

16,334 

88 

2,943,748 

66,903 

23 

13,737 

1,194 

56 

482,750 

17,241 

89 

3,079,853 

69,210 

24 

16,286 

1,357 

57 

518,166 

18,181 

90 

3,220,623 

71,569 

25 

19,175 

1,534 

58 

555,497 

19,155 

91 

3,366,165 

73,982 

26 

22,432 

1,726 

59 

594,810 

20,163 

92 

3,516,586 

76,448 

27 

26,087 

1,932 

60 

636,172 

21,206 

93 

3,671,992 

78,968 

28 

30,172 

2,155 

61 

679,651 

22,284 

94 

3,832,492 

81,542 

29 

34,719 

2,394 

62 

725,332 

23,398 

95 

3,998,198 

84,173 

30 

39,761 

2,651 

63 

773,272 

24,548 

96 

4,169,220 

86,859 

31 

45,333 

2,925 

(»4 

823,550 

25,736 

97 

4,345,671 

89,601 

32 

51,472 

3,217     ' 

65 

876,240 

26,961 

98 

4,527,664 

92,401 

33 

58,214 

3,528 

66 

931,420 

28,225 

99 
100 

4,715,315 

4,908,738 

95,259 
98,175 

n  :  64  =  0.0490874  ;  log  (ir :  64)  =  0.6909699  —  2. 
it:  32  =  0.0981748 ;  log  («■ :  32)  =  0.9919999  —  2. 


294  The  Naval  Constructor 


CHAPTER   II. 

STRENGTH    OF    COLUMNS. 

Johnson's  Formula. 

The  accompanying  table  of  strengths  of  wrought  iron  columns  is 
based  on  the  "straight  line  "  formula  proposed  by  Johnson  and  gen- 
erally used  in  America.  The  value  of  the  constant  K  is  deduced 
by  making  the  straight  line  tangent  to  the  curve  of  Euler's  for- 
mula. 

r 

Where,  P  =  Ultimate  compressive  unit  stress. 
S  =  Maximum  tensile  unit  stress. 
k  —  A  constant  whose  value  depends  on  the  condition 

of  the  ends,  viz.,  fixed,  flat,  hinged  or  round. 
L  =  Length  of  column  in  feet. 
r  =  Least  radius  of  gyration. 

This  formula  may  be  readily  memorized  for  wrought  iron  col- 
umns, thus :  — 

Ultimate  unit  stress  P  =  52,500  —  2700— ,  on  which  basis  the 

r 

table  has  been  calculated. 

Example.  —  It  is  required  to  find  the  safe  load  with  a  factor  of 
safety  of  5  for  a  hollow  wrought-steel  strut  or  column  with  a 
length  of  46  feet,  mean  diameter  20  inches  and  one-half  inch  thick. 
r  =  20  x  .35  =  7. 

r       7 

P  (from  table)  =  6,900  lbs. 
Area  of  column  =  ci re.  x  t  =  62.8  x  .5  =  31.4  D" 
Safe  Load  W=  6,900  lbs.  x  31.40  □"  =  216,660  lbs. 
Or,  if  it  be  required  to  find  the  thickness  t  of  the  column  in  the 
foregoing  example,  the  load  being  216,660  lbs. 

r  =  7. 

-  =  6.57. 
r 


P  =  6,900  lbs.  (from  table). 


Strength  of  Columns  295 


216,660 

Area  =  npoT  =  31-4D  * 

Area      31.4       _  .     . 

t  = ■  =  n — s  =  •  5  inch. 

Circ.      62.8 


Values  of  r  for  various  sections. 


When  t  =  R,  r=.32D. 

jfN         «=i         '=-8132>- 

r— *— i  d 

Fig.  96.  4 

(See  Table  of  Elements  of  Circular  Sections.) 

n 

V      ^M\  Least  radius  of  gyration  =  j. 

Pig.  97. 

1  Tl)  Rectangle  or  square  r  —  .289  D, 


Pig.  98. 


L 


r 
Pig.  99, 


m 

Fig.  100. 

B 

Pig.  101. 


Equal  sided  angle  bar  r  —  -v- 


r  =  .4  D 


296 


The   Naval   Constructor 


VALUES   FOR   JOHNSON'S    FORMULA. 


Column  Material 

and 
How  Supported. 

s. 

k. 

Limit  of  — 

r" 

Mild  Steel  : 

Flat  ends    .... 

52,500 

2,148 

16.3 

Hinged  ends    .     .     . 

52,500 

2,640 

13.3 

Bound  ends     .     .     . 

52,500 

3,408 

10.3 

Wrought  Iron : 

Flat  ends    .... 

42,000 

1,536 

18.2 

Hinged  ends    .     . 

42,000 

1,884 

14.8 

Round  ends     .     .     . 

42,000 

2,436 

11.5 

Cast  Iron : 

Flat  ends    .... 

80,000 

5,256 

10.2 

Hinged  ends    .     .     . 

80,000 

6,444 

8.3 

Round  ends     .     .     . 

80,000 

8,316 

6.4 

Oak: 

Flat  ends    .     .     .     . 

5,400 

336 

10.7 

Strength  of  Columns 


297 


STRENGTH   OF  WROUGHT   IRON   OR   MILD 
STEEL  COLUMNS. 

By  Johnson's  Formula. 


L  in  Ft. 
r    in  In. 

52,500  —  2,700- 
r 

13,125  —  675  - 
r 

10,500  —  540- 
r 

8,750  —  450- 
r 

L 

Ultimate 
Unit  Stress. 

Safe 
Unit  Stress 

Safe 
Unit  Stress 

Safe 
Unit  Stress 

r 

Factor =1. 

Factor  =  5. 

Factor  =  6. 

1.00 

49,800 

12,450 

9,960 

8,300 

1.25 

49,125 

12,281 

9,825 

8,187 

1.50 

48,450 

12,112 

9,690 

8,075 

1.75 

47,775 

11,944 

9,555 

7,963 

2.00 

47,100 

11,775 

9,420 

7,850 

2.25 

46,425 

11,606 

9,285 

7,737 

2.50 

45,750 

11,437 

9,150 

7,625 

2.75 

45,075 

11,269 

9,015 

7,513 

3.00 

44,400 

11,000 

8,880 

7,400 

3.25 

43,725 

10,931 

8,745 

7,287 

3.50 

43,050 

10,762 

8,610 

7,175 

3.75 

42,375 

10,594 

8,475 

7,063 

4.00 

41,700 

10,425 

8,340 

6,950 

4.25 

41,025 

10,256 

8,205 

6,837 

4.50 

40,350 

10,087 

8,070 

6,725 

4.75 

39,675 

9,919 

7,935 

6,612 

5.00 

39,000 

9,750 

7,800 

6,500 

5.25 

38,325 

9,581 

7,665 

6,387 

5.50 

37,650 

9,412 

7,530 

6,275 

5.75 

36,975 

9,244 

7,395 

6,162 

6.00 

36,300 

9,075 

7,260 

6,050 

6.25 

35,625 

8,906 

7,125 

5,937 

6.50 

34,950 

8,737 

6,990 

5,825 

6.75 

34,275 

8,569 

6,855 

5,712 

7.00 

33,600 

8,400 

6,720 

5,600 

7.25 

32,925 

8,231 

6,585 

5,487 

7.50 

32,250 

8,062 

6,450 

5,375 

7.75 

31,575 

7,894 

6,315 

5,262 

8.00 

30,900 

7,725 

6,180 

5,150 

8.25 

30,225 

7,556 

6,045 

5,037 

8.50 

29,550 

7,387 

5,910 

4,925 

8.75 

28,875 

7,219 

5,775 

4,812 

9.00 

28,200 

7,050 

5,640 

4,700 

9.25 

27,525 

6,881 

5,505 

4,587 

9.50 

26,850 

6,712 

5,370 

4,475 

9.75 

26,175 

6,544 

5,235 

4,362 

298 


The  Naval  Constructor 


STRENGTH    OF   WROUGHT  IRON   OR  MILD 

STEEL   COLUMNS.  —  Continued. 

By  Johnson's  Formula.' 


L  in  Ft. 
r  in  In. 

52,500-2,700- 

13,125-675- 
r 

10,500—540- 

8,750-450- 
r 

L 

Ultimate 
Unit  Stress. 

Safe 
Unit  Stress 

Safe 
Unit  Stress 

Safe 
Unit  Stress 

T 

Factor  =  4. 

Factor  =  5. 

Factor  =  6. 

10.00 

25,500 

6,375 

5,100 

4,250 

10.26 

24,825 

6,206 

4,965 

4,137 

10.50 

24,150 

6,037 

4,830 

4,025 

10.75 

23,475 

5,869 

4,695 

3,912 

11.00 

22,800 

5,700 

4,560 

3,800 

11.25 

22,125 

5,531 

4,426 

3,687 

11.50 

21,450 

5,362 

4,290 

3,575 

11.75 

20,775 

5,194 

4,135 

3,462 

12.00 

20,100 

5,025 

4,020 

3,350 

12.25 

19,425 

4,856 

3,885 

3,237 

12.50 

18,750 

4,687 

3,750 

3,125 

12.75 

18.075 

4,519 

3,615  ' 

3,012 

13.00 

17,400 

4,350 

3,480 

2,900 

13.25 

16,725 

4,181 

3,345 

2,787 

13.50 

16,050 

4,012 

3,210 

2,675 

13.75 

15,375 

3,844 

3,075 

2,562 

14.00 

14,700 

3,675 

2,940 

2,450 

14.25 

14,025 

3,506 

2,805 

2,337 

14.50 

13,350 

3,337 

2,670 

2,225 

14.75 

12,675 

3,169 

2,535 

2,112 

15.00 

12,000 

3,000 

2,400 

2,000 

15.25 

11,325 

2,831 

2,265 

1,887 

15.50 

10,650 

2,662 

2,130 

1,775 

15.75 

9,975 

2,494 

1,995 

1,662 

16.00 

9,300 

2,325 

1,860 

1,550 

16.25 

8,625 

2,131 

1,725 

1,437 

16.50 

7,950 

1,987 

1,590 

1,325 

16.75 

7,275 

1,819 

1,455 

1,212 

17.00 

6,600 

1,650 

1,320 

1,100 

17.25 

5,925 

1,481 

1,185 

987 

17.50 

5,250 

1,312 

1,050 

875 

17.75 

4,575 

1,144 

915 

762 

18.00 

3,900 

975 

780 

650 

18.25 

3,225 

806 

645 

537 

18.50 

2,550 

638 

510 

425 

18.75 

1,875 

469 

375 

312 

Pipe  Pillars 


299 


PIPE   PILLARS. 


«3 


10 

n 

12 


Radii  of  Gyration  \  ■y/D2  +  d2. 


Thickness  in  Decimals  of  an  Inch. 


.1 

.67 
1.03 
1.38 
1.73 
2.08 
2.43 
2.79 
3.15 
3.51 
3.86 
4.21 


.2 

.64 
.99 
1.35 
1.70 
2.05 
2.40 
2.76 
3.11 
3.47 
3.82 
4.18 


.3 


.61 
.96 
1.31 
1.66 
2.02 
2.36 
2.72 
3.08 
3.44 
3.79 
4.15 


A 


.58 
.93 
1.28 
1.63 
1.98 
2.33 
2.69 
3.04 
3.40 
3.75 
4.11 


.56 
.90 
1.25 
1.60 
1.95 
2.30 
2.66 
3.01 
3.37 
3.72 
4.08 


.54 
.88 
1.22 
1.57 
1.92 
2.27 
2.62 
2.97 
3.33 
3.68 
4.04 


.7 


.52 
.85 
1.19 
1.54 
1.89 
2.24 
2.59 
2.94 
3.30 
3.65 
4.01 


.51 
.83 
1.16 
1.51 
1.86 
2.21 
2.56 
2.91 
3.27 
3.62 
3.97 


.50 

.81 
1.14 
1.48 
1.83 
2.18 
2.53 
2.88 
3.23 
3.58 
3.94 


lln. 
.50 
.79 
1.12 
1.46 
1.80 
2.15 
2.50 
2.85 
3.20 
3.55 
3.90 


300 


The  Naval  Constructor 


STANDARD    PIPE    ELEMENTS. 


STANDARD  STRENGTH 

PIPES. 

<    . 

si 

o    -< 

-  -  - 
< 

fc  fc  < 

O  J 

en 

g  i 

SgES 

SB 

Resis- 
tance, 

y' 

Radii 
of  Gyra- 
tion, R1. 

t-  H  2 

i 

.406 

.27 

.0573 

.0717 

.001032 

.005195 

.014808 

.241 

1 

.54 

.364 

.1041 

.1249 

.003312 

.012267 

.026508 

.42 

i 

.675 

.494 

.1917 

.1663 

.007267 

.02153 

.043716 

.559 

i 

.84 

.623 

.3048 

.2492 

.017045 

.04058 

.068358 

.837 

1 

1.05 

.824 

.5333 

.3327 

.037035 

.07054 

.111342 

1.115 

i 

1.315 

1.048 

.8626 

.4954 

.10665 

.1622 

.1176721 

1.668 

n 

1.66 

1.38 

1.496 

.668 

.1947 

.2345 

.29125 

2.244 

i* 

1.9 

1.611 

2.038 

.797 

.3091 

.3254 

.46283 

2.678 

2 

2.375 

2.067 

3.356 

1.074 

.666 

.5609 

.61957 

3.608 

2* 

2.875 

2.468 

4.784 

1.708 

1.532 

1.0657 

.89729 

5.739 

3 

3.5 

3.067 

7.388 

2.243 

3.023 

1.7274 

1.3535 

7.536 

3£ 

4 

3.548 

9.887 

2.679 

4.788 

2.394 

1.7868 

9.001 

4 

4.5 

4.026 

12.73 

3.174 

7.23 

3.213 

2.2787 

10.66 

4* 

5 

4.508 

15.96 

3.674 

10.41 

4.164 

2.8326 

12.34 

5 

5.563 

5.045 

19.99 

4.316 

15.21 

5.468 

3.5226 

14.50 

6 

6.625 

6.065 

28.89 

5.584 

28.17 

8.504 

5.0422 

18.76 

7 

7.625 

7.023 

38.74 

6.926 

46.5 

12.197 

6.7165 

23.27 

8 

8.625 

7.982 

50.04 

8.386 

72.35 

16.777 

8.6314 

28.18 

9 

9.625 

8.937 

62.73 

10.03 

108.2 

22.483 

10.782 

33.70 

10 

10.75 

10.019 

78.84 

11.92 

160.9 

29.935 

13.496 

40.06 

11 

12 

11.25 

99.40    . 

13.70 

231.7 

38.617 

16.910 

45.95 

12 

12.75 

12 

113.1 

14.58 

279 

42.765 

19.160 

48.98 

13 

14 

13.25 

137.9 

16.05 

373 

53.286 

23.222 

53.92 

14 

15 

14.25 

159.5 

17.23 

461 

61.467 

26.504 

57.89 

15 

16 

15.25 

182.3 

18.41 

562 

70.25 

30.535 

61.77 

Standard  Pipe  Elements 


301 


STANDARD 

PIPE 

ELEMENTS 

. —  (Continued.) 

A 

35ft  W 

&  . 
©j 

£  i 

OH 

Resis- 
tance, 

/ 

M    PS       - 

<&  o 

K  O  A 

i 

.405 

.205 

.033 

.086 

.001234 

.00609 

.01288 

.29 

1 

.54 

.294 

.068 

.161 

.003807 

.01410 

.02363 

.54 

1 

.675 

.425 

.139 

.219 

.008588 

.02545 

.03977 

.74 

i 

.84 

.542 

.231 

.323 

.020204 

.04811 

.06246 

1.09 

1 

1.05 

.736 

.452 

.414 

.045261 

.08621 

.10276 

1.39 

6 

jz; 

l 

1.315 

.951 

.71 

.648 

.10665 

.16220 

.16466 

2.17 

§ 

U 

1.66 

1.272 

1.271 

.893 

.2442 

.27012 

.27329 

3 

H 

l* 

1.9 

1.494 

1.753 

1.082 

.3952 

.41631 

.36513 

3.63 

< 

H 
X 

- 

2 

2.375 

1.933 

2.935 

1.495 

.8767 

.73827 

.58607 

5.02 

21 

2.875 

2.315 

4.209 

2.283 

1.9434 

1.3522 

.85155 

7.67 

3 

3.5 

2.892 

6.569 

3.052 

3.932 

2.2771 

1.2884 

10.25 

8J 

4 

3.358 

8.856 

3.71 

6.325 

3.1625 

1.7048 

12.47 

4 

4.5 

3.818 

11.449 

4.445 

9.72 

4.3200 

2.1767 

14.97 

5 

5.563 

4.813 

18.19 

6.12 

20.67 

7.4312 

3.38     - 

20.34 

6 

6.625 

5.75 

25.97 

8.505 

40.93 

12.356 

4.8096 

28.58 

1 

.84 

.244 

.047 

.507 

.024266 

.05777 

.04782 

1.7 

1 

1.05 

.422 

.139 

.727 

.058098 

.11066 

.08004 

2.44 

6 

§ 

3 

1 

1.315 

.587 

.271 

1.087 

.14097 

.2144 

.12961 

3.65 

n 

1.66 

.885 

.615 

1.549 

.3426 

.4128 

.22115 

5.2 

H 
«2 

ii 

1.9 

1.088 

.93 

1.905  * 

.57092 

.6010 

.29961 

6.4 

2 

2.375 

1.491 

1.744 

2.686 

1.3194 

1.1117 

.49148 

9.02 

H 
H 
H 

2* 

2.875 

1.755 

2.419 

4.073 

2.8873 

2.0085 

.70910 

13.68 

3 

3.5 

2.284 

4.097 

5.524 

6.030 

3.4457 

1.0916 

18.56 

H 

a 
p 

o 

ft 

3| 

4 

2.716 

5.794 

6.772 

9.895 

4.9475 

1.4610 

22.75 

4 

4.5 

3.136 

7.724 

8.18 

15.38 

6.8355 

1.8803 

27.48 

5 

5.563 

4.063 

12.965 

11.34 

33.63 

12.0906 

2.9636 

38.12 

6 

6.625 

4.875 

18.666 

15.896 

66.87 

20.1872 

4.2285 

53.11 

302 


The  Naval  Constructor 


STEEL    COLUMNS. 


Size  of 
Column. 


12  ins. 
diameter, 
I"  thick, 
R  —  4.03. 

10  ins. 
diameter, 
i"  thick, 
R  =  3.37. 

5  ins. 

diameter, 
'  thick, 
=  2.66. 

6  ins.  r 
diameter,! 
|"  thick,  1 
Vf  =  2.00.  t 

5  ins. 

diameter, 
f"  thick, 
R  —  1.64. 

4  ins. 
diameter, 
\"  thick, 
R  —  1.33. 

3  ins. 
diameter, 
A"  thick, 
7?  =1.00.  ^ 

2  ins. 
diameter, 
\"  thick, 
11  =  0.66. 


O  oo 


Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 


Length  in  Feet. 


10       12       14       16       18 


Greatest  Safe  Load  in  Pounds  per  Sq.  In.  of  Section. 


23,000 
23,000 
•23,000 
23,000 

23,000 
23,000 

23,000 
23,000 

23,000 
23,000 
23,000 
23,000 

23,000 
23,000 
23,000 
23,000 

23,000 
23,000 
23,000 
23,000 

23,000 
23,000 
23,000 
23,000 

20,770 
20,770 
19,990 
18,650 

15,450 
15,450 
14,700 
13,530 


23,000 
23,000 
23,000 
23,000 

23,000 
23,000 
23,000 
23,000 

23,000 
23,000 
23,000 
23,000 

20,770 
20,770 
19,990 
18,650 

17,350 
17,350 
16,630 
15,430 

15,490 
15,490 
14,740 
13,590 

14,000 
14,000 
13,1 
11,540 

11,640 
11,640 
10,570 
8,560 


28,000 

J3,000 
23,000 
23,000 

22,810 
22,810 
22,030 
20,950 

18,600 
18,600 
17,850 
16,480 

15,510 
15,510 
14,760 
13,610 

14,370 
14,370 
13,500 
12,090 

13,550 
13,550 
12,540 
10,820 

11,700 
11,700 
10,650 
8,640 

8,920 
8,650 
7,120 
5,060 


20,920 

20,920 
20,140 
18,760 

17,780 
17,780 
17,040 
15,780 

15,490 
15,490 
14,740 
13,590 


17,050 
17,050 
16,390 
15,260 

15,570 
15,570 
14,830 
13,690 


15,570 
15,570 
14,810 
13,670 

14,500 
14,500 
13, 

12,280 


14,250  13,550 
14,250  13,550 
13,350  12,540 
11,910  10,820 


14,000  12,870  11,700 
14,000  12,870  11,700 
13,060  11,880  10,650 
11,540  10,040   8,640 


13,060 
13,060 
12,080 
10,270 

11,690 
11,690 
10,630 
8,610 

9,720 
9,670 
8,190 
6,110 

6,780 
6,150 
4,640 
2,790 


11,600 
11,600 
10,520 
8,500 

10,170 
10,140 
8,760 
6,680 

8,350 
7,850 
6,350 
4,310 

4,810 
4,040 
2,580 
1,510 


10,360 
10,340 
9,000 
6,940 

8,970 
8,710 
7, 
5,120 

6,850 
6,250 
4,740 
2,860 

3,230 
2,730 
1, 


14,830 

14,030 
13,810 
12,450 

13,870 
13,870 
12,880 
11,340 

12,570 
12,570 
11,560 
9,690 

10,670 
10,660 
9,390 
7,350 

9,280 
9,180 
7,620 
5,550 

7,940 
7,420 
5,920 
3,900 

5,590 
4,790 
3,250 
1,880 

2,290 
2,020 
1,090 


14,0:50 
14,030 
13,090 
11,590 

13,260 
13,260 

12,260 
10,470 

11,690 
11,690 
10,630 


9,720 
9,670 
8,190 
6,110 

8,500 
8,070 
6,550 
4,510 

6, 

6,220 
4,710 
2,850 

4,280 
3,560 
2,230 
1,270 

1,760 

1,450 

790 

450 


13,590 
13,690 
12,680 

10,880 

12,500 
12,500 

11,460 
9,580 

10,900 
10,900 
9,670 
7,650 


8,730 
7,200 
5,140 

7,590 
7,050 
5,550 
3,560 

5,910 
F,120 
3,560 
2,040 

3,300 

2,790 

1, 

910 


Steel   Columns 


303 


STEEL   COLUMNS.  —  Continued. 


Size  of 
Column. 

u 

.1.8 

Length  in  Feet. 

20 

22 

24 

26 

28 

30 

32 

34 

36 

Greatest  Safe  Load  in  Pounds  per  Sq.  In.  of  Section. 

12  ins.     f 
diameter,! 
§"  thick,  ) 
72  =  4.03.   L 

10  ins.     r 
diameter,! 
h"  thick,  J 
72  =  3.37.  L 

8  ins.     r 
diameter,  J 
A"  thick,  1 
72  =  2.66.  t 

6  ins.     r 
diameter,! 
§"  thick,  1 
,8  =  2.00.  L 

5  ins.     C 
diameter,! 
f"  thick,  ] 
72=1.64.  L 

4  ins.     ( 
diameter,! 
i"  thick,  1 
72  =  1.33.  L 

3  ins.     f 
diameter,! 
rV'thick,"] 
72  =  1.00.   ^ 

2  ins.      f 
diameter,! 
£"  thick,  1 
72  =  0.66.   L 

Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 

Fixed    • 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Rouud 

Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 

Fixed 
Flat 
Hinged 
Round 

12,930 
12,930 
11,940 
10,110 

11,770 
11,770 
10,730 
8,720 

10,170 
10,130 
8,760 
6,680 

8,350 
7,850 
6,350 
4,310 

6,730 
6,100 
4,580 
2,750 

4,880 
4,100 
2,620 
1,540 

2,650 

2,280 

1,250 

720 

12,350 
12,350 
11,310 
9,400 

11,150 
11,150 
9,990 
7,960 

9,460 
9,410 
7,870 
5,790 

7,570 
7,030 
5,530 
3,540 

5,990 
5,200 
3,630 
2,080 

4,000 
3,310 
2,050 
1,150 

2,100 

1,860 

1,000 

580 

11,750 
11,750 
10,700 
8,690 

10,550 
10,540 
9,230 
7,180 

8,970 
8,710 
7,180 
5,120 

6,850 
6,250 
4,740 
2,860 

5,160 
4,370 
2,860 
1,670 

3,280 

2,760 

1,610 

910 

1,800 

1,490 

810 

460 

11,230 
11,230 
10,080 
8,070 

9,980 
9^50 
8,520 
6,450 

8,490 
8,050 
6,540 
4,500 

6,250 
5,500 
3,940 
2,300 

4,350 
3,630 
2,280 
1,300 

2,790 

2,380 

1,320 

760 

10,730 
10,710 
9,450 
7,410 

9,430 
9,370 
7,830 
5,750 

7,940 
7,420 
5,920 
3,900 

5,590 
4,790 
3,250 
1,880 

3,720 
3,100 
1,880 
1,050 

2,330 

2,050 

1,110 

650 

10,240 
10,220 
8,850 
6,770 

9,040 
8,830 
7,300 
5,230 

7,350 
6,810 
5,310 
3,340 

4,910 
4,120 
2,640 
1,550 

3,180 

2,700 

1,550 

870 

2,010 

1,760 

940 

550 

9,770 
9,730 
8,260 
6,180 

8,670 
8,090 
6,770 
4,730 

6,830 
6,220 
4,710 
2,850 

4,280 
3,560 
2,230 
1,270 

2,800 

2,390 

1,320 

760 

1,790 

1,480 

800 

460 

9,340 
9,260 
7,710 
5,630 

8,280 
7,780 
6,270 
4,240 

6,380 
5,660 
4,110 
2,420 

3,760 
3,130 
1,910 
1,060 

2,430 

2,120 

1,160 

670 

9,020 
8,800 
7,260 
5,200 

7,820 
7,290 
5,790 
3,780 

5,910 
5,120 
3,560 
2,040 

3,300 

2,780 

1,620 

910 

2,110 

1,870 

1,000 

590 

304 


The  Naval  Constructor 


STRENGTH   OF  METALS    AND    ALLOYS. 

(Stresses  given  in  Pounds  per  Square  Inch.) 


2 

*d 

2 

■s . 

m  UA 

Metal. 

111 

In 

OS    9   » 

892 

If 

I" 

"■3  ■*" 

31 

9  o  g 

3  "83 

Aluminium  Bronze: 

10%  Al,  90%  Cu  (rolled) 
l}%Al,98}%Cu(cast) 
Brass  and  Bronze : 

100,000 
26,800 

60,000 

18.0 

.282 

Copper  Tin    Zinc 

85        15       —        .      . 

35,500 

95,000 

63,000 

20,000 

.319 

90      10      —      .     . 

33,000 

75,000 

52,000 

.  .  . 

140 

.318 

95        5      —       .     . 

30,000 

52,000 

39,000 

16,000 

13.7 

.317 

90      —       10       .     . 

30,000 

48,000 

24,000 

.322 

80      —      20       .     . 

37,000 

65,000 

30,000 

10,000 

12.4 

.316 

70      —      30       .     . 

43,000 

79,000 

36,000 

9,100 

14.0 

.310 

60      —      40       .     . 

49,000 

75,000 

42,000 

16,400 

12.2 

.308 

50      —      50       .     . 

24,000 

117,400 

48,000 

16,900 

11.6 

.304 

86      12        2  {«»»;, 

34,500 

02,400 

12.5 

.315 

70       10      20       .     . 

31,760 

.... 

43,500 

14.5 

.  .  . 

60       10      30       .     . 

21,500 

30,200 

15.8 

.  .  . 

55          \    44§     .     . 
Bronze,  Manganese  (cast) 

68,900 
71,200 

22,000 

17,700 

130, 000 

•  .  . 

.  .  . 

"                "          (rolled) 

100,000 
47,700 
79,400 

80,000 
21,500 
55,400 

"         Phosphor  .     . 
"        Tobin  (rolled) 

175,000 

41,900 

.  •  . 

.296 

Copper  (cast)     .     .     . 
"       (sheet)    .     .     .  • 
"      wire  annealed  . 

24,800 

8,000 

180 

32,600 
39,800 

25,000 

18.0 

Iron  Cast  (average) 

17,000 

100,000 

6,000 

15.0 

.26 

"     Wire  annealed     . 

45,000 
75,000 
50,000 

27,000 

26.0 

' '     Wrgt. ,  rolled  bars 

36,000 

30,000 

29.0 

"         "           "    plates 
Lead 

50,000 
2,050 

30,000 
1,100 

29.0 

7,350 

.  .  . 

0.85 

Steel  (mild)   .... 
Tin 

67,200 
3,500 

35,000 
1,670 

29.00 

6,400 

4.6 

Zinc  (cast)     .... 

5,400 

4,050 

Physical  Properties  of  Timber  305 

PHYSICAL   PROPERTIES    OF  TIMBER. 

The  physical  properties  of  timber,  given  hereafter,  are  derived 
largely  from  the  recent  experiments  of  the  Forestry  Division, 
United  States  Department  of  Agriculture,  which  form  the  most 
complete  and  systematic  series  on  record.  The  following  general 
conclusions  seem  to  be  demonstrated: 

1.  That  bleeding  (the  experiments  were  made  on  long-leaf  yel- 
low pine)  has  no  material  effect  on  the  strength  of  timber,  the 
flexibility  is  slightly  increased,  but  the  bled  timber  will  probably 
endure  exposure  to  the  weather  as  well  as  the  other. 

2.  That  moisture  reduces  the  strength  of  timber,  whether  that 
moisture  be  the  sap,  or  water  absorbed  after  seasoning.  In  gen- 
eral, seasoned  timber,  or  with  not  more  than  12  per  cent,  moisture, 
is  from  75  per  cent,  to  100  per  cent,  stronger  than  green  timber. 

3.  When  artificially  dried,  timber  contains  a  uniform  percent- 
age of  moisture  throughout,  a  condition  requiring  months  or  even 
years  to  attain  in  air-dried  heavy  timber. 

When  kiln-dried  at  usual  temperatures,  wood  shows  no  loss  of 
strength  compared  with  air-dried  timber  of  the  same  percentage 
of  moisture.  The  effect  of  very  high  temperatures  and  pressures 
(as  used  in  vulcanizing)  is  lower  strengths  than  when  air-dried. 

4.  Large  timbers  are  equal  in  strength  per  square  inch  of  sec- 
tion, tested  every  way,  to  small  timbers,  provided  they  are 
equally  sound  and  contain  the  same  percentage  of  moisture. 

5.  The  tests  seem  to  indicate  that  the  strength  of  woods  of  uniform 
structure  increases  with  the  specific  gravity  irrespective  of  species; 
i.e.,  in  general,  the  heaviest  wood  is  the  strongest.  Oak  seems  not 
to  belong  to  the  list  of  woods  to  which  this  general  remark  applies. 

The  data  on  properties  of  timbers  must  be  used  with  consider- 
able judgment  and  caution.  Seasoned  wood  will  gain  weight,  to 
the  extent  of  5  to  15  per  cent.,  if  exposed  to  the  weather,  and  this 
excess  will  be  reduced  if  the  wood  is  kept  a  week  in  a  warm  dry 
place.  Some  of  the  individual  tests  made  by  the  United  States 
Forestry  Division  varied  considerably  from  the  mean  values 
given  in  the  table.  In  the  case  of  tension  tests,  which  varied 
most  from  the  average,  a  few  were  as  low  as  25  per  cent.,  while 
others  reached  190  per  cent,  of  the  mean.  The  elastic  limit  given 
in  connection  with  the  data  from  the  United  States  Forestry 
Division  is  the  relative  elastic  limit  suggested  by  Professor  John- 
son, as  there  is  no  definite  "elastic  limit"  in  timber  similar  to 
that  in  some  metals.  This  relative  elastic  limit  is  taken  where  the 
rate  of  deflection  is  50  per  cent,  more  than  it  is  under  initial  loads. 

Modulus  of  ultimate  bending  is  extreme  fibre  stress  on  beam  at 
rupture.  The  modulus  of  elastic  bending  is  the  fibre  stress  when 
the  rate  of  deflection  is  increased  50  per  cent.  The  modulus  of 
elasticity  is  derived  from  transverse  tests. 


:;<><; 


The  Naval   Constructor 


STRENGTH 

Seasoned  timber,  moisture  12  per  cent  and 


Namk  of  Material 


Ash  (American)    .... 

Birch 

Box 

Cedar  (White) 

Cedar  (American  Red)   .     . 

Chestnut 

Cottonwood  (see  Poplar)     . 
Douglas  Spruce  (Oregon  Pine) 

Fir 

Gum 

Hemlock 

Hickory  (American)  average 

Lignum  Vitae 

Mahogany  (Spanish)       .     . 

Maple 

Oregon   Pine  (see  Douglas 

Spruce) 

Oak  (Red) 

Oak  (Black  or  Yellow)   .     . 

Oak  (White) 

Oak  (Live) 

Pine  (Southern  Yellow,  long 

leafed) 

Pine  (Cuban) 

Pine  (Loblolly)      .... 

Pine  (White) 

Poplar 

Spruce  (Northern)      .     .     . 
Spruce  Pine  (Pinus  glabra 

of  So.  States)     .... 
Walnut  (Black)     .... 


pi 

P3 


17,000 
15,000 
20,000 


10,800 
11,500 


13,000 
13,000 


8,700 
19,600 
11,800 
14,900 
11,150 


10,250 
10,000 
13,600 


13,000 
13,000 
13,000 
10,000 
7,000 
11,000 

12,000 
10,500 


.§5  2  Sf 


®  a>.2 


7,200 
8,000 
10,300 
5,200 
6,000 
5,300 


5,700 

7,100 
5,700 
9,500 
9,900 
8,200 
7,150 


7,200 

7,300 

8,500 

10,400 

8,000 
8,700 
7,400 
5,400 
5,000 
6,000 

7,300 
7,500 


1,900 


700 


800 

i,4ob 

2,700 


1,800 


2,300 
1.800 
2,200 


1,260 

1,200 

1,150 

700 


1,200 
2,500 


1,100 


400 


500 

1,300 

800 

400 

1,100 


500 


1,100 
1,100 
1,000 


835 
770 
800 
400 


400 


800 


Weight  in  Pounds  per 

Cherry 42.0 

Cork 15.6 

Ebony 76.1 


Strength  of  Timber 


307 


OF  TIMBER. 

under.    Stresses  given  in  pounds  per  square  inch. 


ll 

g3 

09         >> 

9     s 

li 

§  eS  tab 

■sii 

o 

.2  3  if 

Ordinary  Working 
Stress. 

Tens. 

Comp. 

Trans. 

7,900 

1,640,000 
1,645,000 

10,800 
11,700 

7,900 

2,000 
2,000 
2,500 
1,200 
1,400 
1,400 

1,000 

1,000 

1,200 

600 

700 

600 

1,200 

1,200 

1,500 

800 

900 

900 

39 
33 

23 

41 

5,800 

910,000 
1,140,000 

6,300 
7,200 
8,100 

5,800 

6,400 
'  7,800 
11,200 

1,680,000 
1,530,000 
1,700,000 

2,390,000 

1,255,000 

7,900 

6,400 

1,400 

700 

1,000 

32 

9,500 

7,100 

16,000 

11,700 

9,550 

10,000 

7,800 

1,200 

900 

900 

750 

1,800 

1,500 

1,500 

37 
25 
50 
83 
53 
49 

11,000 

2,000 
1,500 
1,500 

1,200 
1,200 
1,200 

9,200 
8,100 
9,600 
9,040 

10,000 

11,100 

9,200 

6,400 

8,400 
5,700 

1,970,000 
1,740,000 
2,090,000 
1,851,500 

2,070,000 
2,370,000 
2,050,000 
1,390,000 

1,400,000 

1,640,000 
1,306,000 

11,400 
10,800 
13,100 
11,300 

12,600 

13,600 

11,300 

7,900 

6,500 

8,000 

10,000 
8,000 

9,200 
8,100 
9,600 

1,400 
1,400 
1,700 

900 

900 

1,000 

1,200 
1,200 
1,500 

45 
45 

50 

9,500 

10,640 

9,400 

6,400 

8,400 

1,600 

1,000 

1,500 

38 

1,600 

1,200 

900 

1,200 

1,200 
1,000 

900 
700 
600 
700 

700 
1,000 

1,200 
900 
750 
900 

900 
900 

33 
24 

26 

30 

38 

Cubic  Foot  of  other  Woods. 

Elm 35 

Mahogany  (Honduras) 35 

Sycamore 37 

308 


The  Naval  Constructor 


TABLE    OF    WEIGHT   AND    STRENGTH   OF    WIRE. 


M 
GO 
tf  & 
<-< 

<  . 

Weight  of 

w 

H 

eg  . 
a    w    5c 

00 

Diameter. 

OS 

*%° 

saag* 

5«< 

H 
02 

100 
Yards. 

Mile. 

< 

sse§g 

In. 

MM. 

Sq.  In. 

Lbs. 

Lbs. 

Yds. 

Lbs. 

7/0 

.500 

12.7 

.1963 

193.4 

3,404 

68 

43,975 

6/0 

.464 

11.8 

.1691 

166.5 

2,930 

67 

37,854 

6/0 

.432 

11.0 

.1466 

144.4 

2,541 

78 

32,823 

4/0 

.400 

10.2 

.1257 

123.8 

2,179 

91 

28,144 

3/0 

.372 

9.4 

.1087 

107.1 

1,885 

105 

24,354 

2/0 

.348 

8.8 

.0951 

93.7 

1,649 

120 

21,302 

0 

.324 

8.2 

.0824 

81.2 

1,429 

138 

18,464 

1 

.300 

7.8 

.0707 

69.6 

1,225 

161 

15,831 

2 

.276 

7.0 

.0598 

58.9 

1,037 

190 

13,398 

3 

.252 

6.4 

.0499 

49.1 

864 

228 

11,169 

4 

.232 

6.9 

.0423 

41.6 

732 

269 

9,467 

5 

.212 

6.4 

.0353 

34.8 

612 

322 

7,904 

6 

.192 

4.9 

.0290 

28.5 

502 

393 

6,486 

7 

.176 

4.5 

.0243 

24.0 

422 

467 

5,450 

8 

.160 

4.1 

.0201 

19.8 

348 

566 

4,503 

9 

.144 

3.7 

.0163 

16.0 

282 

700 

3,648 

10 

.128 

3.3 

.0129 

12.7 

223 

882 

2,882 

11 

.116 

3.0 

.0106 

10.4 

183 

1,077 

2,368 

12 

.104 

2.6 

.0085 

8.4 

148 

1,333 

1,903 

13 

.092 

2.3 

.0066 

6.5 

114 

1,723 

1,489 

14 

.080 

2.6 

.0050 

6.0 

88 

2,240 

1,126 

15 

.072 

1.8 

.0041 

4.1 

70 

2,800 

912 

16 

.064 

1.6 

.0032 

3.2 

66 

3,500 

721 

17 

.056 

1.4 

.0025 

2.4 

42 

4,667 

552 

18 

.048 

1.2 

.0018 

1.8 

32 

6,222 

406 

19 

.040 

1.0 

.0013 

1.2 

21 

9,333 

281 

20 

.036 

0.9 

.0010 

1.0 

18 

11,200 

228 

Notes  on  the  Use  of  Wire  Rope       309 


NOTES  ON  THE  USE  OF  WIRE  ROPE. 


05 

o  M 

a  o  » 

u 

&  W  oa 

0 

K><  U 

w  J  M 

- 

J     fc 

M 

Of 

Q 

to 

O 

1-1  »< 

1 

0.63 

57.29 

39.08 

2 

1.26 

28.63 

78.18 

3 

1.88 

19.09 

117.24 

4 

2.51 

14.29 

156.26 

5 

3.15 

11.42 

195.24 

6 

3.78 

9.51 

234.14 

7 

4.42 

8.14 

272.98 

8 

5.06 

7.11 

311.74 

9 

5.70 

6.31 

350.40 

10 

6.34 

5.67 

388.97 

11 

6.99 

5.14 

427.41 

12 

7.65 

4.70 

465.71 

13 

8.31 

4.33 

503.88 

14 

8.97 

4.01 

541.90 

15 

9.64 

3.73 

579.75 

16 

10.32 

3.48 

617.43 

17 

11.00 

3.27 

654.90 

18 

11.69 

3.07 

692.20 

19 

12.39 

2.90 

729.27 

20 

13.10 

2.74 

766.12 

21 

13.82 

2.60 

802.74 

22 

14.54 

2.47 

839.12 

23 

15.27 

2.35 

875.23 

24 

16.02 

2.24 

911.09 

25 

16.78 

2.14 

946.66 

26 

17.56 

2.05 

981.94 

27 

18.34 

1.96 

1,016.93 

28 

19.14 

1.88 

1,051.61 

29 

19.95 

1.80 

1,085.97 

30 

20.78 

1.73 

1,120.00 

31 

21.62 

1.66 

1,153.68 

32 

22.49 

1.60 

1,187.02 

33 

23.37 

1.54 

1,219.99 

34 

24.28 

1.48 

1,252.58 

35 

25.20 

1.42 

1,284.81 

36 

26.15 

1.37 

1,316.62 

37 

27.12 

1.32 

1,348.05 

38 

28.12 

1.28 

1,379.07 

39 

29.14 

1.23 

1,409.67 

40 

30.21 

1.19 

1,439.84 

For  Vertical  Winding  at  high  speeds, 
one-tenth  the  breaking  strain  has  been  adopted 
as  a  sate  working  load  ;  it  may,  however,  be 
increased  to  one-eighth,  according  to  condi- 
tions of  working.  The  gross  weight  hanging 
over  the  pulley  (including  rope)  being  con- 
sidered the  working  load. 

Hauling  on  Inclined  Plane.  —  The  work- 
ing load  is  usually  taken  at  one-sixth  the 
breaking  strain,  and  the  following  formula 
for  ascertaining  the  load  has  been  found  from 
experience  to  give  satisfactory  results  : 

Plane,  800  yds.    Load,  20  tons. 

Maximum  inclination  7  degs.  or  1  in  8.14. 

Cwts.  Qrs.  Lbs. 


Gravity  of  load,  20  tons  x 

272.98  lbs.  per  ton 
Friction  of  load,  20  tons  X 

20  lbs.  per  ton  = 

Gravity  of  rope,  800  yds.  at 

2.15  lbs.,  1720 -f  8.14  = 

Friction  of  rope,  1720—20  = 
2J  Plough  steel  rope 


=   49 


1(3 


=   55        1        12 

Uncoiling  Wire  Rope.  — A  reel  or  turn- 
table should  be  used  to  avoid  "  kinks "  or 
sharp  bends. 

Lubrication  of  Ropes.— Both  winding 
and  hauling  ropes  should  be  well  oiled  to  pro- 
long duration.  The  winding  rope  especially 
ought  to  have  frequent  applications  of  heavy- 
bodied  hydro-carbon  oil,  which  should  be 
well  rubbed  into  the  interstices  with  a  swab, 
as  it  is  important  that  the  inside  of  the  rope 
should  benefit  as  well  as  the  outside  by  its 
application. 

N.  B.  —  An  unlubricated  rope  stood  16,000 
bends  before  fracture,  whilst  the  same  rope 
lubricated  stood  38,700. 


310 


The  Naval  Constructor 


PROOF  OR  TEST  LOAD  FOR  CHAINS. 

d  =  Diameter  of  Iron  in  Inches. 
The  Admiralty  Rules  are : 

Test  Load  in  Tons  =  18rf*  for  Studded  Links. 
Test  Load  in  Tons  =  12rf2  for  Unstudded  Links. 


d. 

18rf». 

I2d». 

d. 

IS  (P. 

12  rf*. 

d. 

18  rf*. 

12  d*. 

1 

.75 

1 

10.1 

6.7 

4 

40.5 

27.0 

.  .  . 

1.17 

V 

11.9 

7.9 

i& 

47.5 

31.7 

I 

1.69 

13.8 

9.2 

if 

55.1 

36.7 

3.46 

2.30 

ft 

15.8 

10.5 

if 

63.3 

42.2 

A 

4.50 

3.00 

1 

18.0 

12.0 

2 

72.0 

48.0 

5.70 

3.80 

*1 

22.8 

15.2 

2f 

81.3 

54.2 

1 

7.03 

4.69 

11 

28.1 

18.7 

H 

91.1 

60.7 

H 

8.51 

5.67 

1| 

34.0 

22.7 

2| 

101.5 

67  7 

The  practice  at  Elswick  is  to  make  the  test  load  10  per  cent, 
higher  than  the  Admiralty  test  load. 


STRENGTH  OF  CHAIN  CABLES  (AMERICAN). 


33 

Break- 

S3 

ing 

Stress 

Recommended 

Admiralty 

Probable  Aver- 

of  Iron 

Proof  Load  on 

Proof  Load  on 

5° 

in  Lbs. 

per  So. 

In. 

Cable. 

Cable. 

Cable. 

In. 

Lbs. 

Tons. 

Lbs. 

Tons. 

Lbs. 

Tons. 

55,596 

33,840 

15.11 

40,320 

18.00 

71,172 

31.77 

it 

55,073 

37,820 

16.88 

45,517 

20.32 

79,544 

35.51 

54,589 

42,053 

18.77 

51,030 

22.78 

88,445 

39.48 

JT% 

54,138 

46,468 

20.74 

56,857 

25.38 

97,731 

43.63 

U 

53,715 

5t,084 

22.81 

63,000 

28.12 

107,440 

47.96 

it 

53,317 

55,903 

24.96 

69,457 

31.01 

117,577 

52.49 

52,941 

60,920 

27.20 

76,230 

34.03 

128,129 

57.20 

if 

52,584 

66,138 

29.53 

83,317 

37.20 

139,103 

62.10 

52,245 

71,550 

31.94 

90,720 

40.50 

150,485 

67.18 

if 

51,922 

77,159 

34.45 

98,437 

43.95 

162,283 

72.45 

51,613 

82,956 

37.03 

106,470 

47.53 

174,475 

77.89 

i? 

51,317 

88.947 

39.71 

114,817 

51.26 

187,075 

83.52 

51,033 

95,128 

42.47 

123,480 

55.12 

200,074 

89.32 

W 

50,760 

101,499 

45.31 

132,457 

59.13 

213,475 

95.30 

50,498 

108,058 

48.24 

141,750 

63.28 

227,271 

101.46 

W 

50,245 

114,806 

51.25 

151,357 

67.57 

241,463 

107.80 

2 

50,000 

121,737 

54.35 

161,280 

72.00 

256,040 

114.30 

Strength  of  Small  Chains 


311 


STRENGTH  OF  SMALL  CHAINS. 

THE  FOLLOWING  RULES  ARE  BA8ED  ON  EXPERIMENTS  CAR- 
RIED OUT  BY  PROF.  H.S.  HALE  SHAW  ON  SMALL  CHAIN8. 
LESS  THANHS 


\  SINGLE  JACK 
'  W=78S0d2 


Fig.  102. 


Fig.  103. 


ORDINARY  WELDED 
W=39,250d2 


Fig.  104. 


TRIUMPH"  WELDLES8 
MACHINE  MADE 
W=78,500d* 


w  =  breaking  load  in  lbs.   d=6ize  of  chain  in  inche8. 

the  safe  load  may  be  taken  a8  one  quarter  of  breaking  load. 

Fig.  105. 


312 


The  Naval  Constructor     • 


DIMENSIONS    AND  WEIGHT    OF  CHAIN  CABLES* 


Size  of  Links  (Out- 

Number 

Weight  per  Fathom. 

Diameter 

side). 

of  Links 
in  One 
Fathom. 

of  Iron. 

Length. 

Width. 

Studded 

Links. 

Open 
Links. 

In. 

In. 

In. 

Lbs. 

U>s. 

5{J 

» 

19i 

57.8 

52.9 

it 

8$ 

is| 

64.7 

60.1 

c! 

4 

18 

77.7 

69.7 

It 

fit 

4* 

17 

84.8 

77.4 

7 

*& 

16 

94.9 

86.8 

it 

7t\ 

i 

15* 

102.9 

95.2 

7ft 

15 

115.5 

106.2 

If 

8 

5ft 

14 

121.7 

113.C 

81 

»x 

13ft 

134.3 

124.2 

1* 

8H 

$ 

13 

144.6 

134.9 

H 

9 

m 

160.0 

146.7 

\l 

y 

6 

12 

170.1 

157.3 

6ft 

Hi 

183.2 

168.9 

11 

10ft 

85 

n 

192.9 

179.1 

10ft 

6| 

n 

215.6 

199.1 

lil 

ioi 

8i 

10£ 

225.0 

209.2 

10$ 

71 

10 

240.8 

219.9 

St 

"ft 

7f 

10 

261.4 

240.5 

12J 

7|. 

9* 

272.1 

250.7 

2ft 

7f 

9 

279.1 

258.8 

ULTIMATE    OR   BREAKING   STRENGTH 
OF   CHAINS. 

The  breaking  stress  of  the  iron  of  which  chains  are  made  varies 
with  the  diameter  of  the  bar,  being  less  the  greater  the  diameter. 

If  /=  breaking  stress  of  iron  in  tons  per  square  inch, 

and  d  =  diameter  of  bar  in  inches, 

then  /=  26.2  -  2.4  d. 

Breaking  load  of  chain  in  tons  =  W=  1.22 d2  (26.2  —  2 Ad). 

This  formula  allows  for  the  bending  action,  and  for  the  loss  of 
strength  due  to  the  weld. 

The  following  table  gives  values  of  W  for  various  values  of  d, 
calculated  by  the  above  formula  : 


d 

w. 

d. 

w. 

d. 

w. 

d. 

W. 

X 

1.95 

1 

11.8 

! 

29.0 

H 

82.2 

* 

3.03 

I 

14.2 

H 

36.3 

H 

93.1 

4.34 

16.7 

if 

44.2 

2 

104.4 

1 

5.87 

f 

19.5 

if 

52.8 

24 

116.2 

7.62 

22.5 

U 

62.0 

21 

128.5 

ft 

9.59 

H 

25.7 

if 

71.8 

2» 

141.1 

*  From  Report  of  Committee  of  Government  Board,  IT.  S.  A.,  1879. 


Elements  of  Angles 


313 


CHAPTER   III. 


ELEMENTS    OF  ANGLES. 


Fig.  106. 


Size  in 
Inches. 

Thick- 
ness. 

A  BE  A 

in  Square 
Inches. 

Weight 

peb  Foot  in 

Pounds. 

Moments  of  Inertia. 

Axis,  AB. 

Axis,  EF. 

8x8 

i 

7.75 

26.4 

48.47 

19.60 

8J  X8J 

1 

15.29 

52.8 

94.14 

39.01 

6X6 

1 

4.36 

14.8 

15.37 

6.20 

6J  X  61 

I 

10.65 

35.9 

36.69 

15.48 

5      X  5 

3.61 

12.3 

8.73 

3.54 

51  X  51 

H 

8.77 

29.4 

20.72 

9.09 

4      X  4 

f  . 

2.40 

8.2 

3.69 

1.50 

41  X41 
3£   X  3£ 

5.69 

18.6 

8.71    . 

3.82 

A 

2.09 

7.1 

2.45 

0.99 

3f  X  3| 

\ 

4.06 

13.7 

4.G0 

1.97 

3X3 

1.44 

4.9 

1.25 

0.50 

8A  x  SA 

2f  X  2| 

3.51 

11.5 

3.01 

1.32 

1 

1.31 

4.5 

0.95 

0.39 

3      X3 

| 

2.70 

8.6 

2.11 

0.90 

2h   X  2£ 

3 

? 

0.90 

3.1 

0.54 

0.22 

2f  X2f 

2.33 

7.8 

1.33 

0.59 

21   X2| 

i 

0.81 

2.7 

0.39 

0.16 

2/3  X  2ft 

1.66 

5.4 

0.85 

0.37 

2      X  2 

1 

0.71 

2.5 

0.27 

0.11 

2,3B  X  2T% 
If  X  if 

1.47 

4.8 

0.61 

0.26 

0.62 

2.1 

0.18 

0.08 

1^1  X  H| 

§ 

1.28 

4.1 

0.39 

0.18 

4 

0.36 

1.2 

0.08 

003 

l|  X  if 

§ 

1.14 

3.5 

0.29 

0.13 

1 1  X  1  J 

4 

0.30 

1.0 

0.05 

0.02 

if  x  if 

1 

0.62 

2.0 

0.10 

0.04 

1       X  1 

^ 

0.23 

0.8 

0.02 

0.01 

H  x  H 

* 

0.49 

1.5 

0.05 

0.02 

314 


The  Naval  Constructor 

ELEMENTS    OF   ANGLES. 


Fig.  106. 


Distance  from 

Radii  of  Gyj 

Resistance. 

Base  to 

Neutral  Axis. 

Axis  AB. 

Axis  EF. 

Axis  AB. 

d. 

2.50 

1.59 

8.34 

2.19 

2.48 

1.60 

16.18 

2.43 

1.88 

1.19 

3.53 

1.64 

1.86 

1.21 

8.43 

1.19 

1.56 

0.99 

2.42 

1.39 

1.54 

1.02 

5.76 

1.65 

1.24 

0.79 

1.28 

1.12 

1.24 

0.82 

3.10 

1.34 

1.08 

0.69 

0.98 

0.99 

1.06 

0.70 

1.84 

1.13 

0.93 

0.59 

0.58 

0.84 

0.93 

0.61 

1.39 

1.02 

0.85 

0.55 

0.48 

0.78 

0.88 

0.58 

1.02 

0.93 

0.77 

0.49 

0.80 

0.70 

0.76 

0.50 

0.75 

0.84 

0.69 

0.44 

0.24 

0.63 

0.72 

0.47 

0.50 

0.75 

0.62 

0.39 

0.19 

0.58 

0.64 

0.42 

0.40 

0.68 

0.54 

0.36 

0.15 

0.51 

0.55 

0.38 

0.30 

0.63 

0.47 

0.28 

0.07 

0.42 

0.50 

0.34 

0.25 

0.57 

0.41 

0.26 

0.06 

0.35 

0.40 

0.25 

0.11 

0.43 

0.29 

0.21 

0.03 

0.30 

0.32 

0.20 

0.07 

0.37 

Elements  of  Bulb  Angles  315 


ELEMENTS    OP  BULB   ANGLES. 


OB 

10 

5M 

&  n  * 

lie 

Moments  of 
Inertia. 

Square  op 

Radius 

of  Gyration. 

Radius 

of 

Gyration. 

Axis 
AB. 

Axis 
CD. 

Axis 
EF. 

Axis 
AB. 

Axis 
CD. 

Axis 
EF. 

Axis 
AB. 

Axis 
CD. 

Axis 
EF. 

7.70 

26.2 

94.17 

7.11 

5.22 

12.23 

0.92 

0.68 

3.50 

0.96 

0.82 

10 

11.24 

38.2 

136.41 

11.93 

9.19 

12.14 

1.06 

0.82 

3.48 

1.03 

0.90 

9 

6.74 

22.9 

67.67 

6.58 

4.68 

10  04 

0.98 

0.69 

3.17 

0.99 

0.83 

9 

9.56 

32.5 

95.71 

10.61 

7.60 

10.01 

1.11 

0.79 

3.16 

1.05 

0.89 

8 

5.62 

19.1 

44.69 

4.09 

3.06 

7.95 

0.73 

0.54 

2.82 

0.85 

0.74 

8 

7.77 

26.4 

61.63 

6.43 

4.83 

7.93 

0.83 

0.62 

2.82 

0.91 

0.79 

7 

4.79 

16.3 

29.74 

3.73 

2.66 

6.21 

0.78 

0.56 

2.49 

0.88 

0.75 

7 

6.41 

21.8 

39.67 

5.58 

3.93 

6.19 

0.87 

0.61 

2.49 

0.93 

0.78 

6 

391 

13.3 

18.31 

3.24 

2.26 

4.68 

0.83 

0.58 

2.16 

0.91 

0.76 

6 

5.24 

17.8 

24.35 

4.81 

3.29 

4.65 

0.92 

0.63 

2.16 

0.96 

079 

5 

2.97 

10.1 

9.84 

1.76 

1.52 

3.31 

0.59 

0.51 

1.82 

0.77 

0.72 

5 

3.97 

13.5 

13.07 

2.64 

1.86 

3.29 

0.66 

0.47 

1.81 

0.82 

0.68 

316 


The  Naval  Constructor 


ELEMENTS    OF   DECK   BEAMS. 


Pig. 


as 

M 

*  3  w 

gig 

ST 

to 
K 

Moments  of 
Inertia. 

Square  of 
Radius  of 
Gyration. 

Radius  of 
Gyration. 

Axis 
AB. 

Axis 
CD. 

Axis 
AB. 

Axis 
CD. 

Axis 
AB. 

Axis 
CD. 

in 

9.51 

32.2 

179.33 

6.36 

18.86 

0.67 

4.34 

0.82 

in 

13.41 

45.6 

224.19 

8.14 

16.72 

0.61 

4.09 

0.78 

10 

8.20 

28.0 

118.55 

6.08 

14.46 

0.74 

3.80 

0.86 

10 

11.32 

38.6 

145.77 

7.54 

12.88 

0.67 

3.59 

0.82 

9 

7.35 

25.0 

84.99 

4.85 

11.56 

0.66 

3.40 

0.81 

9 

9.  GO 

32.6 

100.68 

5.78 

10.49 

0.60 

3.24 

0.77 

8 

6.17 

21.0 

57.75 

3.58 

9.36 

0.58 

3.06 

0.76 

8 

8.43 

28.6 

70.19 

4.44 

8.33 

0.53 

2.89 

0.73 

7 

5.32 

18.0 

36.99 

2.56 

6.95 

0.48 

2.64 

0.69 

7 

7.29 

24.5 

45.32 

3.26 

6.22 

0.45 

2.49 

0.67 

6 

4.27 

14.5 

21.83 

1.62 

5.11 

0.38 

2.26 

0.62 

6 

5.77 

19.6 

26.50 

2.07 

4.59 

0.36 

2.14 

0.60 

5 

3.39 

11.5 

11.96 

1.01 

3.53 

0.30 

1.88 

0.55 

6 

4.64 

15.8 

14.64 

1.29 

3.16 

0.28 

1.78 

0.53 

Elements  of  Deck  Beams  317 


ELEMENTS    OF  DECK  BEAMS.—  (Continued.) 


§ 

H 

g 

53 

03 

H 

H 
O 

H 

t» 

M 

CO 

1 

j 
«2  • 

P  fe  H 

fc  O  o 

53e« 

««!  ? 

Mg 

to 

a 
M 

o 

H  ^  O 

^  *  a 

to  02  « 

«  to%, 
OB. 

a 

8Z& 

2  as 

to  to  g 
O  H" 

Coefficient  for 
Deflection. 

< 

o     2 

U  CO  g 

Distributed 
Load. 

Centre 
Load. 

11§ 

27.9 

0.60 

148.7 

3.22 

.0000089 

.0000143 

48.6 

5.07 

m 

36.0 

0.60 

191.9 

3.22 

.0000071 

.0000114 

119.4 

5.27 

10 

20.7 

0.54 

110.5 

2.86 

.0000135 

.0000217 

40.8 

4.28 

10 

26.4 

0.54 

140.8 

2.86 

.0000107 

.0000172 

96.4 

4.48 

9 

16.7 

0.48 

88.9 

2.55 

.0000188 

.0000303 

39.0 

3.90 

9 

20.3 

0.48 

108.3 

2.55 

.0000159 

.0000256 

79.0 

4.04 

8 

12.8 

0.43 

68.1 

2.28 

.0000277 

.0000446 

32.4 

3.48 

8 

16.0 

0.43 

85.5 

2.28 

.0000228 

.0000367 

72.2 

3.62 

7 

9.3 

0.38 

49.8 

2.02 

.0000432 

.0000695 

30.2 

3.04 

7 

11.8 

0.38 

62.9 

2.02 

.0000352 

.0000568 

64.6 

3.16 

6 

6.4 

0.32 

34.3 

1.69 

.0000733 

.0001180 

24.0 

2.61 

6 

8.1 

0.32 

43.0 

1.69 

.0000604 

.0000972 

50.2 

2.71 

5 

4.3 

0.26 

22.9 

1.39 

.0001337 

.0002147 

21.4 

2.22 

5 

5.4 

0.26 

28.9 

1.39 

.0001093 

.0001755 

42.8 

2.30 

318  The  Naval  Constructor 

ELEMENTS    OF   TEES.  — Uneven  Legs. 


Fig.  109. 


Size 

ITU 

<  <  B 

w  u  Z 

M    fc    » 

HOO 

Moments  of 

INEBTIA. 

Resistance. 

Radius  of 
Gybation. 

1.37 

Inches. 

Axis 

Axis 

Axis 

Axis 

Axis 

Axis 

<JCCm 

^PhP< 

AB. 

CD. 

AB. 

CD. 

AB. 

CD. 

6   x4* 

8.21 

28.2 

14.74 

13.81 

4.71 

4.60 

1.33 

1.29 

6X4 

4.61 

15.6 

5.82 

8.19 

1.92 

2.73 

1.12 

1.33 

0.97 

6    X5i 
5    X3* 

11.58 

39.0 

28.68 

18.75 

8.19 

6.25 

1.57 

1.27 

1.75 

4.95 

17.0 

5.29 

5.47 

2.17 

2.19 

1.03 

1.05 

1.06 

5    X4 

4.54 

15.3 

6.16 

5.41 

2.11 

2.16 

1.17 

1.09 

1.08 

4X2 

1.93 

6.5 

0.53 

1.75 

0.34 

0.87 

0.52 

0.95 

0.46 

4    X3 

2.67 

9.0 

1.99 

2.10 

0.90 

1.05 

0.87 

0.89 

0.78 

4    X3 

3.05 

10.2 

2.24 

2.44 

1.02 

1.22 

0.85 

0.89 

0.81 

4    X4i 

4.29 

14.6 

7.87 

2.80 

2.50 

1.40 

1.37 

0.81 

1.37 

4ix3l 

4.65 

15.8 

4.93 

3.67 

2.05 

1.63 

1.03 

0.89 

1.11 

4X4} 

3.38 

11.4 

6.31 

2.11 

1.96 

1.06 

1.37 

0.79 

1.28 

3ix3 

3    X3 

2.11 

7.0 

1.65 

1.18 

0.75 

0.67 

0.88 

0.75 

0.80 

2.46 

8.5 

1.91 

1.41 

0.88 

0.81 

0.88 

0.75 

0.83 

3   xH 

1.20 

4.0 

0.18 

0.60 

0.16 

0.40 

0.39 

0.71 

0.36 

3    X2 

1.46 

50 

0.78 

0.60 

0.42 

0.40 

0.73 

0.64 

0.66 

3    X2, 

1.76 

6.0 

0.93 

0.74 

0.51 

0.49 

0.73 

0.65 

0.68 

3    X2 

2.06 

7.0 

1.08 

0.89 

0.60 

0.59 

0.72 

0.66 

0.71 

3    X2 ,r 

2.38 

8.0 

1.32 

0.91 

0.78 

0.61 

0.74 

0.62 

0.80 

3    X3 

2.46 

8.3 

2.82 

0.89 

1.17 

0.59 

1.07 

0.60 

1.08 

3    X3j 

2.81 

9.5 

3.19 

1.04 

1.33 

0.69 

1.07 

0.61 

1.10 

% 

[xU 

1.96 

6.6 

0.56 

0.60 

0.50 

0.44 

0.54 

0.56 

0.64 

■1 

X2 

2.14 

7.2 

0.82 

0.61 

0.G6 

0.44 

0.62 

0.54 

0.75 

2 

xH 

X2| 

0.97 

3.3 

0.10 

0.33 

0.11 

0.26 

0.32 

0.58 

0.31 

2 

1.68 

5.7 

1.16 

0.43 

0.60 

0.34 

0.83 

0.51 

0.83 

2 

X3 

1.76 

6.0 

1.48 

0.44 

0.71 

0.35 

0.92 

0.50 

0.93 

$ 

X      ft 

0.66 

2.2 

0.01 

0.24 

0.03 

0.21 

0.14 

0.60 

0.17 

2    X    ft 

0.60 

2.0 

0.01 

0.17 

0.03 

0.17 

0.14 

0.53 

0.17 

2    XlA 

0.62 

2.0 

0.04 

0.16 

0.05 

016 

0.24 

0.51 

0.23 

2    XI 

0.72 

2.5 

0.05 

0.17 

0.07 

0.17 

0.26 

0.49 

0.27 

2   xH 

0.91 

3.0 

0.16 

0.17 

0.15 

0.17 

0.42 

0.44 

0.45 

if  X  1ft 

0.56 

1.9 

0.05 

0.11 

0.06 

0.13 

0.30 

0.45 

0.24 

ifx  11 

1.04 

3.5 

0.12 

0.21 

0.14 

0.24 

0.35 

0.45 

0.40 

i|x  H 

0.41 

1.4 

0.02 

0.07 

0.03 

0.09 

0.22 

0.41 

0.21 

ilx    11 

0.35 

1.2 

20.0 

0.03 

0.03 

0.05 

0.24 

0.30 

0.22 

Elements  of  Tee  Bars 


319 


ELEMENTS   OF   TEES.  —  Even  Legs. 


Pig.  109. 


W 

g 

Moments 

RADI 

ITS    OF 

^g 

lSf§ 

2  o  A 

of  Inertia. 

Resistance. 

Gyration. 

8Sg 

Size  in 
Inches. 

as 

Axis 

Axis 

Axis 

Axis 

Axis 

Axis 

^m 

AB. 

CD. 

AB. 

CD. 

AB. 

CD. 

4    X4 

3.10 

10.9 

4.70 

2.20 

1.64 

1.10 

1.23 

0.85 

1.15 

4X4 

3.98 

13.7 

5.70 

2.79 

2.02 

1.40 

1.20 

0.84 

1.18 

*5g    X   &2 

3|X3£ 

2.08 

7.0 

2.27 

1.03 

0.89 

0.59 

1.04 

0.71 

0.94 

2.65 

9.0 

2.83 

1.32 

1.16 

0.75 

1.03 

0.71 

1.06 

3*x3i 

3.24 

11.0 

3.61 

1.75 

1.49 

1.00 

1.05 

0.73 

1.07 

3x3 

1.91 

6.5 

1.57 

0.75 

0.74 

0.50 

0.91 

0.62 

0.87 

3X3 

2.27 

7.7 

1.82 

0.89 

0.86 

0.60 

0.89 

0.62 

0.88 

2J 

2 

\xty 

1.47 

5.0 

0.79 

0.38 

0.44 

0.30 

0.73 

0.51 

0.69 

X2£ 

1.71 

5.8 

0.95 

0.48 

0.55 

0.38 

0.75 

0.53 

0.76 

■1 

■X2J 

1.94 

6.6 

1.08 

0.56 

0.63 

0.45 

0.75 

0.54 

0.79 

2 

:X2| 

1.18 

4.0 

0.51 

0.27 

0.31 

0.24 

0.66 

0.48 

0.62 

2 

tX2i 

1.18 

4.0 

0.52 

0.26 

0.33 

0.23 

0.66 

0.47 

0.65 

2    X2 

1.03 

3.5 

0.37 

0.18 

0.26 

0.18 

0.60 

0.41 

0.60 

If  X  if 

0.71 

2.4 

0.19 

0.09 

0.15 

0.10 

0.52 

0.36 

0.51 

hi 

0.59 

2.0 

0.12 

0.06 

0.12 

0.08 

0.45 

0.32 

0.47 

0.44 

1.5 

0.07 

0.04 

0.09 

0.06 

0.40 

0.30 

0.43 

1    X  1 

0.29 

1.0 

0.03 

0.02 

0.05 

0.04 

0.32 

0.26 

0.38 

320 


The   Naval  Constructor 

ELEMENTS    OF   Z   BARS. 


A» 

a 

Moment 

OF 

Sgs 

INEBTI.A 

Resistance 

Sizes  in  Inches. 

w  &3 

gO  'A 

*0 

Axis 

Axis 

Axis 

Axis 

Axis 

B 

AB. 

CD. 

EF. 

AB. 

CD. 

2f    X3      X  2|    X    i 

1.94 

6.60 

2.81 

2.61 

0.59 

1.9 

1.0 

2U  X  3 A  X  2U  X  A 

2]   X3JX2?X} 

2.44 

8.29 

3.52 

3.38 

0.74 

2.3 

1.3 

2.94 

10.00 

4.34 

4.22 

0.92 

2.8 

1.7 

2|i  X  3      X  m  X  A 

3.25 

11.15 

4.20 

4.24 

0.95 

2.8 

1.7 

2*8  X  3A  X  2}J  X  4§ 

3.51 

11.93 

4.54 

4.64 

1.01 

3.0 

1.9 

211  X  3A  X  2||  X   i 

3.75 

12.75 

4.88 

5.04 

1.11 

3.2 

2.0 

2JX4      X2fxl 

2.32 

7.88 

5.95 

3.47 

0.95 

3.0 

1.3 

21*  X  4  A  X  211  X  A 

2.91 

9.89 

7.52 

4.49 

1.23 

3.7 

1.6 

3      X  4J  X3      X  § 

3.52 

11.90 

9.14 

5.58 

1.53 

4.4 

2.0 

23*  x  4     x  m  X  A 

3A  X  4A  X3,VX   h 

3A  x  4  j  x  3A  x  A 

3A  X  4      X3AX1 
31  X4iX3^Xli 
3A  X  4|  X  3A  X  I 

3.96 

13.46 

9.40 

6.09 

1.63 

4.7 

2.2 

4.56 

15.50 

10.92 

7.21 

1.94 

5.4 

2.6 

5.16 

17.54 

12.40 

8.40 

2.27 

6.0 

3.0 

5.55 

18.80 

12.11 

8.73 

2.32 

6.1 

3.2 

6.14 

20.87 

13.52 

9.95 

2.67 

6.7 

3.6 

6.75 

22.95 

14.97 

11.24 

3.03 

7.3 

4.0 

3A  X  5      X  3A  X  A 

3  i   X  5A  X3JX1 

3.36 

11.42 

13.14 

5.81 

1.86 

5.3 

1.9 

4.05 

13.77 

15.93 

7.20 

2.25 

6.3 

2.4 

3AX5i  X3AX  x7b 

4.75 

16.15 

18.76 

8.67 

2.75 

7.3 

2.8 

3/,  X  5      X  3A  X  h 

5.23 

17.78 

19.03 

8.77 

2.76 

7.6 

3.0 

3A  x  5A  x  3A  x  A 

3UX54  X  mx   f 
A  X  5      X  3}  X  H 

5.91 

20.09 

21.65 

10.19 

3.20 

8.6 

3.4 

6.60 

22.44 

24.33 

11.70 

3.73 

9.5 

3.9 

6.96 

23.66 

23.68 

11.37 

3.59 

9.5 

3.9 

3A  X  5A  X  3A  x  I 

3>   X6      X3}X| 

7.64 

25.97 

26.16 

12.83 

4.12 

10.3 

4.4 

4.59 

15.61 

25.32 

9.11 

3.11 

8.4 

2.8 

3A  x  6A  x  3A  x  A 

3f  X  61  X3f  X   i 
3$  X  6      X  3i  X  A 
3A  X  6A  X  3A  X   f 
3*  X6i  X3f  X  « 
3|  X  6      X3|xi 

5.39 

18.32 

29.80 

10.95 

3.74 

9.8 

3.3 

6.19 

21.05 

34.36 

12.87 

4.37 

11.2 

3.8 

6.68 

22.71 

34.64 

12.59 

4.37 

11.6 

3.9 

7.46 

25.36 

38.86 

14.42 

4.92 

12.8 

4.4 

8.25 

28.05 

43.18 

16-34 

5.66 

14.1 

5.0 

8.64 

29.37 

42.12 

15.44 

5.61 

14.0 

4.9 

3A  X  6A  X  3A  x  H 
3|  X  61  X3f  X   f 

9.38 

31.89 

46.13 

17.27 

6.16 

15.2 

5.5 

10.16 

34.54 

50.22 

19.18 

6.85 

16.4 

6.0 

Elements  of  Z   Bars 


321 


ELEMENTS    OF   Z    BARS. 

B 


Fig. 

110. 

Radii  of 
Gyration. 

Coefficient  in 
Net  Tons  for 
Greatest  Safe 
LoadDistance. 

Coefficient  for 

Deflection 
about  Axis  AB. 

ft    . 
-  m 

J  o 

gH 

2h 

■<  a 

Axis 
AB. 

Axis 
CD. 

Least 
Axis 
EF. 

Fibre 

Stress 
16,000 
Lbs. 

Fibre 
Stress 
12,000 
Lbs. 

Distribu- 
ted. 

Centre. 

1.20 

1.16 

0.55 

10.0 

7.5 

.0005694 

.0009167 

11.0 

1.20 

1.18 

0.55 

12.3 

9.2 

.0004545 

.0007317 

14.4 

1.21 

1.20 

0.56 

14.8 

11.1 

.0003687 

.0005937 

18.0 

1.13 

1.14 

0.54 

14.9 

11.2 

.0003809 

.0006132 

20.4 

1.14 

1.15 

0.54 

16.0 

12.0 

.0003524 

.0005674 

22.2 

1.14 

1.16 

0.55 

17.0 

12.8 

.0003279 

.0005279 

24.0 

1.60 

1.22 

0.64 

15.9 

11.9 

.0002689 

.0004329 

13.6 

1.61 

1.24 

0.65 

19.7 

14.8 

.0002128 

.0003426 

18.2 

1.62 

1.26 

0.66 

23.6 

17.7 

.0001750 

.0002817 

23.0 

1.54 

1.24 

0.64 

25.1 

18.8 

.0001702 

.0002740 

26,6 

1.55 

1.27 

0.65 

28.7 

21.5 

.0001465 

.0002359 

31.2 

1.55 

1.28 

0.66 

32.1 

24.1 

.0001290 

.0002077 

35.8 

1.48 

1.26 

0.65 

32.3 

24.2 

.0001321 

.0002127 

39.0 

1.48 

1.27 

0.66 

35.5 

26.6 

.0001183 

.0001905 

43.6 

1.49 

1.29 

0.67 

38.7 

29.0 

.0001069 
.0001218 

.0001721 

48.6 

1.98 

1.32 

0.74 

28.0 

21.0 

.0001961 

21.4 

1.98 

1.33 

0.75 

33.6 

25.2 

.0001005 

.0001618 

27.0 

1.99 

1.35 

0.76 

39.1 

29.3 

.0000853 

.0001373 

32.8 

1.91 

1.30 

0.73 

40.6 

30.5 

.0000841 

.0001354 

37.6 

1.91 

1.31 

0.74 

45.6 

34.2 

.0000739 

.0001190 

43.2 

1.92 

1.33 

0.75 

50.6 

38.0 

.0000658 

.0001059 

49.0 

1.84 

1.28 

0.72 

50.5 

37.9 

.0000676 

.0001088 

53.2 

1.85 

1.30 

0.73 

55.1 

41.3 

.0000612 

.0000984 

59.0 

2.35 

1.41 

0.82 

45.0 

33.8 

.0000632 

.0001017 

30.8 

2.35 

1.43 

0.83 

52.4 

39.3 

.0000537 

.0000864 

37.6 

2.36 

1.44 

0.84 

59.8 

44.9 

.0000466 

.0000750 

44.6 

2.28 

1.37 

0.81 

61.6 

46.2 

.0000462 

.0000744 

50.2 

2.28 

1.39 

0.81 

68.4 

51.3 

.0000412 

.0000663 

57.0 

2.29 

1.41 

0.83 

75.2 

56.4 

.0000370 

.0000596 

64.0 

2.21 

1.34 

0.81 

74.9 

56.2 

.0000380 

.0000612 

69.0 

2.22 

1.36 

0.81 

81.2 

60.9 

.0000347 

.0000559 

76.0 

2.22 

1.37 

0.82 

87.5 

65.6 

.0000319 

.0000513 

83.0 

322 


The  Naval  Constructor 


ENDING  MOMENTS    OF  PINS. 

M  , 


Moment  =  ^  Z>y. 


Diameter 


Diam- 
eter of 

Area  of 
Pin  in 

Moments  in  Inch-Pounds  fob 
Strains  of 

Fibre 

Pin  in 

LNCHE8. 

Square 
Inches. 

15,000  Lbs. 

20,000  Lbs. 

22,000  Lbs. 

25,000  Lbs. 

per 

per 

per 

per 

Sq.  Inch. 

Sq.  Inch. 

Sq. Inch. 

Sq.  Inch. 

0.785 

1,470 

1,960 

2,160 

2,450 

i  J 

0.994 

2,100 

2,800 

3,080 

3,500 

ii 

1.227 

2,880 

3,830 

4,220 

4,790 

if 

1.485 

3,830 

5,100 

5,620 

6,380 

lX 

1.767 

4,970 

6,630 

7,290 

8,280 

1| 

2.074 

6,320 

8,430 

9,270 

10,500 

l| 

2.405 

7,890 

10,500 

11,570 

13,200 

l| 

2.761 

9,710 

12,900 

14,240 

16,200 

2 

3,142 

11,800 

15,700 

17,280 

19,600 

21 

3.547 

14,100 

18,800 

20,730 

23,600 

21 

3.976 

16,800 

22,400 

24,600 

28,000 

2f 

4.430 

19,700 

26,300 

28,900 

32,900 

2I 

4.909 

23,000 

30,700 

33,700 

38,400 

2! 

5.412 

26,600 

35,500 

39,000 

44,400 

2f 

5.940 

30,600 

40,800 

44,900 

51,000 

2| 

6.492 

35,000 

46,700 

51,300 

58,300 

3 

7.069 

39,800 

53,000 

58,300 

66,300 

<*i 

7.670 

44,900 

59,900 

65,900 

74,900 

31 

8.296 

50,600 

67,400 

74,100 

84,300 

3| 

8.946 

56,600 

75,500 

83,000 

94,400 

3y, 

9.621 

63,100 

84,200 

92,600 

105,200 

3| 

10.321 

70,100 

93,500 

102,900 

116,900 

3§ 

11.045 

77,700 

103,500 

113,900 

129,400 

33 

11.793 

85,700 

114,200 

125,600 

142,800 

4 

12.566 

94,200 

125,700 

138,200 

157,100 

41 

13.364 

103,400 

137,800 

151,600 

172,300 

41 

14.186 

113,000 

150,700 

165,800 

188,400 

4f 

15.033 

123,300 

164,400 

180,800 

205,500 

4? 

15.904 

134,200 

178,900 

196,800 

223,700 

4| 

16.800 

145,700 

194,300 

213,700 

242,800 

4f 

17.721 

157,800 

210,400 

231,500 

263,000 

? 

18.665 

170,600 

227,500 

250,200 

284,400 

5 

19.635 

184,100 

245,400 

270,000 

306,800 

51 

20.629 

198,200 

264,300 

290,700 

330,400 

51 

21.648 

213,100 

284,100 

312,500 

355,200 

5f 

22.691 

228,700 

304,900 

335,400 

381,100 

5j 

23.758 

245,000 

326,700 

359,300 

408,300 

5f 

24.850 

262,100 

349,500 

384,400 

436,800 

5f 

25.967 

280,000 

373,300 

410,600 

466,600       . 

H 

27.109 

298,600 

398,200 

438,000 

497,700 

Bending  Moments  of  Pins 

323 

BENDING  MOMENTS 

OF  PINS.  —  (Continued.) 

Moment  =  ^  D8/. 

3IW) 

Diameter  =  .  /  \f) 
*       32 

DIAM- 
ETER  OP 

Pin  in 
Inches. 

Area  of 
Pin  in 
Square 
Inches. 

Moments  in  Inch-Pounds  for  Fibre 
Strains  of 

15,000  Lbs. 

20,000  Lbs. 

22,000  Lbs. 

25,000  Lbs. 

per 

per 

per 

per 

Sq.    Inch. 

Sq. Inch. 

Sq.  Inch. 

Sq. Inch. 

6 

28.274 

318,100 

424,100 

466,500 

530,200 

n 

29.465 

338,400 

451,200 

496,300 

564,000 

30.680 

359,500 

479,400 

527,300 

599,200 

6| 

31.919 

381,500 

508,700 

559,600 

635,900 

1 

33.183 

404,400 

539,200 

593,100 

674,000 

34.472 

428,200 

570,900 

628,000 

713,700 

35.785 

452,900 

603,900 

664,200 

754,800 

6$ 

37.122 

478,500 

638,000 

701,800 

797,500 

7 

38.485 

505,100 

673,500 

740,800 

841,900 

71 

39.871 

532,700 

710,200 

781,200 

887,800 

a 

41.282 

561,200 

748,200 

823,000 

935,300 

7§ 

42.718 

590,700 

787,600 

866,300 

984,500 

7£ 

44.179 

621,300 

828,400 

911,200 

1,035,400 

7f 

45.664 

652,900 

870,500 

957,500 

1,088,100 

7f 

47.173 

685,500 

914,000 

1,005,300 

1,142,500 

?1 

48.707 

719,200 

958,900 

1,054,800 

1,198,700 

8 

50.265 

754,000 

1,005,300 

1,105,800 

1,256,600 

8i 

51.849 

789,900 

1,053,200 

1,158,500 

1,316,500 

8$ 

53.456 

826,900 

1,102,500 

1,212,800 

1,378,200 

8| 

55.088 

865,100 

1,153,400 

1,268,800 

1,441,800 

3 

56.745 

904,400 

1,205,800 

1,326,400 

1,507,300 

8f 

58.426 

944,900 

1,259,800 

1,385,800 

1,574,800 

8f 

60.132 

986,500 

1,315,400 

1,446,900 

1,644,200 

H 

61.862 

1,029,400 

1,372,500 

1,509,800 

1,715,700 

9 

63.617 

1,073,500 

1,431,400 

1,574,500 

1,789,200 

94 

65.397 

1,118,900 

1,491,900 

1,641,100 

1,864,800 

1 

67.201 

1,165,500 

1,554,000 

1,709,400 

1,942,500 

69.029 

1,213,400 

1,617,900 

1,779,600 

2,022,300 

H 

70.882 

1,262,600 

1,683,400 

1,851,800 

2,104,300 

9f 

72.760 

1,313,100 

1,750,800 

1,925,900 

2,188,500 

9| 

74.662 

1,364,900 

1,819,900 

2,001,900 

2,274,900 

91 

76.590 

1,418,100 

1,890,800 

2,079.900 

2,363,500 

10 

78.54 

1,472,600 

1,963,500 

2,159,900 

2,454,400 

101 

82.52 

1,585,900 

2,114,500 

2,325,900 

2,643,100 

10£ 

86.59 

1,704,700 

2,273,000 

2,500,200 

2,841,200 

lOf 

90.76 

1,829,400 

2,439,300 

2,683,200 

3,049,100 

11 

95.03 

1,960,100 

2,613,400 

2,874,800 

3,266,800 

53 

99.40 

2,096,800 

2,795,700 

3,075,400 

3,494,800 

103.87 

2,239,700 

2,986,300 

3,284,800 

3,732,800 

12 

113.10 

2,544,700 

3,392,900 

3,732,200 

4,241,200 

/ 

324 


The  Naval  Constructor 


TEES  AS   STRUTS. 

r  =  least  radius  of  gyration. 


Size  of 

Tee  in 

Inches. 

Length  in  Feet. 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

Greatest  Safe  Load  in  Pounds  per  Square  Inch  of  Section. 

4X4) 
r  =.85  \ 

3}x  31  ) 
r  =.73  ] 

3X3) 
r=.62  } 

r  =  54  \ 

2ix2H 
r  =.48  f 

2X2) 
r  =.41  f 

lixU  } 
r  =.36  J 

HxU? 
r  =  .32  \ 

Ux  n  i 

r  =.30  ( 

1  x    11 
r  =.26  \ 

16,280 
14,680 
13,670 
13,010 
12,600 
11,870 
11,130 
10,400 
10,000 
9,060 

12,110 
11,200 
10,210 
9,310 
8,500 
7,330 
6,310 
5,330 
4,780 
3,540 

9,640 
8,600 
7,390 
6,310 
5,330 
3,970 
2,960 
2,340 
2,070 
1,510 

7,610 
6,420 
5,060 
3,860 
2,960 
2,170 
1,660 
1,200 

5,840 
4,550 
3,190 
2,400 
1,910 
1,290 

4,280 
3,060 
2,210 
1,660 
1,200 

3,040 
2,250 
1,690 

2,330 
1,710 

1,840 
1,250 

1,430 

Special  Shackles 


325 


SHACKLES. 

For  most  purposes  in  ship  details  where  shackles  are  used,  it  is 
ommou  practice  to  order  the  shackles  given  in  Table  of  trade 
hackles,  suiting  the  size  to  the  chain,  wire  or  inanila  rope  that 


L — J i 


SPECIAL  SHACKLES 


Fig.  111. 
they  are  linked  with.    Where,  however,  special  cases  arise  in  deal- 
ing with  exceptional  loads  the  size  of  the  shackle  and  pin  should 
be  accurately  calculated,  taking  care  that  the  widths  between  jaws 
and  across  the  bow  are  no  greater  than  necessary  to  take  the  con- 


326  The  Naval  Constructor 


nections,  as  these  dimensions  are  considered  as  the  beams  support- 
ing the  load  as  in  the  diagram. 

The  dimensions  are  required  of  a  shackle  to  take  a  working 
load  of  10  tons  (22,400  lbs.),  with  a  factor  of  safety  of  6  equal  to 
a  unit  stress  of  10,000  lbs.  It  is  assumed  that  the  pin  is  shipped 
in  a  pad-eye,  bearing  along  its  entire  length,  i.e.,  the  load  is  dis- 
tributed.    We  thus  have  the  case  of  a  beam  supported  at  the  ends 

Wl 
and  uniformly  loaded,  the  maximum  bending  moment  M  being---- 

8 
The  length  I  (3")  will  have  previously  been  determined  by  the 
bearing  value  given  in  designing  the  pad-eye.     Then, 

Wl     22,400X3     0.„.    .  .        __ 

-_-  =  =  8,400  inch-pounds  =  M. 

The  moment  of  resistance  of  a  circular  section  (the  pin)  is  equal 
to  Hs  -D8}  therefore  the  diameter  D  which  will  equal  this  bending 
moment  (M)  just  figured  with  a  fibre  stress  of  10,000  lbs.  must  be, 
7)_  3/~ M"~_43/  8,400 

f  V  Y~f  ~ V  :0982  X  10,000  =  204  inches- 
32  X/ 
The  diameter  of  the  wire  forming  the  bow  at  B  is  calculated  in 
a  similar  way,  noting  that  the  load  this  time  is  central,  but  the 
ends  of  the  beam  being  now  fixed,  we  have  the  same  formula  for 

WU 
the  maximum  bending  moment,  viz.,  — - —    Assuming  that  it  has 

8 
been  necessary  to  bow  the  shackle,  "  l\ "  has  now  been  increased 
to  4  inches,  so  that 

Wh     22,400x4      110AA.     .  .        „ 

-g-  =  — — g =  11,200  inch-pounds  =  M, 

and  applying  the  formula  for  a  circular  section  as  in  the  pin,  we 
have  ?/       11,200 

V.0982X  10,000  =  2*  mCheS  dlameter  at  K 

From  the  diameter  B  the  wire  may  be  tapered  to  A,  where  the 
sectional  area  need  only  be  such  as  will  resist  tension,  but  it  is 
usual  in  practice  to  increase  this  amount  by  25%,  owing  to  the  load 
at  times  becoming  eccentric,  thus  throwing  a  greater  stress  on  one 
leg. 

W     22,400  lbs.      atgA        .         nrnl      m  n 

T  =  io!ooo  lbs. =  2-24 sq- ln-  +  25%  =  28 s^  m- 

=  1.4  sq.  in.  per  leg. 
=  1|  in.  diameter  at  A. 


The  sectional 


Special  Shackles  327 


ie  sectional  area  and  dimension  C  are  computed  by  consider- 
ing h  the  length  of  beam  which  is  now  fixed  at  both  ends  and 

uniformly  loaded  when  M  is  equal  to  ~^~-    The  dimensions  are 

lis 

calculated  as  in  the  foregoing,  observing  that  the  resistance  is  now 

for  a  rectangle,  and  the  bending  moment  will  consequently  equal 

AC2    s 


328  The  Naval  Constructor 

CHAPTER  IV. 

STANDARD   RIVETING,   U.  S.  NAVY. 

1.  All  rivet  holes  through  material  1  inch  or  more  in  thickness 
should  be  drilled,  or  if  punched  should  afterwards  be  reamed  to  fin- 
ished size. 

2.  In  cases  where  rivets  connect  plates  of  different  thickness 
the  size  of  rivet  indicated  for  the  greater  thickness  with  corre- 
sponding spacing  will  be  used  where  strength  is  required,  and 
that  indicated  for  the  lesser  thickness  where  water  tightness  is  a 
special  consideration,  always  provided  the  greater  thickness  is  not 
more  than  double  the  lesser. 

3.  Where  tap-rivets  must  be  used  they  should  be  J  inch  larger 
than  the  corresponding  ordinary  rivets  for  the  same  thickness, 
except  taps  into  heavy  castings  and  forgings  such  as  stem  and 
stern  posts,  which  should  be  £  inch  larger.  Where  strength  is 
required,  taps  should  not  penetrate  less  than  one  diameter,  and 
should  penetrate  1£  diameters  when  the  thickness  of  metal  will 
allow  it. 

4.  Where  the  spacing  given  in  Table  No.  3  cannot  be  followed 
exactly,  as  will  generally  be  the  case,  make  the  spacing  a  trifle 
closer  (as  necessary  with  heavier  plating)  and  a  trifle  further  apart 
(as  necessary  with  lighter  plating),  the  division  between  "  heavier" 
and  "  lighter"  plating  coming  at  7^-pound  plates  for  single  rivet- 
ing ;  at  15-pound  plates  for  double  riveting  and  at  25-pound  plates 
for  treble  riveting. 

5.  Where  the  above  distinctions  are  considered  too  complicated 
for  yard  work,  the  general  rule  will  be  to  space  a  trifle  closer  in 
all  cases,  as  necessary  for  equal  spacing. 

6.  Where  strength  is  required  in  laps  and  butted  connections 
of  plating,  with  the  spacing  indicated,  single  riveting  is  suitable 
only  for  plating  under  12£  pounds,  and  double  riveting  for  plating 
under  25  pounds.  For  maximum  strength  in  connections  of  plat- 
ing above  30  pounds  it  will  generally  be  found  that  quadruple 
riveting  is  required. 

Single  Straps. 

7.  Single  butt  straps  and  edge  strips,  when  single  or  double 
riveted,  should  be  the  same  thickness  as  the  plates  connected,  and 
where  the  plates  connected  are  of  different  thickness,  the  straps  or 
strips  should  be  of  the  same  thickness  as  the  lighter  plate.  Single 
butt  straps  when  treble  riveted  should  be  1^  times  the  thickness  of 
the  plates  they  connect. 


Standard  Riveting,  U.S.  Navy  329 


Double  Butt  Straps. 


8.  Double  butt  straps  should  not  be  used  for  water-tight  work, 
owing  to  the  difficulty  in  caulking.  They  may  be  used  to  advan- 
tage in  conditions  requiring  great  strength  but  not  water-tightness. 
The  thickness  of  each  strap  should  be  \  the  thickness  of  plates 
connected  for  double  riveted  straps,  and  §  the  thickness  for  treble 
riveted  straps.  The  spacing  of  rivets  in  rows  should  be  calculated. 
Size  of  rivets  for  double  butt  straps  as  follows  : 

For  plates  from  15  to  20  pounds,  exclusive,  §  inch  rivets. 
•«        "         "     20  to  25       M        inclusive,  f     "        " 
44        "      above  25  pounds,  see  Table  No.  1. 

Distance  between  Rows. 

9.  Centres  of  rivets  should  be  placed  not  less  than  If  times  the 
diameter  from  the  edges  of  plates  connected.  In  double  and  treble 
riveting  for  laps  and  singl entraps,  the  distance  from  centre  to  centre 
of  rows  should  not  be  less  than  2£  diameters;  in  butt  laps  and 
double  butt  straps  the  distance  between  centres  of  rows  should  be 
not  less  than  3  diameters.  (Butt  laps  should  be  at  least  double 
riveted.)  For  zigzag  riveting  the  distance  between  centres  of  rows 
should  not  be  less  than  If  diameters  for  rivets  spaced  4  diameters 
apart  in  rows. 


330 


The  Naval  Constructor 


TABLE   L  — Diameter  of  Rivets. 


Weight  of  Plates. 

oS 
■I 

H  fa  £ 

M    00   > 

58* 

a* 

-<faa 
5° 

For  Torpedo  Boat  Work 

In. 

In. 

Up  to  3  pounds,  inclusive     . 

i 

JL 

3  pounds  to  6  pounds,  exclusive 

52 

H 

6  pounds  to  1\  pounds,  exclusive 

I 

A 

7  \  pounds  to  9  pounds,  exclusive 

A 

i 

9  pounds  to  1 1  pounds,  exclusive 

i 

A 

11  pounds  to  13  pounds,  exclusive 

f 

H 

For  Ship  Work. 

Up  to  3  pounds,  exclusive    . 

* 
i 

A 

3  pounds  to  6  pounds,  exclusive 

. 

r 

6  pounds,  inclusive,  to  8  pounds, 

exclusive, 

1 

T** 

8  pounds,  inclusive,  to  13  pounds, 

exclusive, 

f 

H 

13  pounds,  inclusive,  to  20  pounds, 

exclusive, 

i 

H 

20  pounds,  inclusive,  to  30  pounds, 

exclusive, 

I 

H 

30  pounds,  inclusive,  to  40  pounds, 

exclusive, 

i 

*A 

40  pounds,  inclusive,  to  51  pounds, 

exclusive, 

n 

*A 

51  pounds  and  above    .... 

U 

Breadth  of  Laps  and  Straps 


331 


TABLE   II.  —  Breadth  of  Laps  and  Straps. 


Item. 


Breadth  of  laps  for  single  riveting 

"  "     "     "    double  chain  riveting      .     .     .     . 

"  "      "    u         "       zigzag  riveting   .     .     .     . 

"        "  double  riveted  butt  laps 

u        "  laps  for  treble  riveting       

14  "  treble  riveted  butt  laps  in  outside  plating 

"  "  edge  strip  for  single  riveting        .     .     .     . 

14  "  edge  strip  for  double  riveting      .     .     »     . 

44  "  butt  strap  for  double  riveting      .     .     .     . 

"         "  butt  strap  for  treble  riveting 

44  "  double  butt  strap,  double  riveted      .     .     . 

44  "  double  butt  strap,  treble  riveted .     .     .     . 


Diam- 
eters. 


31 
5f 
5 

61 

in 

iii 

16J 
12* 
181 


332 


The  Naval  Constructor 


TABLE   III.  —  Spacing  of  Rivets. 


Single  riveted  butt  laps  and  butt  straps 

Double  riveted  butt  laps  and  butt  straps 

Treble  riveted  butt  laps 

Treble  riveted  butt  straps  with  alternate  rivets  in  third 
row  omitted x    .     .     . 

All  longitudinal  seams  of  plating  required  to  be  water- 
tight      

Connections  of  transverse  frames  not  water-tight  to 
outside  plating 

Connections  of  deck  plating  to  beams,  of  non-water- 
tight longitudinals  to  outside  plating,  of  the  angles 
and  stiffeners  to  bulkheads  when  entirely  above 
the  water  line,  and  in  general  where  special 
strength  is  not  required 

Connections  of  floor  plates,  brackets,  lightened  inter- 
costals,  etc.,  to  clips  and  angles,  of  the  vertical 
keel  angles  to  the  flat  and  vertical  keel  plates  and 
to  the  flat  keelson  plates  beyond  the  limits  of 
double  bottom,  provided  water-tightness  is  not 
required 

Connections  of  angles  and  other  stiffeners  to  bulkheads 
at  or  below  the  water  line,  of  boiler  and  engine 
bearings  and  foundations  in  general 

Connections  of  inner  bottom  plating  to  all  frames  and 
longitudinals . 

Connections  of  angles  of  water-tight  frames  and  longi- 
tudinals to  all  plating,  and  in  general  where  water- 
tightness  is  required  between  shapes  and  plates    . 

Angles  and  other  stiffeners  to  bulkheads  forming  sup- 
ports to  turrets,  barbettes,  connections  of  armor 
shelf  angles  to  plating,  etc 

Connections  between  staple  angles  of  water-tight  floors 
and  the  floor  plates 

In  special  cases  of  intercostals,  beam  ends,  etc.,  where 
strength  is  required  in  connections  of  limited 
strength  and  in  all  other  exceptional  cases,  spac- 
ing to  be  as  required  by  circumstances,  except  that 
the  rivets  in  the  same  line  should  never  be  less 
than 


Reduction  of  Diameters  to  Inches      333 


3 

a> 

M 

9 

H 

Qi 

W 

a 

<. 

as 

P 

ft 

*H 

O 

0 

M 

a 

0 

i 

s 

p 

o 

B 

* 


s? 


sff 


3 


3.0 


JSH2'**»1S-»«oPhw2h'*b 


Tj*i0«0  00  05 


xJliOCNMOtN^CDCDO 
i— I  i-h  t— (  i— I  i— I  <N 


^SHS- 


COM'<i(ui©t'0>ON'*>0 


(M  (M  M  M  •*  iC  ®  t- 00  OJ  O 


(NNMMtHOCNOOOO 


MBHW 


HNNNM^iiio^t-eo 


rHi-tfNtNOOCO^OCOr-t- 


r+fHUMHi       HN       Hn       Hn 
r-li-li-<i-l(NC^COCO'*'*>.0 


o-CHci-rm- 


HHHHNINNMM'* 


r-HHHNcqcOMM 


HHHHNNIMW 


rH  r-(  r-l  »-H  i-t  <M 


The  Naval  Constructor 


TABLE  V.  —  Combination  Table  for  Ship  Work. 


H 

fa 

Widths  of 

©  ^ 

W 

J 

Breadth  of  Laps. 

Strips  &  Sin- 

< 

a 

fa 
O 

O 

M 
fa 
o 

gle  Stkai-s. 

a 

if 

Bj 

"8  . 

fa 

0 
N 

fa* 
o 

as 
w 

as 
fa 

H 

MI3 

©J 

So* 

o.2 

33 

1! 

,2  c 

|| 

5? 

p 

O 

W 

S 

fa 

5 

£5 

a" 

1* 

0>£ 

*1 

-I 

Pounds 

■     00 

per 

•^o*-S 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

Tn. 

In. 

In. 

Sq.  Foot, 

Up  to  3  Ex. 

Up  to  2 

1 

9 

32 

H 

iA 

n 

2tV 

1A 

2A 

11 

21 

4J 

3-6     « 

2-5 

i 

ft 

iA 

2J 

M 

*A 

2A 

»A 

2A 

*A 

«A 

6-8     " 

5-7 

i 

9 

if 

2i 

2J 

41 

3J 

4| 

31 

of 

81 

8-13  " 

7-11 

1 

u 

2A 

3f 

3* 

&A 

3}| 

oil 

*A 

7A 

ioa 

13-20  " 

11-15 

i 

it 

2A 

*A 

3| 

«A 

4i 

«tt 

41 

8f 

12  | 

20-30  " 

15-24 

i 

11 

5 

4| 

7A 

n 

8A 

5| 

ioa 

14A 

30-40  " 

24-32 

i 

1A 

5| 

5 

H 

6i 

9i 

6i 

Hi 

16  J 

40-51  " 

32-41 

il 

1A 

•j 

7 

10  | 

7A 

12H 

ISA 

61  & over 

41  &» 

over  1 

H 

1 1 1 

10A 

H! 

11    9 

lxT* 

B| 

14  | 

20  f 

Lloyd's  Countersinks 


335 


FORM  OF  RIVET  TO  BE  U8E3  IN  OUTSIDE 


5     S 


THE  TAPERED  NECK  OF  RIVET  TO  BE  OF  8UITABLE 
LENGTH  IN  RELATION  TO  THE  THICKNESS  OF  PLATE 
IN  WHICH  IT   18  INTENDED  TO  Bf  USED. 

Fig.  117. 


336 


The  Naval  Constructor 


LLOYD'S   RIVETING 
Showing  Diamett  n  and  Spacing  of  J  U  rets  and 


Thickness  of  plates 

Diameter  of  rivets 

Breadth  of  treble  riveted  straps  in  inches  .  .  , 
"  "  double  riveted  straps  in  inches  .  .  . 
"  "  quadruple  riveted  butt  laps  in  inches 
"  "  treble  riveted  butt  laps  in  inches  .  , 
•»  "  double  riveted  butt  laps  in  inches  .  , 
"  "  treble  riveted  edge  laps  in  inches  .  , 
M  *«  double  riveted  edge  laps  in  inches  . 
44        "  single  riveted  edge  laps  in  inches    . 

In  f  butts   of  outside  pitting,  and  of  upper,  spar  and  middle  deck 

irs  of  D  " 


'3*  dia. 
c.  to  c. 

4  dia. 
c.  toe. 

4£dia. 
c.  to  c. 

5  dia. 
c.  to  c. 

7  dia. 
c.  to  c. 


ngt-n 

gtb.  of  the  vessel  amidships    (except  quadruple  riveted  butt  laps), 
buttsof  deck  plating,  margin  plat 


In  quadruple  riveted  butt  laps 
girders,    lower     deck    and  bold  stringers,  tie  plai 
stringer  plates  >n  other  deck  erections ;  also  butts  and  edge 


floor   plates,  and 


margin  plate  angles,  edges  and  butts  of  bulkhead  plating. 

In  flat  keel  angles,  bulkhead  frames  where  caulked,  butts  and  edges 
of  mast  plates,  and  deck  plating  to  beams  where  single  flange  beams 
are  fitted  to  alternate  frames. 

In  *  frames,  reversed  frames,  floors,  keelsons,  beam  angles,  deck  and 
hold  stringer  angles,  face  angles  on  web  frames  and  side  stringers, 
bulkhead  stiffen  ens,  longitudinal  angles  on  continuous  girders,  verti- 
cal angles  connecting  floors  and  girders  and  deck  plating  to  beams 
except  where  single  flange  beams  are  fitted  to  alternate  frames, 


II 


4-1 


t  In  butts  connected  by  single  butt  straps  alternate  rivets  may  be  omitted 
in  the  back  row  of  treble  riveting  when  the  plating  number  is  20,000  and  un- 
der ;  when  above  this  number,  the  rivets  in  the  back  row  are  not  to  be 
more  than  5  to  5J  diameters  apart  from  centre  to  centre.  All  overlapped 
butts  are  to  have  complete  rows  of  rivets. 

*  When  the  rule  frame  spacing  is  26  inches  or  above,  the  rivets  in  the 
edges  of  outside  plating  (forward  and  aft)  are  not  to  exceed  4  diameters 
apart  from  centre  to  centre,  and  the  rivets  attaching  the  outside  plating 
to  frames  are  to  be  spaced  not  more  than  6  diameters  apart  from  centre 
to  centre. 

In  deep  water  ballast  tanks  above  the  level  of  inner  bottom,  and  in  fore 
and  after  peak  water  ballast  tanks,  the  rivets  through  frames  and  outside 
plating  are  to  be  spaced  not  more  than  6  diameters  apart  from  centre  to 
centre. 

Before  the  three-fifths  length  of  a  steamer  having  a  tonnage  coefficient  of 
.78,  or  having  a  full  form  at  the  fore  part,  the  rivets  in  the  landing  edges  of 
the  strakes  of  plating  forming  the  flat  of  the  bottom  to  be  spaced  not  more 
than  4  diameters  apart  from  centre  to  centre.  The  rivets  in  the  plating  and 
frames  in  way  of  the  same  to  be  spaced  not  more  than  5J  diameters  apart 
from  centre  to  centre. 

Rivets  to  be  \  of  an  inch  larger  in  diameter  in  the  stem,  stern  frame,  and 
keel,  but  in  no  case  need  these  exceed  11"  in  diameter,  and  to  be  spaced  5 
diameters  apart  from  centre  to  centre.  In  single  screw  steamers  above  350 
feet  in  length,  the  after  lengths  of  shell  plating  are  to  be  connected  to  the 
portion  of  the  stern  frame  below  the  boss  with  3  rows  of  rivets. 

Rivets  in  side  plate  rudders  to  be  of  not  less  size  than  those  required  for 
the  upper  edge  of  garboard  strake  amidships,  and  to  be  spaced  not  more  than 


Lloyd's  Riveting  Table 


337 


TABLE,  1903. 

Breadths  of  Straps,  Butt  Laps,  and  Edge  Laps. 


// 

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5  diameters  from  centre  to  centre.  The  rudder  plates  are  to  be  countersunk 
and  the  rivets  are  to  have  full  heads  and  points. 

Rivets  in  single  plate  rudders  are  to  be  of  not  less  size  than  required  for 
attaching  the  outside  plating  to  the  stern  frame,  and  spaced  not  more  than 
5  diameters  apart  from  centre  to  centre.  The  rivet  holes  are  to  he  counter- 
sunk both  in  rudder  plates  and  the  arms,  and  the  rivets  are  to  have  full 
heads  and  points. 

Rivets  in  the  edges  of  deck  plating  are  to  be  spaced  not  more  than  4  to  4J 
diameters  apart  from  centre  to  centre. 

In  single  riveted  seams  one  frame  rivet  is  to  bo  fitted  through  the  landing 
edges  at  each  frame.  In  double  riveted  seams  one  frame  rivet  is  to  be  fitted 
through  the  landing  edges  at  each  frame,,  except  where  the  frames  or  tbe 
edges  of  the  outside  plating  are  joggled  when  two  rivets  are  to  be  fitted.  In 
treble  riveted  seams  two  frame  rivets  (the  upper  and  lower)  are  to  be  fitted 
through  the  landing  edges  at  each  frame. 

Where  the  fore  and  aft  flange  of  the  frame  does  not  exceed  3  inches,  the 
rivets  attaching  the  outside  plating  thereto  should  not  exceed  g  inch  in 
diameter,  and  where  it  is  3£  inches  wide,  they  should  not  exceed  1  inch  in 
diameter. 

There  are  to  be  at  least  four  rivets  in  each  flange  of  the  angle  bars  be- 
tween the  frames  which  connect  the  stringer  plates  and  intercostal  plates 
to  the  outside  plating.  Where  the  frames  are  spaced  less  than  29  inches 
apart,  and  where  the  spacing  is  29  inches  and  not  more  than  32  inches  there 
are  to  be  five  rivets  in  each  flange. 

The  rivets  in  the  beam  knees  are  to  be  in  number  and  size  as  required. 

The  rivets  in  the  vertical  angles  connecting  floors  and  outside  brackets  to 
margin  plates  are  to  be  in  number  and  size  as  required. 

The  rivets  in  the  connecting  g traps  for  web  frames  and  side  stringers  are 
to  be  in  number  and  size  as  required. 


:;:;s 


The   Naval  Constructor 


STANDARD   RIVETS. 

(See  Table  Opposite.) 


OOUNTeRBINK  OR    PLUG  HEADS 


BUTTON  MEAD 


CLASS  A  ,       CLASS  B  ,  CLASS  A  CLASS  B  CLASS  A  CLA88  B 


fy^ff^, 


Figs.  11&-129. 


Standard  Rivets 


339 


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The  Naval  Constructor 


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Riveting  Table 


341 


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Strength  of  Riveting  in   Ships  343 


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Ordered  Lengths  of  Rivets 


345 


346 


The   Naval   Constructor 


STRENGTH   OP 
Table  IV.— 


Rivet  in 

J 

2 

r. 

Frames  and 
Outside 

One  Tier  of  Beams. 

Two  Tiers  of  Beams. 

w 

H 

Plating. 

00 

an  w 

"J  . 

Moo 

2 

0  w 

°  * 

00 

s 

<41    V 

u 

0 

s 

CO1-1 

3 
fft 

OH 

72 

1-1  S 

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u  a 

®  a 

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o  s 
|  g 

"13 

02  t* 

s 

Fran 

Rever 
e-      Fram 

»e   g-g 

i.     ©  c 

as 

8,5? 

Frame. 

Reverse 
Frame. 

Ii 

.sa 

I50 

03 

(X). 

(0. 

(<*). 

(<*,). 

Inch< 

js.      Inche 

02 
3. 

Inches. 

Inches. 

100 

A 

20 

1 

.687 

4.50 

2ix2i> 

<&     None 

2H-2i- 

<&     Alter 

.93 





150 

A 

21 

J 

.812 

5.25 

3  X3  > 

1.50 

natelj 

r. 

200 

A 

22 

u 

« 

" 

4JX3  > 

<&4  X3  X 

&3.06 

3£x3  X& 

3  X2*X& 

4.30 

250 

*8 

23 

i 

.937 

6.25 

5  X3  > 

<>&5  X3  X 

&2.83 

4ix3  X& 

3  X3  Xja 

4.10 

300 

H 

24 

" 

" 

«« 

6  X3i> 

<&  5jx3ix 

A  3.30 

5ix3jx& 

4  X3JXA 

4.60 

350 

*3 

24 

li 

" 

ii 

6  X3JXA 

6  X3JXA 

4.80 

400 

L3 

25 

" 

" 

" 

Qhxtyxhi 

GhXtyXhi 

4.80 

450 

ht 

26 

1 

1.062 

7.00 

7hX3hXhi 

7  X3jxig 

4.00 

500 

hi 

27 

" 

" 

6.50 

,  .  .  . 



550 

hi 

28 

(( 

" 

ii 



600 

hi 

29 

" 

M 

6.00 

650 

hi 

30 

11 

1.187 

6.75 



700 

hi 

31 

" 

" 

" 

Strength  of  Riveting  in  Ships  347 


RIVETING  IN   SHIPS. 
Frame  Riveting. 


Three  Tiers  of 
Beams. 

Four  Tiers  of 
Beams. 

Five  Tiers  of 
Beams. 

Frame. 

Reverse 
Frame. 

u 

a    . 

00    A 

C    in 
oo    3 

|w 
a? 

Frame. 

Reverse 
Frame. 

u 

a 

§0 

00  a1 
OS 

Frame. 

8® 

h 

0) 

!l 

a  s 

oo     O* 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

' 

*y$  X  *>2  X  20 

6  X32x2g 

7  X3£xjg 

4  X32X& 

ax^xig 

4£X4  X2g 

6.90 
6.70 

5.55 

8X3JX32X2S 
8X3SX32X2E 
8X4  X4  X48 

None. 

4X4XM 
Alter- 
nately. 

5.90 
5.55 
6.62 

•' 

9x4x4x28 
9X4X4X2§ 

None 

6.15 
6.00 

348 


The  Naval   Constructor 


SHEARING   AND    BEARING 
All  Dimensions 


Diameter  t>F 
Rivet  (In.). 

Area 

in  Sq. 

In. 

Single 
Shear  at 

«,0UULhs. 

Bearing  Value  for 

i 

A 

1 

A 

Fnu'tioii. 

Decimal. 

f 
1 
1 

I 
i 

1 

.375 
.500 
.625 
.750 
.875 
1.000 

.1104 
.1963 
.3068 
.4418 
.6013 
.7854 

660 
1,180 
1,840 
2,650 
3,610 
4,710 

1,130 
1,500 
1,880 

1,410 

1,690 

2,630 

1,880 
2,340 
2,810 

2,250 
2,810 
3,380 
3,940 

3,280 
3,940 
4,590 
5,250 

2,250 
2,630 
3,000 

3,280 
3,750 

4,500 

Diameter  of 
Rivet  (In.). 

Area 

in  Sq. 

In. 

Single 
Shear  at 
7,500  Lbs. 

Bearing  Value  for 

i 

A 

f 

A 

Fraction. 

Decimal. 

I 
1 

f 

! 

1 
i 

.375 
.500 
.625 
.750 
.875 
1.000 

.1104 
.1963 
.3068 
.4418 
.6013 
.7854 

830 
1,470 
2,300 
3,310 
4,510 
5,890 

1,410 
1,880 
2,340 

1,760 

2,110 

3,280 

2,340 
2,930 
3,520 

2,810 
3,520 
4,220 
4,920 

4,100 
4,920 
5,740 
6,560 

2,810 
3,280 
3,750 

4,100 
4,690 

5,620 

Diameter  of 
Rivet  (In.). 

Area 

in  Sq. 

In. 

Single 
Shear  at 
10,000  Lbs. 

Bearing  Value  for 

* 

A 

i 

A 

Fraction 

Decimal, 

i 
i 

f 
i 

I 
i 

.375 
.500 
.625 
.750 
.875 
1.000 

.1104 
.1963 
.3068 
.4418 
.6013 
.7854 

1,100 
1,960 
3,070 
4,420 
6,010 
7.850 

1,880 
2,500 
3,130 

2,340 

2,810 

4,380 

3,130 
3,910 
4,690 

3,750 
4,690 
5,630 
6,570 

5,470 
6,560 
7,660 
8,750 

3,750 
4,380 
5,000 

5,470 
6,250 

7,500 

Diameter  of 
Rivet  (In.). 

Area 

in  Sq. 

In. 

Single 
Shear  at 
12,000  Lbs. 

Bearing  Value  for 

J 

A 

1 

A 

Fraction. 

Decimal. 

i 

1 
I 

! 

i 

l 

.375 
.500 
.625 
.750 
.875 
1.000 

.1104 
.1963 
.3068 
.4418 
.6013 
.7854 

1,320 
2,360 
3,680 
5,300 

7,220 
9,430 

2,350 
3,130 
3,910 

2,930 

3,520 

5,470 

3,910 
4,880 
5,860 

4,690 
5,860 
7,030 
8,210 

6,840 

8,210 

9,580 

10,940 

4,690 
5,470 
6,250 

6,840 
7,820 

9,380 

In  above  tables  all  bearing  values  above  or  to  right  of  upper  zigzag  lines 
ar©  greater  than  double  shear.    Values  between  upper  and  lower  zigzag 


Shearing  and  Bearing  Value  of  Rivets     349 


VALUE   OF   RIVETS. 

in  Inches. 


Different  Thicknesses  of  Plate  in  In.  at  12,000  Lbs.  per  Sq.  In. 

} 

A 

t 

ii 

I 

1  g 

1 

H 

1 

3,000 
3,750 

4,220 

4,690 
5,630 

6,190 

6,750 
7,880 

8,530 
9,750 

9,190 
10,500 

9,840 
11,250 

12,000 

4,500 
5,250 
6,000 

5,160 
5,910 
6,750 

6,560 
7,500 

7,220 
8,250 

9,000 

Different  Thicknesses  of  Plate  in  In.  at  15,000  Lbs.  per  Sq.  In. 

i 

9 

f 

tt 

i 

if 

1 

H 

1 

3,750 
4,690 

5,280 

5,860 
7,030 

7,720 
9,030 

8,440 
9,850 

5,630 
6,560 
7,500 

6,330 
7,380 
8,440 

10,670 
12,190 

11,480 
13,130 

12,300 
14,060 

15,000 

8,200 
9,380 

10,310 

11,250 

Different  Thicknesses  of  Plate  in  In.  at  20,000  Lbs.  per  Sq.  In. 

\ 

rs" 

i 

tt 

I 

]  s 

1 

if 

1 

5,000 
6,250 

7,030 

7,810 
9,380 

10,310 
12,030 

11,250 
13,130 

7,500 

8,750 

10,000 

8,440 

9,840 

11,250 

14,220 
16,250 

15,310 
17,500 

16,410 

18,750 

20,000 

10,940 
12,500 

13,750 

15,000 

Different  Thicknesses  of  Plate  in  In.  at  25,000  Lbs.  per  Sq.  In. 

1 

A 

1 

H 

i 

1  3 

I 

if 

1 

6,250 
7,810 

8,790 

9,770 
11,720 

12,890 
15,040 

14,060 
16,410 

9,380 
10,940 
12,500 

10,550 
12,310 
14,060 

17,770 
20,320 

19,140 
21,880 

20,510 
23,440 

25,000 

13,670 
15,630 

17.190 

1.8,750 

lines  are  less  than  double  and  greater  than  single  shear.    Values  below  and 
to  left  of  lower  zigzag  lines  are  less  than  single  shear. 


Section  III. 

DETAILS,   STRUCTURAL. 


KEELS. 

In  steel  ships  the  keel  is  invariably  one  of  the  three  forms  of  bar, 
flat  plate  or  side  bar,  the  first  and  third  being  almost  entirely  su- 
perseded by  the  flat  plate  type 
which  is  on  all  points  a  much 
better  method  of  construction 
than  the  others,  besides  having 
the  great  advantage  of  saving 
from  6  to  12  inches  of  draft,  there- 
by increasing  the  dead  weight 
carrying  capacity  from  about  15  FlG 

to  1,500  tons  respectively   on  a 

given  immersion.     Bar  keels  should  have  no  place  in  modern  ship 
construction,  unless  when  required  for  rubbing  purposes  only. 


Bar  Keels. 

These  should  be  made  of  rolled  steel  universal  bar  in  preference 
to  the  old-fashioned  scrap  iron  forgings  and  scarphed  together  in 
long  lengths  by  right  and  left-handed  scarphs.  The  scarphs  are 
mostly  made  nine  times  the  thickness  of  the  bar  in  length,  and  the 
jog,  or  check,  and  point  should  be  one  fourth  the  thickness. 
Scarphs  of  keel  should  be  close  fitting  and  for  that  reason  must  be 
machined,  the  connection  holes  for  rivets  are  drilled,  and  in  addi- 
tion a  few  holes,  about  one  third  the  number  of  regular  ones,  should 


-\ 


a 


o  j»  o 


■J 


o      o      oj     I 

O         O    •!  o 


T 


TACK  RIVETS 

FlO.  133. 

be  drilled  of  smaller  diameter,  but  countersunk  on  both  sides,  for 
tacking  the  various  lengths  together  before  erecting  and  riveting 
the  garboard  strakes.  Care  should  be  taken  that  these  scarphs  are 
shifted  well  clear  of  the  garboard  strake  and  centre  keelson  butts 
and  that  the  joints  of  scarphs  are  caulked  watertight. 

351 


352 


The   Naval  Constructor 


The  diameter  of  the  rivets  should  be  in  accordance  with  the  re- 
quirements of  the  riveting  tables  given  on  p.  200,  and  staggered 
as  shown.  The  vertical  spacing  requires  special  care  in  keeping 
clear  of  the  radius  of  garboard  plate  and  also  the  caulking  edge  of 
same  at  bottom,  which  is  raised  about  half  an  inch  from  lower  edge 
of  bar.  For  this  reason  it  is  advisable  to  set  off  the  bar  full 
size,  drawing  in  the  flanges  of  garboards  before  fixing  on  centres 
of  rivet  holes. 

Flat  Plate  Keels. 

Keels  of  this  type  are  made  of  a  thick  plate  forming  the  bottom 
member  of  a  girder  of  which  the  centre  keelson  is  the  web.  The 
forms  mostly  in  use  are  shown  by  the  Figs.  134  and  135.     Fig.  136 


Fig.  134 

shows  a  very  efficient  and  economical  form  of  flat  plate  keel  and 
centre  keelson  devised  by  the  author  and  designed  with  a  struc- 
tural /section  for  small  and  moderate  sized  vessels  with  ordinary 
floor  construction.  Where  a  suitable  I  section  is  not  obtainable 
the  same  construction  may  be  retained  with  advantage  with  built- 
up  section. 

The  flat  plate  keel  should  always  be  arranged  as  an  inside  strake, 
as  by  so  doing  the  keel  and  its  sister  member  may  be  laid  on  the 


Fig.  135. 

keel  blocks  right  away  without  anticipating  linering  in  addition  to 
making  a  more  solid  job  and  saving  a  small  amount  of  draught. 
It  is  a  fallacy  to  place  it  outside  with  the  intention  of  disturbing 


Stems 


353 


only  one  plate  in  the  event  of  damage  —  a  remote  contingency 
which  should  not  be  allowed  to  interfere  with  good  construction. 

Where  a  doubling  is  required  by  the  classification  societies'  rules 
it  will  be  found  advantageous,  where  practicable,  to  increase  the 
plate  keel  to  a  sectional 
area  equivalent  to  that  of 
the  keel  and  doubling,  and 
if  double  buttstrap  be  re- 
quired, the  inside  one  may 
be  fitted  in  two  pieces. 

Scantlings  and  riveting 
will  be  as  specified  or  to 
rule  requirements. 

At  the  forward  and  after 
ends  the  keel  plate  must 
efficiently  incorporate  with 
the  stem  and  stern  frame 
Respectively,  a  short 
^breeches"  plate  being 
usually    worked    for    this  FlG  136 

purpose.      In  small    con- 
struction a  "spoon"  plate  is  welded  to  the  bottom  of  stem  bar 
in  lieu  of   the  short  plate  referred  to,  and  a  similar  plate   of 
"  gutter  "  form  welded  to  stern  frame. 


STEMS. 

The  remarks  on  bar  keels  apply  equally  as  regards  details  to 
atems.      The  classification  societies'  rules  allow  a  reduction  in 


MID.  ]SL    BREADTH  OF   FLAT  OF  KEEL 
/  STEM  OF   UNIVERSAL   BAB 


Fig.  137. 


354  The  Naval   Constructor 

sectional  area  at  stem  heads,  but  as  the  practice  is  now  to  make  the 
stem  from  universal  rolled  bar,  it  will  prove  no  economy  to  taper 
it.  The  usual  method  of  connecting  lower  part  of  stem  to  keel 
plate  are  shown  by  Fig.  137.  In  straight  stems  the  profile  line 
should  be  cambered  about  §"  to  \"  from  where  it  joins  the  fore- 
foot curve  to  stem  head,  to  guard  against  the  illusion  of  the  contour 
line  appearing  hollow. 

STERN   FRAME. 

These  frames  are  mostly  forged  or  cast  in  steel  in  one  piece  for 
small  and  moderate  sized  steamers,  and  in  two  or  more  parts  for 
the  larger  vessels.  As  in  the  case  of  stems,  bar  keels,  etc.,  the 
scantlings  are  determined  from  the  corresponding  numeral  of  the 
societies'  rules  to  which  the  ship  is  being  constructed.  The  two 
posts  comprising  the  stern  frame,  viz.,  rudder  and  body  posts  with 
the  joining  arch,  are  of  similar  scantlings,  but  the  keel  piece  con- 
necting the  posts  at  bottom  while  of  the  same  sectional  area  as  tlffl| 
posts,  is  flattened  out  to  allow  of  the  keel  line  being  curvecT 
upwards  to  the  clump  for  keel  pintle  bearing  of  rudder  for  pro- 
tection to  the  latter  in  the  event  of  grounding. 

Gudgeons  are  forged  on  the  rudder  post  of  frame  from  4  to  b\ 
feet  apart  to  take  the  pintles  ;  one,  or  two  in  large  vessels,  being 
so  shaped  as  to  engage  the  rudder  stop  at  hard-over.  This  post  is 
connected  to  the  main  structure  on  a  deep  transom  plate  clipped 
to  its  fore  side,  and  in  vessels  of  over  about  300  feet  in  length  the 
forward  or  body  post  must  also  be  carried  up  and  secured  in  a 
similar  manner.  The  body  post  is  swelled  around  the  stern  tube, 
having  a  sectional  area  through  the  eye  equal  to  the  frame  and 
meeting  the  post  above  and  below  in  a  fair  curve  ;  the  spur  or  keel 
part  of  frame  must  not  be  too  long  to  facilitate  handling,  the 
general  rule  being  about  2\  frame  spaces  before  the  body  post, 
where  it  incorporates  with,  or  scarphs  into,  the  keel  as  already 
described. 

In  steamers  over  350  feet  length  where  these  frames  are  of 
considerable  weight,  the  riveting  connecting  body  post  to  hood  ends 
of  shell  plating  should  be  treble  below  boss  and  of  increased 
diameter  and  an  addition  made  to  the  plating  thickness.  As  in 
the  keels,  these  holes  must  be  carefully  drilled  and  where  scarphs 
are  introduced  as  in  the  case  of  frames  of  two  or  more  pieces  the 
riveted  connection  should  be  developed  to  equal  the  bar.  It  is 
common  to  make  the  contour  of  body  post  curvilinear,  thus  effect- 
ing an  appreciable  saving  in  weight  over  the  straight  line,  besides 
giving  a  more  graceful  form. 

In  small  steamers  the  after  or  rudder  post  may  be  dispensed 
with,  a  spur  being  carried  aft  from  body  post  to  support  heel  pintle. 


Rudders 


355 


For  single  screw  steamers  classed  to  Lloyds  the  weight  of  stern 
frame  may  be  very  closely  approximated  by  taking  the  first 
numeral  to  upper  deck  and  multiplying  it  by  240  for  vessels  over 
300  feet  in  length,  or  by  155  for  those  under  this  dimension,  as  first 
number  x  240  =  weight  in  pounds. 


RUDDERS. 

Some  of  the  more  common  forms  of  rudders  are  shown  in  Figs. 
138  to  143.  The  stresses  to  which  they  are  subjected  and  the 
method  of  determining  the  diameter  of 
stock  has  already  been  fully  described. 
The  single  plate  rudder,  Fig.  138,  is  the 
type  most  commonly  adopted  in  merchant 
steamers,  and  is  usually  built  in  three  parts, 
viz.  :  the  frame,  norman  head  and  plate. 
The  frame  may  be  either  cast  or  forged,  bolted  i 
having  arms  or  stays  projecting  from  the 
stock  on  alternate  sides  of  centre  line  spaced 
opposite  each  of  the  gudgeons,  which  are 
from  4'  to  5'  6"  apart. 

The  norman  head  or  stock  should  be 
forged  in  iron  or  steel  with  a  coupling  palm 
at  lower  end  to  connect  with  a  similar 
palm  on  head  of  frame.  Allowance  should 
be  made  on  this  forging  for  machining  a 
key  to  lock  the  norman  head  to  the  frame, 
and  in  addition  turned  coupling  bolts  are 
fitted  with  nuts  on  under  side,  threads 
turned  off  to  a  thimble  point  and  split  pins 
fitted.  These  bolts  are  from  one  to  three 
inches  in  diameter  in  practice.  Their  size, 
however,  is  not  important,  as  the  shearing 
stresses  are  all  taken  on  the  key.  The 
stock  need  only  be  turned  in  wake  of  the 
rudder  quadrant  where  it  is  sometimes 
increased  in  diameter  to  compensate  for 
cutting  the  key  way. 

The  single  plate  forming  the  rudder  blade  is  fitted  between,  and 
riveted  to,  the  supporting  arms,  besides  engaging  a  groove  cut 
down  the  back  of  rudder  stock.  Its  thickness  ranges  from  about 
|"  in  small  steamers  to  1J  inches  in  liners. 

Braces  are  formed  at  the  ends  of  supporting  arms  which  are 
turned  out  to  take  fitted  pintles.  One  (two  in  large  rudders)  of 
these  braces  must  be  shaped  to  act  as  a  stopper  when  the  rud- 
der is  put  hard-over.     The  pintles  should  preferably  be  fitted 


Fig.  138. 


356 


The   Naval  Constructor 


separately  and  of  the  cone  type  shown  in  the  detail.  It  is  bad 
practice  to  forge  pintles  on  the  frame,  as  besides  the  difficulty  of 
turning  them  in  a  lathe  they  have  the  disadvantage  of  not  being 
readily  renewable.  The  best  manner  of  bushing  the  pintles  is  a 
matter  of  opinion,  the  simplest  and  probably  the  one  most  favored 
being  to  make  the  bushes  of  hard  steel  with  a  flange  to  take  the 
tap  screws  securing  them  around  the  eye  of  the  braces.  The 
weight  of  the  rudder  in  small  vessels  is  taken  on  a  hard  steel  disc 
placed  in  the  heel  step  bearing  with  a  hole  through  the  heel  step 


BOLTED  COUPLING 


RIVETED  JOINT 


RIVETED  JOINT 


Fig.  139. 


Fig. 140. 


for  backing  it  out.  In  large  steamers,  however,  where  the  weight 
of  rudder  is  many  tons,  the  weight  should  always  be  taken  by  a 
carrier  seated  inside  the  counter.  Various  types  of  these  are 
shown  by  engravings  144  to  146.  Provision  must  be  made  on  the 
back  of  rudder  well  clear  of  water  line  to  fit  a  Jew's  harp  shackle 
for  securing  the  emergency  chains,  which  are  from  thence  carried 
up  the  counter,  being  stopped  with  ratline  stuff  to  tapped  eyes 
spaced  about  thirty  inches  apart. 

Next  in  favor  to  the  single  plate  is  the  cast  steel  rudder,  Fig.  139, 
although  where  only  one  is  being  made  its  cost  is  against  it.  For 
the  largest  sizes  its  difficulty  of  successful  manufacture  is  also  to 


Rudders 


357 


its  disadvantage,  although  this  is  got  over  by  casting  it  in  two  or 
more  pieces,  see  Fig.  140,  keying  these  together  and  riveting  them 
through  coupling  flanges.  When  rudders  are  designed  to  be  cast 
in  one  piece,  the  ribs  which  are  cast  on  the  blade  to  act  as  stays 
should  be  of  easy  section,  so  as  not  to  interfere  more  than  neces- 
sary with  the  contraction  of  the  casting  in  cooling. 

The  oldest  method  of  making  the  rudder  for  steel  ships  is  the 
built  type,  Fig.  142,  which  consists  of  a  forged  frame  having  stock, 
stays,  and  back  piece  in  one,  with  two  side  plates  riveted  to  same 


Fig. 141. 


Pig.  142. 


Fig.  143. 


after  having  the  inside  filled  in  with  fir  coated  with  tar.  Its  great 
objection  is  the  cost  of  forging,  especially  for  large  rudders.  It  has 
gone  completely  out  of  favor  unless  for  yachts,  where  its  appear- 
ance commands  its  use,  and  in  light  craft  of  the  torpedo  boat  kind 
where  sufficient  stiffness  would  not  be  obtainable  in  a  single  plate 
without  going  into  a  thickness  which  would  make  the  weight  pro- 
hibitive. It  is  also  often  used  with  the  frame  cast  in  gun  metal 
and  the  side  plates  of  16  gauge  brass  sheet,  for  wood  speed 
launches,  vedettes,  pinnaces,  etc.,  although  for  these  craft  a  cheaper 
and  lighter  rudder  may  be  obtained  by  casting  it  complete  in  gun 
metal  or  bronze. 


358 


The  Naval  Constructor 

RUDDERICARRIER 


Fig.  144, 


Rudders 


359 


RUDDER 

CARRIER. 


Fig.  145. 


360 


The  Naval  Constructor 


WOOD  FITTED  AFTER  RUDDER 
18  HUNG  4   THICKNESS  MADE  ACCORCINGLV 


Fig.  146. 


Rudders 


361 


ELEVATION  OF 
COUPLING 


FlG.  147. 


362  The  Naval  Constructor 


Where  the  rudder  stock  enters  the  vessel,  watertightness  must 
be  ensured  by  fitting  a  trunk  having  a  stuffing  box  and  gland  at 
its  top.  This  latter,  however,  may  be  dispensed  with  where  a 
carrier  is  arranged  for,  this  being  an  additional  element  in  favor 
of  the  adoption  of  these  supports.  Before  fixing  on  the  counter 
dimension  of  the  rudder  trunk,  care  should  be  taken  that  ample 
clearness  is  given  to  ship  and  unship  the  rudder.  It  will  be  seen, 
therefore,  that  the  hole  through  the  counter  is  much  in  excess  of 
the  diameter  of  stock,  and  if  not  filled  in  would  be  unsightly,  be- 
sides allowing  a  considerable  volume  of  water  continually  at  play 
inside.  It  is  covered  in  with  a  tail  plate  fitted  in  halves  and  secured 
with  hexagon  head  taps  to  the  counter  plating,  so  as  to  be  easily 
removable  to  permit  of  unshipping  the  rudder. 

Good  proportions  for  such  details  as  pintles,  gudgeons,  braces, 
couplings,  etc. ,  to  meet  most  requirements  are  shown  in  Fig.  147. 

PROPELLER   STRUTS. 

These  brackets  for  supporting  the  outer  end  of  tail  shaft  are  gen- 
erally of  pear-shaped  section  as  being  the  form  of  least  resistance. 
It  is  usual  to  cast  them  in  steel,  although  they  are  also  sometimes 
built  up. 

In  selecting  a  suitable  area  of  arm  shipbuilders  are  guided  mostly 
by  experience,  hence  the  divergent  results  seen  in  practice.  The 
author  has  therefore  devised  the  formula  given  on  p.  109,  in  which 
he  has  attempted  to  secure  a  uniform  relationship  between  the  size 
of  these  struts  and  the  power  transmitted  through  them. 

Where  possible  the  centre  of  the  propeller  bracket  should  be 
placed  on  a  frame  to  obtain  the  maximum  of  stiffness,  and  the 
palms  of  upper  and  lower  arms  may  be  cast  on  or  connected  with 
angle  clips.  A  web  spur  is  sometimes  cast  or  worked  on  keel 
length  of  stern  post  to  take  the  palm  of  lower  arm  instead  of  flang- 
ing the  latter  and  riveting  it  through  the  keel  to  it,  securing  inde- 
pendent connection  for  each  strut. 

In  wake  of  the  upper  palm  additional  stiffening  must  be  worked 
by  fitting  a  short  local  doubling  on  shell  and  a  stringer  inside.  The 
number  and  diameter  of  palm  fastenings  should  be  developed  ac>- 
cording  to  the  sectional  area  of  the  arm,  these  being  in  most  cases 
overdone. 

The  sectional  area  of  arms  must  not  be  tapered  towards  the 
boss,  as,  although  theoretically  considered  as  a  cantilever,  this  would 
be  rational,  it  must  not  be  lost  sight  of  that  the  greatest  stresses 
are  borne  by  the  ends  of  the  arms  adjoining  the  boss,  and  are,  be- 
sides, alternating  ones  inducing  fatigue. 

The  engineer  will  determine  the  length  of  boss  barrel  suitable 
for  bearing  and  also  the  finished  diameter  of  the  hole,  but  ample 


Casting  at  Stern  Tube 


363 


allowance  should  be  made  for  boring  out  to  this  dimension  and 
also  adjusting  to  centre  line  of  shaft ;  this  is  most  important  when 
dealing  with  cast  steel,  as  it  provides  the  opportunity  to  detect 
hidden  blow  holes.  A  mass  of  metal  should  be  avoided  where  the 
arm  swells  to  meet  the  boss  either  by  reducing  the  fillet  to  a  mini- 
mum or  coring  out  the  metal  inside  the  boss,  as  otherwise  internal 
stresses  will  be  set  up  in  cooling  or  dangerous  blow  holes  developed. 
In  high  speed  vessels  it  is  important  to  make  the  pattern 
"wind"  conforming  to  the  run  of  the  water  line,  thus  obviating 
the  arms  being  dragged  across  the  stream  lines  and  creating  eddies. 
It  is  surprising  the  amount  of  power  absorbed  by  this  resistance 
when  brackets  are  badly  set  or  not  set  at  all. 

SPECTACLE   FRAMES. 

Spectacle  frames  have  nearly  superseded  the  open  A  brackets 
for  large  merchant  vessels.  They  are  enveloped  in  the  hull  of  the 
ship,  the  plating  being  webbed  out  and  bossed  around  the  shaft  for 
this  purpose,  as  fully  explained  in  the  chapter  on  Design,  which  see. 

Where  the  plating  ends  on  the  arms  of  these  frames  a  good 
riveted  connection  must  be  made,  usually  double  and  increased  to 
treble  tap  rivets  around  the  boss.  Local  strengthening  must  also 
be  fitted  in  wake  of  spectacle  frames  by  increasing  the  deep  floors 
in  thickness  and  doubling  the  ship's  frames  in  their  vicinity. 


CASTING  AT   STERN   TUBE. 

The  outboard  end  of  stern  tube  in  vessels  fitted  with  A  brackets  is 
supported  by  and  connected  to  a  steel  casting  or  forging.  Its  func- 
tion is  similar  to  the  boss  on  body  post  of  a  single  screw  steamer. 

STEEL  CASTING 
COMPOSN.  BUSHING 


RABBET  FOR  FAIRWATER^y 


HORIZONTAL  SECTION. 
Fig.  148. 


364  The  Naval  Constructor 

In  large  steamers  it  is  usual  to  extend  this  casting  over  two 
frames  in  length  to  give  additional  support,  as  shown  in  Fig.  148, 
but  in  small  vessels  the  tube  end  support  need  only  be  from  2  to 
4  inches  thick,  and  shaped  like  Fig.  149.  Usually  a  watertight 
bulkhead  is  fitted  at  the  forward  and  after  ends  of  the  stern-tube, 
the  former  one  being  bossed  and  spectacled  at  the  wings  in  the 
manner  depicted  in  the  detail  given. 

The  inboard  palm  of  the  tube  end  forging  is  securely  riveted  to 


DEEP  FLOOR,  OR  BULKHEAD 


Fig.  149. 

wing  plate  of  bulkhead,  which  must  be  increased  in  thickness  for 
the  heavier  riveting  necessarily  employed  for  this  purpose. 

FRAMING. 

In  ships  having  ordinary  floors  the  frames  are  invariably  run  in 
one  piece  from  centre  line  to  gunwale,  and  where  channel  bars  or 
bulb  angles  are  employed  with  this  construction,  the  floor  plates 
may  be  reduced  in  consideration  of  the  excess  strength  given  in 
their  wake.  Vessels  having  a  double  bottom  on  the  cellular 
system  need  only  have  angle  frames  on  the  deep  floors  with  flanges 
sufficient  to  take  the  size  of  riveting  required.  Forward  in  the 
flat  of  bottom  in  full  vessels  these  should  be  doubled  inside  tank 
and  in  addition  local  fore  and  aft  stiffening  fitted  to  reenforce 
against  "pounding."  Where  vessels  are  classed,  as  they  mostly 
are,  the  scantlings  of  the  frames  are  obtained  from  the  rules  of  the 
classification  bureau.  The  angle  bars  of  which  they  are  made  is 
always  one  with  unequal  legs,  the  larger  flange  standing  vertically 
to  the  shell  plating  to  obtain  the  greatest  section  modulus  in  the 
direction  of  the  pressure. 


Framing 


365 


Where  frames  are  cut  at  margin  plates 
of  inner  bottoms  or  at  water  tight  fiats, 
efficient  bracket  plates  of  such  dimen- 
sions as  will  permit  of  riveting  to  develop 
the  strength  of  frame  bars  should  be  fitted. 
See  Fig.  153  and  159.  In  wake  of  flats 
where  bracket  knees  are  objected  to  on 
account  of  the  broken  stowage  created,  or 
their  interference  with  cabin  arrange- 
ments, the  framing  may  be  continuous 
and  smithed  angle  collars  or  pressed  plate 
chocks  fitted  around  them  to  ensure  water 
tightness  as  in  Fig.  150.  For  simplicity 
in  forming  collars,  frame  and  reverse  bar 
or  channel  section,  the  reverse  bar,  or 
flange,  may  be  cut  off  and  the  frame  bar 
doubled  for  a  short  distance  above  and 
below  the  flat  as  compensation  as  in  Fig. 
151. 

Where  main  frames  are  stopped  at 
weather  deck  when  the  bridge  house  or 
superstructure  requires  a  bar  of  smaller 
section,  the  connection  between  weather 
deck  stringer  and  frame  may  be  com- 
pleted with  a  spirketting  plate  in  lieu  of 
;  the  ordinary 
bracket     knee 


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where  the 


Fig. 150. 


Fig.  151. 


latter 

would  encroach  on  the  berth- 
ing space,  as  shown  at  Figs. 
152  and  153. 

The  inboard  member  of  a 
ship's  framing,  called  the  re- 
verse  bar,   whose    functions 
are  to  provide  a  flange  where- 
on to  fasten  the  ceiling,  or 
I  lining,  and  to  give  the  neces- 
!  sary  section  modulus  by  ad- 
'  ding  area  at  a  point  subjected 
to  corrosion  and  rough  treat- 
ment, is  commonly  made  of 
angle  section  or  by  the  em- 
ployment of  channel  bar  for 
the   framing.      In  steamers, 
however,  under  about  100  feet 
it  will  be  found  economical 


300 


The  Naval  Constructor 


besides  being  good  construction  to  omit  the  reverse  bar  altogether 
and  increase  the  sided  flange  of  frame  angle  to  give  an  equivalent 


Fig. 152. 


Fig.  153. 


REVERSE   FRAME 


Fig.  154. 


I.      A  saving  in   material,  riveting  and  bending  will    thus  be 

effected.  In  light  vessels  where  weight  must  be  cut  down  with- 
out encroaching  on  the  strength,  the  maximum 
section  modulus  may  be  obtained  for  a  given  depth 
of  web  by  employing  two  bars  of  such  dimension 
of  leg  as  will  just  give  the  requisite  size  of  lap  to 
take  the  proper  riveting,  as  in  Fig.  164. 

The  practice  in  vogue  for  many  years  of  plac- 
ing the  frame  and  reverse  bars  back  to  back  has 
given  place  to  that  of  fitting  them  bosom  to 
bosom  where  deep  framing  is  adopted,  as  by  this 

method  the  beam  knees  can  be  fitted  without  linering  in  wake  of 

reverse  frames. 

FLOORS. 

The  deep  plates  riveted  to  the  bottom  framing  of  ships  and  known 
as  the  floors,  are  placed  there  to  resist  the  transverse  stresses  to 
which  the  bottom  plating  is  subjected,  due  to  the  great  water  pres- 
sure externally  applied,  and  the  inside  forces  created  by  the 
weight  of  the  structure  and  cargo. 

Ordinarily  in  ships  without  an  inner  bottom  these  are  of  a  size 
based  upon  the  breadth  and  depth  of  the  vessel  and  carried  in  a 
fair  line  up  the  bilge  to  a  height  equal  to  twice  the  centre  line  di- 
mension as  in  Fig.  155.  It  will  be  seen  that  this  contour  at  the 
bilge  necessitates  furnacing  the  tail  ends  to  bend  them  to  the  re- 
quired curve,  a  costly  and  therefore  an  objectionable  feature.  For 
this  reason  ordinary  floors  should  be  increased  in  their  sided  areas 
and  carried  straight  across,  striking  the  bilge  at  a  point  somewhat 
lower  down  than  with  the  curved  floor.  This  method  permits  of 
the  floor  being  flanged  across  top  in  lieu  of  fitting  a  reverse  bar, 


Floors  367 

although  some  of  the  classification  bureau  penalize  flanging  plates 
to  the  extent  of  adding  one-twentieth  to  their  thickness ;  this  need 
not,  however,  be  made  unless  where  specifically  required  and  for 
that  reason  cheaper,  lighter,  and  equally  efficient  construction 
will  be  obtained. 

In  small  freight  steamers  and  barges  a  strong  and  inexpensive 
floor  is  obtained  by  using  structural  channel  section  thus  elimi- 
nating the  riveting  to  frame  and  reverse  bar  altogether. 

Floors  in  inner  bottoms  are  almost  entirely  fitted  as  deep  solid 
plates  in  one  piece  from  centre  vertical  keel  to  margin  plate,  light- 
ened with  large  manholes  to  cut  out  superfluous  material  and  pro- 
vide access  to  the  various  compartments  into  which  the  bottom  is 
sub-divided  by  the  floors  and  intercostal  girders.  Deep  floors 
should  be  lapped  to  the  bottom  frames  just  sufficient  to  take  the 
riveting.     In  wake  of  watertight  bulkheads  or  at  ends  of  ballast 


Fig.  155.  Fig.  156. 

tanks  where  the  floors  are  watertight,  no  holes  whatever  must  be 
cut  in  them.  The  margin  plate  of  inner  bottom  being  continuous, 
is  connected  to  the  main  frame  by  a  large  bracket  plate  or  tail 
piece,  and  by  double  angles  having  a  specified  number  of  rivets 
and  a  gusset  plate  at  top,  or  in  the  largest  vessels  a  continuous 
stringer.  The  connection  to  the  siding  flange  of  main  frame 
is  by  lap  of  sufficient  width  to  take  the  riveting.  See  Figs.  157 
and  158. 

At  the  ends  of  the  vessel  where  the  waterline  at  top  of  floor 
would  necessarily  be  comparatively  narrow,  increased  depth  must 
be  given  to  provide  compensatory  area  and  also  ensure  sufficient 
width  to  clip  the  centre  keelson  to  floors.  In  the  fore  peak  this 
additional  depth  is  required  to  resist  buckling  and  panting,  and  gen- 
erally to  give  local  stiffening  at  a  part  subjected  to  unusual 
stresses.  It  is  also  necessary  to  increase  the  floors  considerably  in 
depth  in  after-peak,  owing  to  the  severe  stresses  encountered  when 
the  propeller  "  races  "  and  the  stern  is  in  air. 


3G8  The  Naval  Constructor 


INNER  BOTTOM. 

Double  bottoms  are  fitted  in  vessels  to  enable  them  to  safely 
make  voyages  "in  ballast"  without  incurring  heavy  expenses  by 
loading  and  discharging  dry  ballast.  For  this  purpose  the  floors 
are  plated  over,  forming  an  inner  bottom  enclosing  with  the  ship's 
plating  a  pontoon  in  which  to  carry  sea  water  as  ballast,  an  expe- 
ditious, inexpensive  and  clean  method  of  doing  so.  Two  or  three 
methods  of  fitting  water  bottoms  are  met  with  in  practice,  but  as 
these  have  given  way  to  the  cellular  system,  it  is  unnecessary  to 
describe  them.  This  method  consists  in  the  subdivision  of  the 
space  formed  by  the  pontoon  referred  to,  into  a  great  number  of 
small  compartments  or  cells  bounded  by  the  floors  in  a  fore  and 
aft  direction  and  transversely  by  intercostal  girder  plates,  making 
these  cells  approximately  two  feet  by  four  feet,  respectively,  by 

the  depth  of  water  bot- 
tom. The  water  pas- 
ses freely  between  these 
cells  as  the  floors  and 
intercostals  are  pierced 
with  access  holes  unless 
where  mentioned  here- 
after. The  cells  are 
arranged  in  separate 
groups  or  compartments 
enclosed  by  the  centre 
vertical  girder,  water- 
tight floors  and  the 
margin  plate,  this  larger 
Fig.  157.  subdivision  being  neces- 

sary for  trimming  and  filling  purposes,  as  otherwise  a  large 
surface  of  free  water  would  be  highly  dangerous  in  certain 
conditions. 

As  mentioned,  the  centre  vertical  plate  is  continuous  fore  and 
aft,  fitted  usually  watertight  and  connected  top  and  bottom  to  in- 
ner plating  and  plate  keel  with  suitable  angle  bars.  No  holes  what- 
ever should  therefore  be  cut  through  vertical  keel  plate,  and  al- 
though it  is  not  necessary  to  caulk  it  in  way  of  ballast  tanks,  the 
riveting  should  be  of  watertight  pitch.  Of  course  where  fresh 
water  is  carried  this  longitudinal  girder  must  be  properly  caulked. 
At  the  ends  of  the  vessel  where  fore  and  aft  subdivision  is  unnec- 
essary the  centre  plate  may  have  access  manholes  as  in  the 
floors. 

The  butt  connections  are  preferably  formed  with  double  butt 
straps,  each  of  about  two-thirds  the  thickness  of  plate.     Through 


Inner  Bottom 


369 


Fig.  158. 


butts  should  not  be  used  here,  as  besides  interfering  with  the 
passage  of  the  fore  and  aft  angles  they  only  give  single  shear 
value  to  the  riveted  con- 
nection. 

The  outboard  side  of  the 
inner  bottom,  or  margin 
plate,  is  fitted  to  shell  by 
means  of  a  continuous  an- 
gle bar,  the  main  frames  of 
the  ship  being  cut  for  that 
purpose.  At  the  top  this 
plate  is  flanged  in  board  to 
take  the  inner  bottom  plat- 
ing as  shown  in  Fig.  157.  The  butts  of  margin  plate  are  covered 
with  single  strap  fitted  on  the  inside  of  tank. 

This  plate  may  also  be  fitted  with  advantage  as  shown  in  Fig. 
158  devised  by  the  author,  which  consists  in  flanging  the  plate  out- 
board,   a  shape  that  the  plate  will  take  more  naturally  where 

there  is  curvature  in  a  fore 
and  aft  direction.  This  out- 
board flange  will  also  permit 
of  machine  riveting  and  con- 
necting to  the  reverse  flange  or 
bar  on  the  floor  bracket,  thus 
forming  a  continuous  stringer  ; 
or,  angle  section  may  be  sub- 
stituted for  the  flange  where 
facilities  for  bending  are  not 
obtainable. 

Another  method  of  fitting 
the  margin  is  illustrated  by 
Fig.  159,  where  the  top  plat- 
ing is  carried  right  out  to  the 
shell  and  flanged  upwards  to 
take  staggered  riveting.  Flan- 
ging is  preferable  to  fitting  an  angle  bar,  as  in  the  latter  case 
difficulty  would  be  experienced  in  putting  in  the  rivets  on  the 
horizontal  flange  of  the  bar.  It  is,  however,  a  cheap  method  of 
construction,  its  principal  objection  being  the  broken  stowage 
caused  by  the  brackets  connecting  frame  to  inner  bottom. 

The  inner  bottom  plating  will  be  of  such  thickness  as  the 
classification  societies  stipulate  where  the  vessel  is  classed,  when 
it  will  be  found  that  increased  scantling  is  required  under  engines 
and  boilers,  and  of  course  the  centre  strake  and  margin  plate  will 
also  be  thicker  than  the  rest  of  the  plating,  owing  to  the  former 
being  the  rider  plate  member  of  the  girder  formed  by  the  centre 


Fig.  159. 


370 


The  Naval   Constructor 


vertical  keel  and  keel  plate,  and  the  latter  being  an  important 
factor  in  the  longitudinal  strength  of  the  ship.  For  this  reasom 
when  arranging  the  access  manholes,  these  must  always  be  kept 
clear  of  the  centre  strake.  A  good  shift  of  butts  must  be 
arranged  for  the  plating,  and  these  shifted  clear  of  the  butts  of 
shell,  margin  plate  and  longitudinals. 

Where  the  strakes  of  inner  bottom  plating  are  arranged  u  in  and 
out,"  the  packing  liners  to  outside  strakes  should  be  fitted  short, 
the  unfilled  spaces  acting  as  air  holes. 

The  practice  of  fitting  wood  ceiling  on  tank  tops  is  giving  way 
to  coating  the  plating,  with  tar  or  bitumastic  cement,  as  this  pre- 
vents the  deterioration  that  goes  on  under  the  wood,  besides  adding 
to  the  stowage  capacity .     Where,  however,  wood  ceiling  is  required, 

it  must  be  laid  on  fore  and 
aft  bearers  and  screwed  to 
same  and  not  fastened  through 
tank  top.  For  this  reason, 
i.e.,  guarding  against  leakage 
the  heels  of  the  hold  pillars 
are  riveted  to  vertical  flange 
of  tee  or  angle  lugs  which 
are  first  riveted  through  in- 
ner bottom. 

In  arranging  the  manholes 
care  should  be  exercised  that 
they  are  located  in  accessible 
parts  of  holds  and  clear  of 
cargo  hatches.  In  holds  of 
ordinary  length  one  each 
side  at  each  end  about  quar- 
ter the  beam  outboard  will 
be  sufficient,  and  in  long  holds 
an  additional  one  about  the 
middle  of  the  length.  In  no 
case  as  previously  pointed 
out  should  they  go  through 
the  centre  strake.  The  best 
location  aft  will  of  course  be 
in  tunnel  alleyways,  and  in 
machinery  spaces  they  should 
be  fixed  by  the  engineers. 
This  arrangement  will  contribute  to  the  best  circulation  of  air 
when  the  covers  are  taken  off  for  ventilating  purposes.  Ample 
room  must  be  allowed  for  rim  of  manhole  to  clear  landings, 
butts,  longitudinal  clips,  etc. 

The  shell  plating  forming  the  bottom  of  tanks  may  be  reduced 


Fig.  160. 


Beams  371 

in  thickness  in  consideration  of  the  extra  strength  added  by  this 
construction,  and  the  broad  liners  fitted  to  outside  strakes  in  wake 
of  watertight  bulkheads  may  be  replaced  by  narrow  liners  at 
watertight  floors  in  tanks. 

To  drain  the  various  compartments  of  the  double  bottom  when 
the  ship  is  in  dry  dock,  screw  plugs  of  composition  are  fitted  in 
the  garboard  strake  and  a  compensating  plate  riveted  around  the 
hole.  A  detail  of  such  a  fitting  is  shown  by  Fig.  160.  It  is  usual 
to  fit  similar  plugs  in  the  trimming  tanks  at  fore  and  after  peaks. 


BEAMS. 

Beams  are  fitted  at  various  levels,  or  decks,  to  tie  the  ship  to- 
gether and  afford  supports  whereon  to  lay  the  decks  to  take  car- 
goes. The  strength  of  these  will  depend  therefore  on  the  load  as 
well  as  the  span  or  breadth  of  beam,  as  it  will  be  seen  that  a 
weather  deck  beam  need  not  be  as  strong  as  the  one  under  it,  and 
so  on  —  each  successive  tier  taking  the  accumulated  load  super- 
imposed. 

It  is  common  practice  to  give  all  decks  a  round-up  or  camber, 
an  expensive  practice  that  is  unnecessary  unless  on  the  weather 
deck,  and  only  necessary  there  in  a  modified  sense  to  obtain  the 
statutory  freeboard  or  to  conform  to  classification  requirements. 
It  is  a  fallacy  to  imagine  that  strength  is  gained  by  cambering  the 
beams  thus  supposedly  constructing  an  arch,  as  you  cannot  have 
a  compressed  beam  without  abutments,  which  the  sides  of  the  ship 
are  not.  To  meet  the  requirements  mentioned  above,  the  weather 
deck  should  have  the  standard  camber  of  one-quarter  inch  to  the 
foot  of  length,  thus  a 
beam  40  feet  long  will 
have  a  round-up  at  cen- 
tre line  of  ten  inches. 
This  curve  may  be  set 
off  very  quickly  with 
the  aid  of  a  common 
slide  rule  by  setting  the 
courser  to  the  required  Fig.  161. 


£l 


round-up  on  the  first  or 
top  scale  and  to  the  half  beam  on  the  third  scale,  when  the 
camber  at  any  desired  distance  in  board  of  ship's  side  may  be 
found  by  moving  the  courser  to  the  dimension  required  and  read- 
ing off  on  top  scale.  The  reading  subtracted  from  the  total 
camber  will  give  the  required  round-up.  This  may  also  be  figured 
as  shown  in  Fig.  161.     The  beams  are  connected  to  the  main 


372 


The  Naval   Constructor 


Figs.  162-167. 


Beams 


373 


THICKNESS    OF    BRACKETS    DEPENDS    ON 
WEIGHT    OF   BEAM   PER   FOOT. 

(See  Figs.  162-1G4.) 


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374 


The  Naval  Constructor 


TO    FIT    CARNEGIE'S    1897     PATTERNS. 


HJ-H-jf   4n- 


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Beams  375 


frames  by  welded  knees  or  bracket-plates,  the  latter  being  much 
the  cheaper  and,  where  appearance  is  not  important,  the  better 
method.  The  depth  of  these  knees  is  commonly  2£  times  the 
depth  of  beam  if  of  channel  or  bulb  tee  section,  and  three  times 
the  depth  if  angle  bar  be  used.  The  thickness  should  be  the  same 
as  the  beam  unless  where  welded  knees  are  fitted,  when  it  is  good 
practice  to  increase  the  plate  one-sixteenth  to  allow  for  loss  in 
smithing.  When  dealing  with  beams  conforming  to  Lloyd's  Rules, 
it  should  be  noted  that  the  bracket  knees  are  regulated  in  depth 
and  thickness  by  the  size  of  the  bulb  plate  required  by  the  table, 
irrespective  of  the  dimensions  of  the  substituted  equivalent  sec- 
tion of  channel,  bulb  angle,  or  bulb  tee.  For  example,  if  the  rules 
require  a  built  beam  of  bulb  plate  and  angles,  the  former  being 
10 1"  x  W't  and  it  was  decided  to  fit  the  equivalent  channel  bar 
of  11"  X  81"  x  y",  then  the  bracket  knee  would  be  26^"  x  \tf'\ 

Standard  beain  knees  as  used  in  Navy  practice  are  shown  by 
Figs.  162  to  167.  In  arranging  the  riveting  in  plate  knees,  the  re- 
quired number  is  usually  specified  for  classed  vessels,  and  as  these 
are  invariably  staggered,  it  is  well  to  locate  the  first  rivet  hole  as 
far  outboard  on  the  beam,  and  down  on  the  frame,  as  practicable. 
Those  in  the  corner  may  be  treated  as  common  to  both  arms  in 
counting  the  number  required. 

Where  unsheathed  steel  decks  less  than  ^V'  thick  are  fitted,  beams 
must  be  fitted  on  every  frame,  with  stronger  beams  at  ends  of  cargo 
hatchways.  Where  the  thickness  is  ^  or  over,  the  beams  may  be 
fitted  on  alternate  frames  with  half  beams  on  every  frame  abreast 
of  hatches.  When  this  spacing  is  adopted,  most  societies  require 
closer  spacing  of  rivets  through  deck  plating,  viz.,  5  diameters 
apart  as  against  7  to  8  diameters  with  the  closer  spaced  beams,  so 
that  it  is  doubtful  economy  at  a  sacrifice  of  efficiency  to  space 
them  on  alternate  frames. 

In  the  machinery  spaces  of  steamers  it  is  necessary  to  fit  beams 
of  extra  strength  wherever  these  can  be  worked  without  interfer- 
ing with  the  arrangement  of  engines  and  boilers.  These  through 
beams  compensate  for  the  loss  in  transverse  strength  through  the 
severance  of  the  regular  deck  beams  at  the  large  machinery  open- 
ings, and  serve  to  tie  the  ship  together  and  prevent  panting  of  the 
sides  at  a  part  where  a  considerable  weight  is  permanently 
carried.  In  large  steamers  the  machinery  arrangement  often 
permits  of  tw6  adjoining  through  beams  being  tied  together  by 
cover  plates,  thus  forming  an  exceptionally  strong  beam  of  box  sec- 
tion. Where  strong  beams  cannot  be  fitted  in  one  piece,  owing  to 
interference  with  the  shipping  of  parts,  they  should  be  efficiently 
bracketed  to  the  casing  coamings,  care  being  taken  that  the  con- 
nection develops  the  strength  of  beam.  When  practicable  the  pil- 
lars in  machinery  spaces  should  be  fitted  on  these  through  beams. 


376 


The  Naval  Constructor 


ANGLE  BEAM  COLLAR 


The  term  half  beam  is  applied  to  those  deck  beams  which  are 
severed  in  wake  of  hatch  openings.  Their  inboard  ends  abut  on 
the  hatch  side  coaming  plates,  which  are  in  consequence  made 
thicker  than  the  end  ones,  and  the  connection  is  commonly  by  a 
single  angle  clip  (taking  a  specified  number  of  rivets)  if  a  continu- 
ous fore  aud  aft  angle  is  fitted  at  bottom  of  plate  to  support  the 
beam  ends,  or  the  coaming  plate  is  flanged  under  the  beams  for  a 
like  purpose.  It  will  be  thus  seen  that  this  rest  will  take  a  great 
deal  of  the  shear  off  the  rivet  connection,  besides  adding  to  the 
strength  of  the  girder  formed  by  the  coaming. 
In  wake  of  small  deck  openings  the  inboard  beam  end  may  be 

supported  by  a  carling,  or  fore 
and  after,  of  similar  section  to 
the  beam,  except  where  bulb 
tee  is  used  with  the  heel  of  the 
carling  abutting  on  beam  end 
and  connected  to  same  with, 
preferably,  double  clips  so  as 
to  get  double  shear  value  from 
the  rivets. 

Where  heavy  local  weights 
or  deck  machinery  are  secured, 
the  beams  in  wake  of  same 
should  be  increased  in  sec- 
tion, aud  special  pillaring  or 
deck  girders  fitted.     It  is  like- 


Ji ±__ 


Fig.  171. 


wise  necessary  to  increase  the  strength  of  the  beams  at  the  ends 
of  hatchways  by  adding  to  their  sectional  area  —  but  not  to  their 
depth  if  avoidable. 

The  beams  supporting  bridge  or  shade  decks  fitted  over  houses 
and  extending  to  ship's  side  are  frequently  carried  thwartship  in 
one  bar,  the  casings  being  scored  out  and  watertight  collars  fitted, 
in  preference  to  cutting  the  beams  and  fitting  bracket  plates. 
These  collars  are  shown  by  Fig.  171,  and  may  be  smithed,  stamped, 
or  cast  in  steel  or  malleable  cast  iron. 


Hold  Pillars 


HOLD    PILLARS. 


377 


Support  is  given  the  beams  on  the  various  decks  by  stanchions. 
Various  sections  are  employed  for  this  purpose,  as  round  bar,  pipe, 
I  section  and  columns  built  of  channel  or  plate  and  angle  bar. 
For  vessels  carrying  general  cargoes,  the  pipe  section,  being  circu- 
lar and  light,  is  probably  the  best.     The  I  section  makes  a  very 


H_x  sJ/|6x«7/iexi^ao 


a    HAND    HOlI 


8'/aX3>j   X^0SlNOLE 


Fig.  172. 


cheap  and  efficient  column,  as  forged  ends  are  done  away  with  ; 
and  in  vessels  requiring  large,  clear,  stowage  spaces  in  holds,  built 
columns  should  be  fitted  connected  to  strong  deck  girders.  A 
very  efficient  type  of  built  column  is  shown  by  Fig.  172,  passed  by 
Lloyd's  Register  for  a  span  of  80  feet. 


378 


The  Naval  Constructor 


DETAILS    OF   HEADS    AND    HEELS   FOR  PB?E 
STANCHIONS. 


SOLID  HEADS  AND  HEELS  FOR  PIPE  STANCHION8 


t-T\**         "?191'/2LB8. 


(.-v-HX---^ 


H-7"  «j 


JL,J_ 


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31s 


F& 


S3   (3 


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(*_9t^_»i 


5^-t iw 


K-12- 


11-- -j 


le- W 


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-*-.68VJ  Lesr 


flap 


u 


r  -  -109>4— «j  —eiy 


S3  [0 


yqr     1 

I   [j      49LB8-  Or 


r— iov£-h 


ILOtGS  REQUIRE   IHESi   TO  B£  FOD&EB   AND   WEEDED    INTO   P.IPE 
WITH    A  SUITABLE   HAMMER  TKEY   MAY   BC  OlE'ORBED 
FuA  SHIPS  NOT  CLASSED  AT  LLOYDS   A  STEEL  CASTING. 
WILL  BC  MORE  ECONOMICAL  AND  CO.UAILT  fjff ItltNT.. 


5?      n 


NOTE:    FOR  STANDARD   PIPE  ELEMENTS.     SET  TABLE* 


Figs.  173  to  186. 


Hatches  379 

Where  pipe  pillars  are  adopted,  the  accompanying  diagram 
giving  types  of  solid  heads  and  feet  will  be  found  useful. 

It  will  be  obvious  that  the  hold  pillars  must  be  stronger  than 
those  in  the  lower  'tween  decks,  the  sizes  being  gradually  reduced 
as  we  approach  the  upper  works,  owing  to  the  reduction  in  the 
load  which  the  successive  tiers  of  pillars  support. 

As  pillars  are  intended  to  take  compressive  stresses  their  relative 
strength  with  a  given  section  is  entirely  in  the  end  connections, 
and  as  the  strongest  of  these  is  a  fixed  closely  fitted  flat  end,  this 
form  should  be  adopted  wherever  possible.  Where,  however,  it 
cannot  be  fitted,  as  on  tank  tops  and  with  beams  of  section  other 
than  channel  where  no  ridge  bars  are  worked,  care  should  be 
taken  to  fit  closely  the  heads  and  heels  on  their  supports,  so  that 
the  load  shall  be  taken  on  the  column  and  not  as  a  shearing  stress 
on  their  fastenings,  which  should  be  relieved  wherever  possible  of 
doing  work. 

In  larger  vessels,  ridge  bars  of  channel  section  are  fitted  under 
the  beams  to  distribute  the  load  taken  by  the  pillars  over  all  the 
beams  and  also  to  prevent  the  beams  from  tripping.  In  wake  of 
hatchways  where  pillars  are  omitted  or  are  fewer  in  number,  inter- 
costal plates  are  fitted  between  the  beams  and  riveted  to  deck  as 
compensation,  thus  forming  a  deck  girder. 

When  hold  pillars  are  stepped  on  inner  bottom  plating,  a  short 
piece  of  tee  bar  must  first  be  riveted  to  tank  top  and  caulked,  and 
the  heel  of  pillar  afterwards  riveted  to  the  vertical  stem  of  tee  bar. 
A  similar  arrangement  is  adopted  on  expansion  trunk  tops  of  oil 
steamers  for  heels  of  gangway  stanchions. 

Where  grain  or  other  cargoes  liable  to  shift  are  carried  occasion- 
ally, the  hold  pillars  may  be  staggered,  the  heads  taking  alternate 
flanges  of  the  centre  line  ridge  bar,  thus  providing  an  intervening 
space  in  which  to  fit  the  shifting  boards. 

BATCHES. 

It  will  be  seen  that  a  serious  loss  in  transverse  strength  is  sus- 
tained by  cutting  the  beams  and  decks  to  form  hatchways,  and  it 
has  been  explained  under  the  caption  beams  how  this  loss  is  com- 
pensated for  in  the  deck  framing  and  by  increasing  the  sectional 
area  of  the  side  coaming  plates. 

Hatchways  should  be  no  larger  than  the  demands  of  the  par- 
ticular trade  call  for,  and  the  corners  of  these  openings,  at  least 
on  the  strength  deck,  should  be  round.  While  it  is  cheaper  to 
make  them  square,  it  will  be  found  false  economy.  In  addition  to 
making  them  round  on  the  strength  deck  the  corners  must  be  re- 
enforced  with  doubling  plates  extending  about  2  frame  spaces  each 
way  and  carried  18  inches  or  so  around  the  corners.    The  coam- 


380 


The  Naval   Constructor 


ing  angle  bar  must  be  welded  ;  or  a  much  better  method  is  to  run 
this  bar  to  within  nearly  four  feet  of  the  corners  around  which 

another  section  Is  fitted  having 
a  much  broader  flange  on  deck ; 
this  will  permit  of  staggering 
the  rivets  and  so  allow  more 
space  for  sufficient  riveting  at 
the  junction  of  this  bar  with 
the  deck  beam.  No  bosom  piece 
need  be  fitted  to  cover  the  butt 
of  the  corner  piece  with  the 
straight  length  of  coaming  an- 
gle, Fig.  187. 

End  coaming  plates  should 
have  "pitch"  in  preference  to 
camber,  as  they  are  more  easily 
made  and  allow  of  better  fitting 
the  wood  hatch  covers.  The 
height  of  coamings  on  weather  deck  must  be  from  2  feet  to  2  feet 
6  inches,  and  on  other  decks  from  9  to  12  inches,  care  being 
taken  that  sufficient  height  is  given  to  permit  of  the  hatch  batten- 


I      ^  STANDARD 

It j-2y"a---*|     HATCH  CLEAT 


DRILL  FOR  %  DlA. 
CSK.  RIVET 


Fig.  188. 

ing  cleats  being  fitted.  At  butts  of  coaming  plates  the  covering 
strap  should  be  fitted  on  the  outside  and  the  rivets  countersunk 
on  both  sides. 

A  typical  battening  cleat  is  shown  by  Fig.  188.  These  may  be 
either  die  forged  or  cast  in  steel  and  spaced  not  greater  than  2 
feet  apart  along  the  coaming  plate,  beginning  about  nine  or  ten 


Web   Frames 


381 


inches  from  the  corners  and  sufficiently  far  down  to  give  an  easy- 
fit  for  tarpaulin.  The  battening  bar  is  of  galvanized  flat  iron 
about  2£  x  §",  and  the  butts  of  same  must  not  be  at  corners,  the 
bar  being  bent  round  these  to  allow  of  fitting  the  canvas  snugly. 
The  tarpaulin  is  then  secured  by  elm  or  oak  wedges. 

The  ledges  on  top  of  coamings  are  mostly  made  of  a  special 
rolled  section  as  shown,  although  where  this  is  not  obtainable  a 
zee  bar  will  answer  equally  well.  These  ledges 
should  be  mitred  at  the  corners  and  of  sufficient 
depth  to  house  the  hatch  covers.  In  addition  to 
the  support  afforded  these  by  the  ledge  bar,  fore 
and  afters  must  be  fitted,  as  well  as  bridle  beams, 
to  tie  the  hatchway,  in  number  and  scantling  as 
required  by  the  classification  societies.  The  fore 
and  afters  are  supported  by  rests  riveted  inside 
the  end  coamings  and  the  hatch  beams  by  socket 
slides  on  the  sides.  The  only  other  mountings  re- 
quired on  cargo  hatches  are  a  couple  of  lashing 
rings  on  each  side  fitted  about  four  feet  from  the 
ends ;  these  may  be  riveted  on  coaming  plate  or 
deck  at  discretion. 

The  wood  covers  should  not  exceed  24  inches  in  width,  as  other- 
wise they  are  too  heavy,  and  are  usually  made  of  three  pine  deals, 
tie  bolted  with  three  g"  diam.  blind  bolts.  On  the- right  hand 
sides  of  top  a  lifting  bar  of  iron  through-fastened  with  two  clench 
bolts  is  fitted,  one  at  each  end,  and  the  wood  drilled  out  about  5 
inches  in  diameter  to  form  a  receptacle  for  the  hand.  These 
covers  must  have  properly  cut-in  marks  to  facilitate  replacing 
them. 

WEB  FRAMES. 

Web,  or,  as  they  are  sometimes  called,  belt,  frames  are  commonly 
formed  by  fitting  a  plate  from  15"  to  30"  deep  to  the  ordinary 
ship's  frame,  and  riveting  an  angle  bar  on  the  inner  edge  to  stif- 
fen and  add  to  the  resistance  of  the  web.  They  may  be  also  built 
with  double  channel  frames  with  a  covering  plate  on  face  —  an  ad- 
vantageous method  where  increased  room  or  stowage  capacity  is 
desired.  Still  another  method  is  to  fit  frames  and  reverse  bars  of 
similar  section  of  angles,  webbing  them  as  far  apart  as  possible 
consistent  with  the  requirements  of  the  riveted  overlap.  These 
various  methods  of  constructing  web  frames  have  all  the  same  ob- 
ject in  view,  viz.  :  to  give  the  equivalent  compensatory  transverse 
strength  lost  by  omitting  hold  beams  where  large  spaces  are  re- 
quired for  the  stowage  of  certain  freights  or  in  machinery  spaces 
where  hold  beams  cannot  be  fitted.  It  will  be  seen  that  these 
beams  really  perforin  the  function  of  struts  tending  to  resist  the 


382  The  Naval  Constructor 


water  pressures  oif  the  ship's  sides  and  the  hold  cargo  ;  and  for  this 
reason,  as  well  as  those  already  given,  should  have  no  camber 
which  it  is  conceivable  tends  to  weaken  them.  If  the  hold  beams 
then  be  left  out,  the  necessary  resistance  may  be  given  by  increas- 
ing the  section  modulus  of  the  side  framing,  and  this  is  obtained 
by  adding  webbed  frames  at  stated  intervals  along  the  sides,  and 
by  the  more  uniform  subdivision  in  a  vertical  direction  of  the 
areas  enclosed,  by  side  stringers  fitted  intercostally  between  webs 
having  a  covering  plate  at  their  intersection,  of  diamond  or  half- 
diamond  shape.  The  side  stringers  should  stand  squarely  to  the 
ship's  frame,  thereby  insuring  the  maximum  moment  of  resistance 
from  the  material  used,  as  well  as  avoiding  much  bevelling  of  angle 
bars. 

In  addition  to  the  foregoing,  web  frames  are  fitted  wherever 
local  losses  in  transverse  strength  take  place,  as  at  the  sides  of 
cargo  doors  and  similar  openings  and  over  abrupt  terminations  of 
transverse  strength,  such  as  take  place  where  a  watertight  bulk- 
head stops  short  of  the  strength  deck.  They  are  also  necessary 
where  exceptional  local  stresses  of  the  nature  indicated  are  applied. 

KEELSONS. 

The  value  of  keelsons  lies  in  their  contribution  to  the  lon- 
gitudinal strength  of  the  structure,  and,  where  they  are  fitted 
in  conjunction  with  intercostal  plates  having  a  shell  connec- 
tion, to  the  additional  assistance  given  to  the  hull  plating.  In 
general  practice  it  would  seem  that  too  much  prominence  is  given 
to  their  strength  as  individual  members  rather  than  treating  them 
as  component  members  of  the  main  structure,  or  ship  itself  viewed 
as  a  girder ;  this  is  seen  in  the  deep  centre  line  keelsons  fitted  on 
top  of  ordinary  floors;  where  continuous  centre  vertical  plates  are 
also  fitted,  the  necessary  efficiency  and  strength  required  locally 
may  be  obtained  by  thickening  the  lower  parts  of  the  member,  as 
shown  in  Fig.  135,  and  at  the  same  time  increasing  the  moment  of 
inertia  of  the  ship's  section  as  a  whole  about  the  neutral  axis. 

nSide  stringers  should  be  treated  similarly,  as  illustrated 
by  the  adjoining  sketch,  the  web  instead  of  one  flange 
of  the  channel  being  fitted  against  the  reverse  frame, 
permitting  of  a  better  connection  thereto,  at  the  same 
time  distributing  the  resistance  to  fluid  pressures  over 
a  greater  surface  and  adding  appreciably  to  the  stow- 
age capacity  of  the  vessel. 

Where  the  plates  forming  side  stringers  are  18  inches 
(or  over)  wide,  bracket  plates  must  be  fitted  underneath 
to  support  and  keep  them  standing  to  their  work,  except 
'         '   where  webs  are  8  feet  apart.    These  brackets  should  be 
fitted  midway  between  the  web  frames. 


Bulkheads  383 


The  practice  of  piercing  watertight  bulkheads  with  keelsons  and 
stringers,  and  fitting  angle  collars  around  them  to  insure  water- 
tightness,  should  be  discouraged,  as  a  much  stronger  member  is  ob- 
tained by  cutting  the  keelson  or  stringer  and  connecting  same  by- 
bracket  plates  to  the  bulkhead.  This  method,  besides,  gives  a 
more  reliably  watertight  connection. 

In  arranging  keelsons  or  bottom  longitudinals,  these  where  pos- 
sible should  be  incorporated  with  engine  foundation  girders,  or  if 
this  be  impracticable,  an  efficient  scarph  should  be  made  by  con- 
tinuing them  past  one  another  for  about  three  frame  spaces  before 
terminating. 

In  ships  of  full  form  or  where  the  flat  of  floor  is  carried  well 
forward,  additional  intermediate  longitudinals  must  be  fitted 
locally,  about  half  the  depth  of  centre  girder  and  connected  to 
bottom  plating  to  re-enforce  the  shell  against  "  pounding." 

Keelsons,  longitudinals,  or  side  stringers  should  never  terminate 
abruptly,  but  wherever  practicable  should  be  ended  on  and  brack- 
eted to  such  supports  as  bulkheads,  web  frames,  deep  floors,  etc. 
Care  should  also  be  taken  to  arrange  the  butts  of  these  members 
clear  of  shell  butts  as  well  as  "  shifted  "  with  one  another.  The 
rivets  in  the  strap  pieces  should  be  developed  to  equal  the  strength 
of  the  member,  and  double  shear  value  obtained  in  these  connec- 
tions wherever  possible. 

BULKHEADS. 

The  steel  divisional  partitions,  built  in  ships,  called  "bulkheads," 
were  primarily  fitted  to  isolate  the  living  and  machinery  spaces 
from  the  cargo  holds  proper,  but  were  soon  recognized  as  having  a 
more  important  mission  in  subdividing  the  ship  into  watertight 
compartments  besides  adding  considerably  to  transverse  strength. 
So  that  in  later  years  it  has  become  a  canon  in  ship  design  that  a 
vessel's  bulkheads  shall  be  in  number  and  arrangement  sufficient 
to  keep  the  ship  afloat  with  any  two  compartments  open  to  the 
sea.  Watertight  bulkheads  must  always  be  carried  to  the  deck 
above  the  load  waterline,  and  in  the  case  of  the  collision  or  fore- 
most one,  to  the  weather  deck,  as  the  forepeak  is  the  most  liable 
to  damage  and  flooding,  producing  a  great  alteration  in  trim. 
They  may  be  plated  either  vertically  or  horizontally,  and  efficiently 
stiffened  in  accordance  with  the  requirements  of  the  classification 
societies'  rules,  observing  in  arranging  stiffeners  that  these  are 
placed  on  the  reverse  to  the  caulking  side.  In  most  yards  the 
practice  is  to  fit  watertight  bulkheads  continuous  from  tank  top 
to  deck  level,  but  it  is  considered  better  construction  to  fit  the 
steel  decks  continuous  and  the  bulkheads  intercostally. 

As  these  steel  partitions  are  connected  to  the  ship's  side  by  single 


384  The  Naval  Constructor 


or  double  angle  frames  with  closely  spaced  rivets  in  the  sided 
flange,  it  will  be  seen  that  this  line  of  perforations  around  the  shell 
is  a  source  of  weakness.  To  compensate  as  far  as  possible  for 
this,  it  is  necessary  to  fit  doubling  plates,  or  "liners,1'  where 
practicable,  i.e.,  in  wake  of  the  outside  strakes  of  shell  plating. 
These  liners  may  extend  from  frame  to  frame,  or,  as  is  more  often 
done,  for  a  sufficient  distance  on  each  side  of  bulkhead,  to  take  an- 
other row  of  rivets,  observing  that  these  holes  need  only  be  spaced 
for  watertight  riveting  on  the  caulking  side  of  bulkhead. 

Owing  to  the  water  pressures  being  greatest  on  the  bottom,  the 
plating  is  graded  in  thickness  towards  the  top,  and  of  course  the 
section  of  stiffening  bars  is  likewise  reduced.  The  lower  stiffeners 
require  bracketing  to  tank  top  ;  and  in  detailing  the  riveting  of 
these  brackets,  it  should  be  borne  in  mind  that  one  arm  takes 
tensile  and  the  other  shearing  stresses.  Watertight  spacing  is 
required  for  all  riveting  except  stiffeners  and  their  connections. 

Where  web  frames  or  deep  framing  is  substituted  for  hold 
beams,  additional  horizontal  stiffening  must  be  given  the  bulkheads 
at  the  level  at  which  the  lower  deck  would  ordinarily  support  the 
bulkhead,  and  in  addition  a  deep  centre  line  web  fitted. 

Generally  it  will  be  found  convenient  to  arrange  for  the  caulk- 
ing side  of  bulkhead  to  be  that  side  on  which  the  open  bevel  frame 
shows,  that  is,  the  after  side  in  fore-body  bulkheads,  and  the 
forward  side  in  after-body  bulkheads.  There  are  exceptions, 
however,  to  this  rule  which  will  suggest  themselves  in  considering 
deep  tank  and  peak  water  tests.  As,  of  course,  it  is  only  necessary 
to  caulk  one  side  of  the  bulkhead,  the  stiffening  bars  should  be 
arranged  on  the  opposite  side. 

Where  stiffening  bars,  especially  angles,  are  exposed  in  cargo 
holds  or  between  deck  spaces,  their  sharp  edges  must  be  protected 
by  fitting  wood  chafing  pieces  projecting  about  an  inch  and  a  half 
beyond  the  toe  of  bar  and  bolted  to  the  stiffening  flange. 

SHELL   PLATING. 

The  skin  of  the  ship  when  constructed  of  steel  is  almost  invari- 
ably arranged  in  fore  and  aft  strakes  "  in  "  and  "  out  "  alternately. 
For  the  reasons  given  when  treating  on  keels,  the  flat  plate  should 
be  fitted  as  an  "  in  "  strake,  so  also  should  the  sheerstrake  except 
in  large  steamers  where  a  doubling  is  required.  For  fitting  and 
shoring  purposes,  it  is  an  advantage  to  fit  the  bilge  strake  "  inside," 
as  well  as  strakes  adjoining  longitudinals. 

In  laying  off  the  widths  of  strake  on  the  midship  section,  it  will 
facilitate  interchangeability  of  individual  plates  if  all  strakes  of 
the  same  thickness  are  made  similar  in  width.  It  will  also  be 
found  advantageous  to  work  the  bilge  strake  narrower  than  the 


Shell  Platini 


385 


others  where  an  odd  size  is  unavoidable.  In  moderate  sized 
Vessels  the  outside  strakes  are  usually  from  40  to  46  inches  wide, 
and  the  inside  ones  48  to  54  inches,  but  in  the  largest  ships  it  will 
be  good  practice  to  increase  these  widths,  although  by  so  doing 
increased  riveting  of  butts  will  be  necessary.  On  the  other  hand, 
when  dealing  with  small  vessels  or  light  scantling  craft  narrower 
plates  should  be  worked. 

The  widths  having  been  arranged  satisfactorily  on  the  midship 
section,  should  now  be  transferred  to  a  body  plan  and  run  in  to  the 

PLATE  LINES 


Fig.  191. 


eye  as  shown  by  Fig.  191,  observing  that  in  the  fore  body  above 
the  waterline  the  widths  are  kept  parallel,  which  necessitates 
working  stealers  in  the  under- water  body  at  the  fore  end.  Kun- 
ning  these  plate  widths  parallel  gives  a  straight,  sharp  appearance 
to  the  sight  edges,  a  very  important  point  when  lining  off  a  very 
full  ship,  as  otherwise  the  rounding  up  lines  developed  would 


ssr, 


The  Naval  Constructor 


Fig.  192. 


Shell  Plating  387 

accentuate  and  exaggerate  the  bluff  lines.  In  addition  it  enables 
us  to  work  the  narrow  plates  where  the  form  is  most  difficult  to 
work.  In  the  after  body  different  conditions  exist,  the  most 
important  plate  line  being  that  which  ends  at  the  oxter,  so  that  it 
is  only  necessary  to  divide  the  space  intervening  between  that 
point  and  the  sheer  strake  into  the  number  of  strakes  obtaining 
amidships.  The  ending  of  a  plate-line  in  the  oxter  is  advisable  to 
obtain  all  the  furnacing  and  difficult  work  on  one  plate  only. 

Having  run  the  plate  lines  on  body  plan  to  fulfil  the  foregoing 
conditions,  these  may  then  be  taken  off  and  faired  up  on  the 
model. 

If  it  be  found  that  one  of  the  landings  crosses  the  continuous 
angle  of  tank  margin  plate  or  watertight  flat,  the  line  must  be 
stopped  abruptly  near  the  point  of  intersection  and  "jogged" 
across  for  a  sufficient  distance  before  resuming  its  flight. 

Before  any  butts  whatever  are  laid  off,  either  for  stringers  or 
shell  plating,  a  small  diagram  should  be  drawn  giving  the  general 
scheme  for  the  shift  of  butts  which  will  enable  the  various  structu- 
ral plans  to  proceed  simultaneously  and  independently.  No  butts 
on  adjacent  strakes  should  be  placed  nearer  one  another  than  two 
frame  spaces,  or  one  frame  space  where  a  strake  intervenes.  The 
ideal  shift  of  butts,  however,  is  that  which  shall  have  not  more 
than  one  shell  butt  in  any  one  frame  space  from  keel  to  gunwale. 
After  the  shell  plate  butts  have  been  arranged,  those  of  stringers, 
longitudinals,  keelsons,  etc.,  may  be  set  off  in  the  best  positions  in 
relation  to  shell.  Such  plates  as  require  furnacing  should  be 
arranged  as  short  as  possible,  the  most  difficult  of  these  being  the 
"hip  "  plate  on  the  quarters,  oxter  plate,  boss  plate,  the  "breeches  " 
plate  taking  stern  frame  and  plate  keel,  and  the  similar  plate  of 
spoon  form  forward  adjoining  the  stem.  In  some  forms  of 
vessels  it  is  also  advisable  to  make  a  short  plate  of  those  having 
double  set  at  fore  and  after  ends  of  bilge  where  the  latter  begins 
to  curve  into  the  entrance  and  run  of  vessel  respectively. 

A  scheme  of  butts  such  as  the  one  suggested  is  shown  by  the 
accompanying  diagram,  Fig.  192. 

The  "landings,"  as  the  edge  overlaps  of  the  in  and  out  strakes 
of  plating  are  called,  should  be  of  the  width  necessary  to  take  the 
required  size  of  rivets,  which  must  be  spaced  for  watertight  work, 
i.e.,  4  to  4^  diameters  apart,  observing  that  where  double  riveting 
is  employed  a  single  rivet  only  should  be  inserted  at  the  closing, 
or  caulking  edge,  in  wake  of  all  frames.  In  yacht  construction 
where  a  perfectly  smooth  topside  is  desired,  the  plating  is  often 
arranged  edge-butt  fashion  with  an  inside  continuous  seam-strap  — 
a  more  expensive  and  less  efficient  method  than  the  other,  and 
adopted  solely  for  appearance. 

In  small  moderate  sized  vessels  the  garboard  and  sheerstrake 


388  The  Naval  Constructor 


landings  only  are  double  riveted,  but  in  large  vessels  all  of  the 
landings  should  be  provided  with  two  rows;  and  where  exceptional 
local  loads  are  carried,  as  in  deep  tanks,  or  in  vessels  above  480 
feet  in  length,  M  the  lauding  edges  should  be  treble  riveted  for  one 
fourth  of  the  vessel's  length  in  the  fore  and  after  bodies  for  a  depth 
of  one  third  the  vessel's  depth."  Vessels  slightly  under  this 
dimension  may  have  double  riveted  landings  with  an  additional 
rivet  added  in  each  frame  space  within  the  zone  mentioned. 
Where  a  change  is  made  from  a  treble  to  a  double,  or  from  double 
to  single  riveted  landings,  the  taper  must  of  course  be  made  on  the 
inside  or  hidden  edge,  and  should  extend  over  a  frame  space. 

Individual  plates  of  strakes  should  be  fitted  in  as  long  lengths 
as  the  steel  makers'  limits  allow,  or  the  facilities  of  the  particular 
yard  permit,  consistent  always  with  good  practice.  The  old 
method  of  fitting  these  with  edge-butts  having  an  inside  covering 
strap  has  been  almost  entirely  superseded  by  overlapping  the  plates, 
a  stronger  and  more  enduring  method.  There  are  some  strakes 
and  special  cases,  however,  where  it  is  still  advisable  to  retain  the- 
edge-butt  connection,  as  in  flat  plate  keels,  sheerstrakes  and  the 
strake  in  wake  of  bilge  keels,  as  by  this  means  we  get  a  closer  fit- 
ting for  keel  angles,  stringer  bars  and  mouldings  and  bilge  bars,  elim- 
inating unsightly  work,  trouble  and  the  expense  of  fitting  liners. 

Where  the  overlapped  landing  of  an  outside  strake  crosses  the 
buttlap  of  the  adjacent  inside  strake,  it  will  readily  be  seen  that  a 
small  wedge-shaped  space  is  formed.  To  close  this  up  and  so  ob- 
tain the  necessary  watertightness,  it  is  customary  to  scarph  the 
corner  of  the  overlap,  allowing  it  to  be  drawn  home.  In  wake  of 
the  outside  strake  overlaps,  where  they  adjoin  the  inside  landing 
edge,  planing  is  impracticable,  and,  as  a  similar  wedge-shaped 
aperture  interferes  here  also  with  watertightness,  this  is  secured 
by  fitting  a  tapered  liner  long  enough  to  take  three  rivets.  A 
similar  tapering  away  of  the  outside  landing  edge  is  performed 
where  the  strakes  end  on  stem  and  stern  post,  thus  giving  the  ap- 
pearance of  one  flush  thickness  at  these  parts. 

Wherever  the  shell  plating  is  cut  to  form  cargo  doors,  coal 
chutes,  sea  connections,  sidelights,  etc.,  compensation  must  be 
given  for  the  loss  in  strength  sustained.  More  especially  is  this 
imperative  where  these  openings  occur  amidships  through  the 
sheerstrake,  as  it  is  then  obvious  that  the  strength  is  reduced  to  a 
maximum,  being  at  the  extreme  fibres  and  where  the  greatest 
bending  moments  are  produced.  To  avoid  abrupt  discontinuities 
as  much  as  possible,  the  corners  of  all  such  holes  where  not  circu- 
lar should  have  a  bold  radius,  and  in  addition  kept  well  clear  of 
butts.  In  addition,  doubling  plates  must  be  fitted,  observing  that 
these  should  be  over  the  openings  and  encircling  the  upper  stresses 
acting  on  the  upper  corners,  as  the  stresses  acting  on  the  upper 


Detail   Fittings  389 

works  which  need  resisting  most  are  tensile.  Where  sidelights 
are  cut  through  the  sheerstrake,  compensation  may  be  given  by 
slightly  increasing  this  strake  in  thickness  or  by  fitting  compensat- 
ing angle-bars  over  the  openings. 

The  shell  plating,  as  will  be  seen,  really  forms,  in  conjunction 
with  the  strength  deck,  the  sides  and  bottom  and  top  members  re- 
spectively of  the  ship  viewed  as  a  box  girder.  For  this  reason  the 
parts  taking  the  greatest  stresses  are  those  at  the  greatest  distance 
from  the  neutral  axis  ;  and  as  a  ship  is  not  always  in  the  upright 
position  in  a  seaway,  it  will  be  evident  that  these  parts  are  the 
sheerstrake,  bottom  and  bilges.  Thus  the  classification  societies 
stipulate  for  thicker  plating  at  these  parts.  As  the  greatest  bend- 
ing moments  are  exerted  amidships,  diminishing  towards  the  ends, 
they  require  that  the  maximum  thickness  shall  be  retained  for  a 
quarter  of  the  vessel's  length  before  and  abaft  the  dead  flat  frame. 
There  are,  however,  certain  localities  beyond  these  limits  where 
the  midship  thickness  must  be  maintained  if  not  increased  where 
abnormal  local  conditions  demand  it.  Conditions  such  as  are  re- 
ferred to  exist  at  the  ends  of  plates  adjoining  the  stern  frame, 
where,  besides  making  the  connection  to  a  heavy  forging  requir- 
ing very  large  rivets,  excessive  vibration  of  a  fatiguing  nature  is 
encountered  ;  and  at  the  bossed  plating,  oxter  and  hip  plates  re- 
quiring furnacing  and  much  consequent  hammering,  where  a  se- 
rious reduction  in  the  original  thickness  takes  place  in  addition  to 
the  distress  to  the  plate  consequent  on  the  treatment  to  which  it 
is  subjected.  Also  doubling  or  increased  thickness  must  be  pro- 
vided at  abrupt  breaks  in  the  longitudinal  strength,  as  at  ends  of 
poops  or  bridge  deck  superstructures,  in  wake  of  hawse  pipes,  etc., 
and  at  other  points  which  present  themselves  and  will  be  evident 
to  the  observant. 

DETAILS.     FITTINGS. 

Only  next  in  importance  to  the  structural  details  are  the  deck 
and  other  fittings,  on  which  the  convenient  and  safe  handling  of 
the  ship  depends.  These  in  many  cases  do  not  receive  that  consid- 
eration which  their  importance  merits.  Instead  of  being  calcu- 
lated on  a  rational  basis  and  designed  accordingly,  ship  fittings  are 
too  often  left  to  the  guesswork  of  the  technically  untrained,  with 
the  result  that  we  often  find  in  these  fittings  a  wide  variation  in 
the  scantlings  employed  for  a  given  duty  even  amongst  like  fittings 
on  the  same  ship  where  different  sizes  are  used. 

With  the  object,  then,  of  proportioning  these  fittings  from  a 
rational  unit  and  standardizing  them,  the  following  tables  of  fit- 
ting details  have  been  prepared  or  collected.  The  basis  on  which 
the  unit  is  founded  is  in  many  cases  given,  enabling  the  expe- 


390 


The  Naval  Constructor 


Bill  of  Material 


391 


rienced  to  determine  for  themselves  what  variation  may  safely  be 
made  where  fittings  are  being  designed  for  special  work. 

In  the  preparation  of  details  it  will  be  found  to  contribute  much 
to  their  elucidation  if  a  "  fitting  list  "  or  "bill  of  material"  be 
added  alongside  the  detail  delineated,  and  each  and  every  part  of 
the  fitting  given  a  special  "  piece  number."  The  number  plan  of 
the  general  arrangement  on  which  the  details  are  assembled 
should  likewise  be  given,  and  of  course  these  piece  numbers  in- 
dicated on  this  assembly  drawing  for  identification.  The  piece 
numbers  will  also  prove  helpful  as  reference  numbers  in  discus- 
sions or  correspondence  relating  to  the  particular  fitting. 

The  adjoining  specimen  plate,  with  its  accompanying  bill  of  mate- 
rial, has  been  prepared  to  illustrate  the  method  advocated. 


BILL   OF  MATERIAL  FOR   ONE   BOAT. 


9 

1 

.g 

i 

0 

H 

U 

%  6 

So 

Name. 

44  ft. 

6 

Pat.  79 

Socket    

M.C.I. 

86-370 

12 

7 

Die  670 

Rail  stanchion  .... 

W.I. 

«< 

70 

8 

"    673 

"           "       

W.I. 

" 

26  yd. 

12 

Safety  chain 

Red  metal 

1 

I 

" 

12 

23 

Pat.  103 

Thumb  screw     .... 

Comp.  N. 

" 

43 

42 

Screw  eye 

Brass 

^ 

£ 

M 

56 

as 

Die  685 

Eye  bolt 

W.I. 

" 

28 

94 

1"  W.  I.  gas  pipe  sleeve, 

W.I. 

*s 

« 

58 

96 

\"  split  pin 

W.I. 

(galv'd.) 

^ 
X 

M 

74 

96 

Die  691 

Eye  in  end  of  rail  .    .    . 

W.I. 

e 

(t 

810  ft. 

97 

\\"  rod  (top  rail)    .    .    . 

W.I. 

- 

2,365  " 

98 

1"  rod  (middle  and  lower) 

W.I. 

» 

88 

170 

l£"  tap  bolt 

W.I. 

" 

86 

171 

Die  675 

Rail  stanchion   .... 

W.I. 

" 

44 

172 

"     676 

it            <« 

W.I. 

" 

392 


The  Naval  Constructor 


STANDARD    HATCHING   FOR    VARIOUS 
MATERIALS. 


CELLULOSE 

GLA88 

^J%jJ 

^^^^ 

«^ 

RED 

GREEN  &  WHITE     U.S. 

*mm 


**&Z6 


■■ 


YELLOW,    BROWN   4   GREEN 


Figs.  194-211. 


Graphic  Division  of  One   Inch         393 

GRAPHIC   DIVISION    OF   ONE    INCH. 

1  INCH  DIVIDED  INTO 


STEEL  PLATE* 

LBS.  PER  SQ. 

FT. 

16™§ 

2QIH8 

32NDS. 

4QTHS 

MILLIMETERS. 

IRON  PLATES 

LBS.  PER  SQ. 

FT. 

40.80 

16 

20 

32 

40 

40 

38/76 

- 

-            — 

—             — 

25 

—    24 

t 

38 

38 

1 

14 

18 

36.72 

36 

36 

-     28    - 

-"     22 

34.68 

- 



34 

34 

| 

~" *    16 

32.64 

32 

"     20 

32 

12 

—            — 

- 

30.60 

-    24    - 

30 

30 

- 

14 

—             — 

28.56 

28 

18 

28 

26  52 

26 

10 

—     20    — 

~     16 

24.48 

12 

_            _ 

24 



24 

L      - 

"      14 

22.44 

22 

22 

8 

10 

— 

-L 

20.40 

-    16    - 

20 

20 

O 

- 

—            — 

-     12 

z 

18.36 

-    14    - 

18 

18 

8 

16.32 

6 

— 

16 

—    10 

16 

-     12     - 

14.28 

—           — 1 

14 

14 

6 

-     10    - 

—     8 

12.24 

12 

12 

4 

—            — 

- 

10.20 

—     8     — 

10 

'     6 

10 

—            — 

- 

8.16 

4 

—     6      — 

8 

8 

2 

-             - 

6.12 

6 

4 

6 

-     4      " 

— 

4.08 

2 

—              — 

4 

4 

1 

~~      1 

2 

2.04 

2 

1 

2 

1.02 

-            - 

1      " 

1 

1 

—             — 

— 

V 

394 


The  Naval  Constructor 


BALDT  ANCHOR. 


Fig.  212. 


Dimensions  of  Baldt  Stockless  Anchors     395 


DIMENSIONS   OF  BALDT   STOCKLESS   ANCHORS. 

(Cast  Steel.) 
Weight  in  Pounds. 


Lbs. 

5,600 

5,400 

4,760 

2,940 

1,820 

1,680 

840 

A 

n 

23 

23 

21J 

20 

171 

I64 

14 

B 

16 

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m 

14 

10  J 

101 

9 

C 

10 

10 

10 

»i 

6 

6 

4f 

D 

w 

H 

81 

8£ 

7* 

n 

51 

E 

n 

n 

«i 

6| 

JH 

41f 

5ft 

F 

9 

9 

9 

9 

8 

8 

4i 

G 

60 

60 

56J 

504 

44  4 

41 

331 

H 

35 

35 

334 

30J 

25  | 

251 

20 

I 

53 

63 

51f 

45f 

37  J 

37  f 

30  | 

J 

161 

16| 

m 

13J 

10  | 

10  f 

8| 

K 

12 

12 

llf 

8f 

7 

7 

6 

L 

5| 

5f 

H 

5 

81 

8f 

3 

M 

7 

7 

H 

6 

44 

44 

3& 

N 

23| 

23J 

21i 

20 

15  4 

15  4 

121 

0 

2| 

n 

3 

24 

24 

If 

If 

P 

iei 

16| 

16J 

151 

114 

114 

91 

Q 

6 

6 

H 

5 

*J 

44 

3 

B 

72 

72 

72 

66 

54 

54 

40 

s 

8| 

8! 

8| 

n 

n 

61 

4TV 

T 

10 

10 

9| 

H 

6« 

6f 

54 

IT 

5 

5 

5 

4 

3 

3 

2| 

V 

6 

6 

51 

4| 

31 

8| 

3 

W 

18 

18 

17 

16 

12 

12 

»4 

X 

9 

9 

8f 

8 

61 

61 

5 

Y 

6f 

n 

n 

6| 

61 

51 

34 

Z 

CWT. 

8 

8 

n 

7 

n 

51 

4§ 

50 

48| 

m 

26J 

161 

15 

74 

396 


The  Naval  Constructor 


HALL   ANCHOR. 


Dimensions  of  Hall  Anchors 


39' 


DIMENSIONS- OF    HALL   ANCHORS. 


°^  . 

Hog 

life 

II 

1 

ii 

H 

ii 

ii 

II 

II 

i 

% 

II 

S 

II 

li 

165 

3.07 

1.93 

4.92 

1.26 

2.64 

29.53 

14.76 

3.62 

7.36 

10.47 

4.06 

2.20 

220 

3.39 

2.09 

5.43 

1.38 

2.91 

32.52 

16.26 

3.98 

8.11 

11.54 

4.49 

2.44 

330 

3.86 

2.36 

6.18 

1.57 

3.31 

37.05 

18.54 

4.53 

9.25 

13.15 

5.12 

2.80 

440 

4.25 

2.64 

6.81 

1.73 

3.66 

40.00 

20.43 

5.00 

10.20 

14.49 

5.63 

3.07 

550 

4.61 

2.87 

7.36 

1.89 

3.94 

40.28 

22.13 

5.43 

11.06 

15.71 

6.10 

3.31 

660 

4.88 

3.03 

7.80 

2.00 

4.17 

46.90 

23.47 

5.75 

11.73 

16.65 

6.46 

3.50 

880 

5.35 

3.35 

8.54 

2.20 

4.61 

51.42 

25.71 

6.30 

12.87 

18.27 

7.09 

3.86 

1,100 

5.79 

3.58 

9.25 

2.40 

4.96 

55.63 

27.80 

6.81 

13.90 

19.72 

7.68 

4.17 

1,320 

6.14 

3.82 

9.80 

2.52 

5.28 

59.02 

29.40 

7.24 

14.76 

20.95 

8.11 

4.41 

1,540 

6.46 

4.02 

10.32 

2.68 

5.55 

62.02 

30.91 

7.60 

15.51 

22.00 

8.54 

4.65 

1,765 

6.77 

4.21 

10.83 

2.80 

5.79 

65.04 

32.52 

7.95 

16.26 

23.11 

8.98 

4.88 

1,985 

7.05 

4.37 

11.26 

2.91 

6.02 

67.68 

33.86 

8.27 

16.93 

24.06 

9.33 

5.12 

2,200 

7.28 

4.53 

11.65 

2.99" 

6.26 

69.96 

35.00 

8.58 

17.48 

24.88 

9.65 

5.28 

2,760 

7.83 

4.88 

12.56 

3.23 

6.73 

75.28 

37.64 

9.21 

18.82 

26.73 

10.35 

5.67 

3,310 

8.35 

5.20 

13.35 

3.43 

7.17 

80.16 

40.42 

9.80 

20.04 

28.54 

11.02 

6.02 

3,860 

8.78 

5.47 

14.06 

3.62 

7.52 

84.33 

42.50 

10.35 

21.06 

29.96 

11.61 

6.34 

4,410 

9.17 

5.71 

14.69 

3.78 

7.87 

88.47 

44.39 

10.79 

22.00 

31.30 

12.13 

6.65 

4,960 

9.53 

5.95 

15.24 

3.94 

8.15 

91.54 

46.09 

11.22 

22.87 

32.52 

12.60 

6.89 

5,510 

9.88 

6.14 

15.79 

4.06 

8.46 

94.92 

47.82 

11.61 

23.74 

33.70 

13.07 

7.13 

6,610 

10.51 

6.54 

16.81 

4.33 

9.02 

100.99 

50.81 

12.36 

25.24 

35.87 

13.90 

7.60 

7,720 

11.06 

6.89 

17.68 

4.57 

9.49 

106.26 

53.49 

13.03 

26.58 

37.76 

14.65 

7.95 

8,820 

11.58 

7.20 

18.50 

4.76 

9.92 

111.30 

55.93 

13.62 

27.80 

39.83 

15.32 

8.35 

9,920 

12.00 

7.48 

19.21 

4.96 

10.28 

115.36 

58.02 

14.13 

28.82 

41.32 

15.91 

8.66 

11,020 

12.44 

7.76 

19.88 

5.12 

10.67 

120.28 

60.06 

14.65 

29.88 

42.78 

16.46 

8.98 

13,230 

13.23 

8.23 

21.14 

5.43 

11.34 

127.09 

63.88 

15.55 

31.77 

45.46 

17.52 

9.57 

398 


The  Naval  Constructor 


ADMIRAL   ANCHOR. 


Admiral  Anchor 

ADMIRAL   ANCHOR. 


399 


9,240 

7,840 

3,080 

1,340 

6,104 

5,180 

1,792 

910 

/  // 

/  /' 

/  // 

/  // 

/  n 

/  // 

/  // 

/  // 

A 

8  0 

59 

4  6 

3  6J 

5  5 

4  11 

3  64 

3  1 

B 

2  9 

27 

1  11 

1  8 

2  5 

2  14 

1  8. 

1  6. 

C 

2  4 

22 

1  6 

1  3 

2  0 

1  84 

1  3 

1  1 

D 

1  10 

1  8 

1  2$ 

l  14 

1  54 

1  4 

Hi 

m 

F 

1  4 

13 

OlOf 

0  8J 

1  1 

0  114 

O84 

0  74 

G 

1  2 

1  1 

0  9 

0  7J 

1  0 

0  10J 

0  74 

0  64 

H 

4  8 

44 

3  2i 

2  6i 

3  llj 

3  6J 

2  6i 

2  3 

I 

1  8 

16 

i  i'i 

Oil 

1  44 

1  3 

0  11 

0  94 

J 

12  8J 

117$ 

8  0 

6  4 

9  8 

9  6 

7  4i 

5  6 

K 

48 

45 

3  4 

2  7| 

4  1 

3  8J 

2  7J 

2  34 

L 

22 

20 

1  6 

1  2i 

1  94 

1  9 

124 

1   i 

M 

07 

00 

0  4J 

0  31 

0  54 

0  51 

04 

0  3J 

N 

13 

1  1 

0  9 

0  74 

0  11 

OlOf 

0  73 

0  6§ 

0 

08 

0  7J 

0  5J 

0  41 

0  64 

0  6 

0  44 

0  3J 

P 

0  4i 

04 

0  3 

0'  24 

0  3| 

0  34 

0  2f 

0  2 

Q 

10  2 

96 

8  84 

5  3f 

8  3 

8  0 

64 

4  6J 

R 

0  8i 

0  7i 

0  6 

0  41 

0  7 

0  64 

05 

0  41 

S 

0  7J 

0  6^ 

0  5 

0  41 

0  6 

0  61 

0  44 

0  3| 

400 


The   Naval    Constructor 


INGLEFIELD   ANCHOR. 

Unit  A"  =  .5693 yj  W,  where  W=  weight  in  lbs. 


^^& — k 


^§^  r 


A  =  unit  in  inches. 
5  =  9.5  A, 
(7=2.5  A. 
J)  =1.25  A. 
E=z  .6  A. 
F=    .37  A. 


O  =  2.24  A. 

H=    .624  A. 

/  =    .773  A. 

K=    .70  A. 

L=    .50  ^4. 

Jf=    .85  A. 


Fig.  215. 


Number  of  Deck  Bolts 


401 


3 
- 

a 

% 

1 

\ 

^_, 

£ 

M 

3 

\ 

0 

fe 

8 

^S8S8^S 


■  CO  rti  ^  iO  iO  «D  ' 


S- 


M  o  g 

5*3 


(N^iOCOOONNCOHOO 
HMTjtiOHHCONIMN 


NHHH(DiONOiOO 
-  lO 


0>0(N 


ooonoow;  i 


S©iO©"*OOOOC5© 


(MtJHiOOOI^i-iCOOQO 

rHCO00»OO>CONO5CON 


8£2: 


(NOiiOCOt^.^T-(OOOiCO 

C<1  i-l  t-I  i-l  T-H 


HCOINiOOHOH^N 
NOfOWHOOJOONCi 

<N  C^J  T-H  T-l  i-H  T-H 


©lOiooiaoo-^eocoio 
OOCOOOOit^T-iOiO'-iTti 
OCNt^-^INT-HCiqOOOt^ 


?i 


402 


The   Naval   Constructor 


ANCHOR    CRANE    STRESSES. 

In  figuring  the  stresses  on  an  anchor  crane  it  is  assumed  that 
the  post  acts  as  a  cantilever,  the  maximum  stress  on  which  occurs 
at  the  upper  deck  bearing.  The  jib  is  always  exposed  to  a 
direct  compression,  while  the  tierods  are  subjected  to  tension. 

The  weight  of  the  crane  it- 
self may  be  omitted  in  the 
calculation,  as  the  stresses 
which  occur  as  a  conse- 
quence thereof  arc  of  small 
importance  compared  with 
stresses  produced  by  the 
weight  suspended  at  the 
head. 

If  Q  =  load  in  pounds, 

Qi  —  load  on  hoisting 
rope  in  pounds, 

/  =  spread  in  inches, 


Fig.  216 


then  tension  on  the  tierods :  — 

QXf  +  QxXl 

k 

*  >    Compression  on  the  jib:  — 

QXf  +  QiXh 


Cm 


If  arrangement  cf  blocks  as  shown,  then 


Qi  = 


Q 


In  calculating  the  dimensions  of  the  crane  post  the  load  on 
the  hoisting  rope  =  Qi  applied  at  the  foot  block,  usually  fitted 
to  a  wrought  iron  ring  around  the  post,  has  to  be  taken  into 
account.  Note  that  this  block  should  be  placed  as  low  as  pos- 
sible to  reduce  the  stresses  on  the  post. 

The  shearing  stresses  at  A :      The  shearing  stresses  at  B: 


Pi  =  QXf  +  QrXb 


P2  = 


QXf  +  Qi(a+b) 


Anchor  Crane  Stresses 


403 


Now  that  the  forces  in  all  the  points  A,  B,  C,  D  and  E  are 
known  the  bending  moment  in  way  of  each  one  has  to  be  figured 
out. 

As  for  T  and  C,  bending  stresses  will  be  produced  only  from 
the  horizontal  components  Tx  =  T  X  cos  a.  and  C\  =  C  X 
cos  /?,  while  of  the  vertical  com- 
ponents Ti  and  C2  equal  to 
T  X  sin  a  and  C  X  cos  0  respec- 
tively. T2  will  subject  the  post 
to  tension  on  the  part  DE,  while 
C2  —  T2  will  act  as  a  compres- 
sive load  between  A  and  D. 
As  the  forces  keep  the  crane 
in  equilibrium,  it  will  be  seen 
that: 

Pi  +  Qi  +  Tx  must  equal  P2  +  Cx. 

Bending  moment  at  A,  Ma  =  0. 

Bending  moment  at  B,  Mp  =  Pi  X  a. 

Bending  moment  at  C,  Mc  =  Pi  =  Pi  (a  +  b)  —  P2  X  b. 

Bending  moment  at  D,  Ma  -  Pi  (a  +  b  +  c)  -  P2  (b  +  c) 

+  Qi  X  C,  or  also  Md  =  Ti  X  d. 

Diagram  of  Bending  Moments.  —  Along  the  vertical  lines 
at  B,  C  and  D  set  off  at  any  scale  the  bending  moments  as  found 
above,  and  join  the  points  as  shown  on  sketch.  From  this  dia- 
gram the  moment  Mx  at  any  intermediate  point  may  be  scaled. 


Graphic  Method  to  Determine  T  and  S.  —  The 

on  the  different  members  of  the  crane  may  be  conveniently  found 
j      by  graphic  construction,  and  in  most 
cases  the  result  thus  obtained  is  suf- 
ficiently accurate  for  practical  pur- 


Take  at  any  scale  the  vertical  line 
ab  to  represent  the  load  Qi  draw  be 
parallel  to  the  direction  of  the  hoisting 
rope  and  equal  to  Qi.  The  dotted 
line  will  therefore  represent  their  re- 
sultant, and  drawing  ad  and  cd  par- 
allel respectively  to  DF  and  EF,  these 
lines  will  represent  the  stresses  on  jib 
and  tierods.  From  d  and  c  draw  horizontally  the  lines  de  and  cf, 
and  from  d  vertically  the  line  df.     Then  we  get  de  =  Ti  =  TX  cos  a, 


Fig.  218. 


404 


The   Naval  Constructor 


and  cf  m  Ci  «=  CX  cos  a.  Further  ae  =  Tt  =  T  X  sin  a  and  d/= 
d  =  C  X  sin  a,  the  difference  between  these  equal  to  fg  repre- 
senting the  compression  on  the  lower  part  of  the  post. 

For  getting  out  the  shearing  stress  Pi  draw  on  a  sketch  of  the 
crane  a  vertical  line  through  F  meeting  the  horizontal  line  from 
B  at  U,  then  draw  AG  and  make  AH  at  any 
scale  equal  to  Q.  Then  HK  will  represent 
the  shearing  at  A  produced  by  Qx.  Draw 
Ah  horizontally  and  equal  to  BC  and  make 
AM  equal  to  Qi.  If  then  from  M  a  line 
is  drawn  parallel  to  BL  the  total  shearing 
stress  at  A  will  be  represented  by  HK  -\-AN. 


LNA 


Calculation  of  Strength.  —  In  figuring 
the  dimensions  of  the  different  members  in 
the  anchor  crane  it  is  advisable  not  to  use 
Fia.  219.  a  factor  of  safety  less  than  6,  which  for  ordi- 

nary wrought  steel  means  a  stress  of  material 
=  10,000  pounds  per  square  inch,  especially  if  the  weight  of  the 
crane  itself  is  omitted  in  the  calculation.  Based  upon  a  factor  of 
safety  =  6,  the  following  formulae  are  derived :  — 

For  the  tierods,  d  =  0.08  VT  where  d  =  diameter  in  inches  and 
T  =  tension  on  tierods,  two.  of  which  are  supposed  to  be  fitted. 
For  the  jib,  if  solid  circular  section  is  being  used, 

d  =  0.026  v'CZ2  where  d  =  diameter  in  inches, 
C  =  compression  on  jib  and  I  =  length  of  jib. 

For  the  cranepost,  if  solid  circular  section  is  being  used, 
d  =  0.1  ^/M  where  d  =  diameter  in  inches, 
and  M,  =  bending  moment  in  inch-pounds. 

In  this  latter  formula  the  stress  of  material  is  assumed  equal  to 
9500  pounds  as  against  10,000  pounds  in  the  former  ones  to 
compensate  for  the  stress  produced  by  the  compressive  load 
(Cj  —  T2)  which  is  not  included  in  the  calculation. 


Mitre  and   Bevel  Gears 


405 


FORMULAS   FOR  LAYING   OUT   BEVEL  AND 
MITRE   GEAR   BLANKS. 


Bevel  Geara. 
Planed  or  Cast 


Mitre  Geara.  . 

Planed  or  Cast     |  /f. 


Fig.  220. 
Formulas  for  Bevel  Gears. 

Y  =  No.  of  teeth  in  pinion. 

YP 
D  =  —  =  0.318  YP. 

IT 

Y       D 
Tan£  =  ^-  =  g>. 

B  =  D  +  (0.636  P  cos  S). 
0.318  P      K  _  2  cos^ 

H  H  Y 

0.368P^L      2.314  cosy 
H  H  Y 

0  =  S  +  E. 
A=S-R. 

M  =  ~-  (0.318  P  sin  £). 

iV  =  itf -FcosO. 

P  =  circular  pitch. 

Y'  =  no.  of  teeth  in  gear. 

D'  =  —  =  o.3i8  yp;  y  =  90°  -  y 

IT 

B'  =  D'  +  (0.636  P  cosy). 


Tan# 
TanP 


M' -FcosO'. 
D 

2  cosy' 


406  The  Naval   Constructor 

K  =  0.318  P;    L  =  0.368  P. 
0'  =  S'  +  E;    A  =S  -R. 
When  to  be  cast  K  =  0.3  P.        L  =  0.4  P. 

M'=^  -  (0.318  P  sin  5'). 

Formulas  for  Mitre  Gears. 

P  =  circular  pitch. 
N  =  number  of  teeth. 

ATP 
D  =  0.318  iVP  =  —- 

IT 

B  =  D  +  (0.636  P  sin  45°)  =  D  +  0.449  P. 
A  =  45°  -  S. 

TWQ  „ '  ^  .     0368P 

lMfl     I     ;DX  0.707 

£  =  45°  +  C. 

.      TanC  =  £        0318P 


#      D  X  0.707 

M  =  |  -  (sin  45°  X  0.318  P)  =  ^  -  0.224  P, 

0  =  M-  (FcosE). 
H  =  D  x  0.707. 

L  =  0.368  P;     K  =  0.318  P  (when  cast 
L  =  0.4P;    X  =  0.3P). 


NAVAL   ANCHOR   CRANE. 

Fibre  Stresses. 
Crane  Post  at  Forecastle  Deck.  — 

Bending  moment  Wl  =  3,260,000  in.-lbs. 
Diameter  D  =  16§  ins. 
Fibre  stress  =  /. 

—  D* 

64  7T 

Moment  of  resistance  =  /  — jr—  =f  —  D3, 


Naval  Anchor  Crane  407 


WIV  =  3,260^00X32  _  ^  ^         sq  fe 
tD3  7r  X  16.53 

At  A: 

Wl  -  2,405,000  in.-lbs.,  D  =  16|  ins. 
,_  ^2  .  2^5,000X32  =  54601bs.pers,in. 

AtB: 

Wl  =  1,577,000  in.-lbs.,  Z)  =  13.25  ins. 
;      W132      1,577,000X32      „mnlu 

*  =  "ST  "     yXlS.25»      =  691°  lb8'  PCT  Sq-  m- 
AtC: 

WZ  =  1,150,000  in.-lbs.,  D  =  11.6  ins. 

AtD: 

WZ  =  725,000  in.-lbs.,  D  =  9.95  ins. 
.      W7  32      725,000  X  32      -_nn  .. 

*  =  ^ST  =     xX  9.953     =7500  lbs.  per  sq.  m. 

At#: 

W  =  300,000  in.-lbs.,  D  =  8.25  ins. 
'       WIZ2      300,000X32       -AKtlfU 
/  =  -T=     rx  8.253      =  545°  lbs'  per  Sq-  m- 

Jib.  —  Total  compression  on  jib  -  P  =  80,000  lbs.  +  3500  lbs. 
=  83,500  lbs.  8-inch  extra  strong  pipe,  outside  diameter 
D  =  8.625  ins.,  inside  diameter  d  =  7.625  ins. 

Modulus  of  elasticity  E  =  25,000,000. 

Moment  of  inertia  /  =  ^  (D4  -d4)  =  ^  (8.6254  -  7.625)4  =  106. 

Length  I  =  189  ins. 
Coefficient  of  safety  =  n. 

e!  EI  >      =  *2E' l  =  2  x  25>ooo>ooo  x  106  =  o 

P  "  n  '  I2  '    n       P-l2  83,500  X  1892  = 


408' 


The   Naval  Constructor 


DIAGRAM    OF   STRESSES    AND    BENDING 
MOMENTS    ON   ANCHOR    CRANE. 


img  foments  on 


Vertical  Bending 
Moments  onSpreai 
1-IOQOOOinLbs. 
WOO* 


Bending  Momenta 
„     onPost 
C-lOO00OOinLbs 


MainDech.  / 


Fig.  221. 


Anchor  Crane  Stresses  409 

Area  of  section  =  12.7  sq.  ins. 
Fibre  stress  -  ^^  =  6580  lbs.  per  sq.  in. 

Tie  Rods.  —  Diameter  =  2\  ins.,  tension  on  one  tie  rod  - 

24,250  ins. 

24,250  fiCQft « 

Fibre  stress  =  21252Xt  =  6830  lbs' 

Spreader.  —  Section  at  hub  of  spreader. 
Moment  of  inertia  for  axis  x-x\  =  lx  =  2267, 

Z£=  ?267  =252. 
Cx         9 

Bending  moment  for  axis  x  -  x:  =  507,000  in.-lbs. 
Fibre  stress/,  =  ^~  =  2010  lbs.  per  sq.  in. 
Moment  of  inertia  for  axis  y  -  y:  ~  h  =  186> 

h=  i?|  =  41.3.  X     „.. 

Cy       4.5  ^    ,^_ 


Bending  moment  for  axis  y  -  y  =  200,000  -,-r    | 

in.-lbs.  Y-H^ 


.       200,000 
Fibre  stress  fv  =     41  3  \<--l&'- 

A 

=  4830  lbs.  per  sq.  in.  Fjq  m 

Area  of  section  =  49.5  sq.  ins. 
Compression,  18,800  lbs. 

Fibre  stress  fc  =  i^5  =  380  lbs.  per  sq.  in. 

Total  fibre  stress 

/»+/»+/*-  2010  +  4830  +  380  -  7220  lbs.  per  sq.  in. 
Section  18  ins.  from  hub. 

Ix       701_112 


A. 


410 


The   Naval   Constructor 


Bending  moment  for  axisz —  x  =  267,000  in.-lbs 
x  _..  267,000 


Fibre  stress/* 


112 


=  2380  lbs.  per  sq.  in., 


■**t!P^j*CjH"f*       Bending  moment  for  axis  y —y  =  91,000  in.-lbs. 


/«_"*_„.,. 


Fia.  223. 


Fibre  stress  fv  =        q    =4150  lbs.  per  sq.  in. 


Area  of  section  33.8  sq.  ins. 

Compression,  18,800  lbs. 

18  800 
Fibre  stress  fc  =      '        =  560  lbs.  per  sq.  in. 
00.8 

Total  fibre  stress  =  fx  +fy  +/c  =  2390  +  4150  +  560 
=  7100  lbs.  per  sq.  in. 


Tie  Rod  Heel  Pin.  —  Pin    considered    as   beam    uniformly 
loaded  and  fixed  at  ends. 


8       ;32 
Tension  on  one  tie  rod  P  =  24,250  lbs. 


r*#a 


/- 


PI  32      24,250  X  5.5  X  32 


8ttZ)3         8XttX2.8753 
=  7150  lbs.  per  sq.  in. 


VJ4i     -O-l 


y 


Fia.  224. 


^fe£ 


*  I 


1 


-U 


*1H 


¥J/pJedef 


2PT3 


Fig.  225. 


Tie  Rod  Eye  Pin.  —  Figured  as  tie  rod 
hub  pin. 

8       J32      ' 

PZ  32      45,800  X  7.5  X  32 
J      8irD*  8XttX4s 

=  7240  lbs.  per  sq.  in. 


Dimensions  of  Anchor  Cranes 


DIMENSIONS    OF  ANCHOR    CRANES. 


411 


«  0 

sa 

One 

Two 

H 

One 

Two 

2|?g 

*  X 

Tie 

Tie 

Jib. 

2*?VH 

H    g 

Tie 

Tie 

Jib. 

H.2  Jift 

02  P3 

Rod. 

Rods. 

EC      * 

Rod. 

Rods. 

Foot- 
cwts. 

Dia. 

Dia. 

Dia. 
each. 

Dia. 
mid- 
dle. 

Foot- 
cwts. 

Dia. 

Dia. 

Dia. 
each. 

Dia. 
mid- 
dle. 

180 

6 

If 

hy 

3 

540 

8f 

2§ 

If 

fl 

200 

9k 

" 

550 

220 

6j 

If 

If 

31 

560 

" 

" 

" 

225 

585 

9 

2k 

1« 

It 

240 

6f 

M 

" 

" 

600 

»• 

250 

" 

" 

« 

605 

" 

" 

i< 

260 

♦' 

" 

M 

M 

630 

91 

" 

ii 

270 

7 

2 

li 

3tt 

650 

" 

" 

275 

" 

" 

660 

M 

" 

" 

280 

" 

" 

" 

M 

675 

9* 

n 

2 

4* 

295 

71 

" 

" 

H 

700 

u 

300 

M 

" 

11 

715 

M 

" 

«• 

325 

M 

" 

M 

" 

720 

it 

<( 

'« 

330 

n 

v\ 

Ij[b 

3J 

750 

9| 

" 

" 

350 

" 

770 

«« 

" 

360 

»< 

" 

" 

" 

780 

» 

u 

•« 

375 

7f 

m 

" 

M 

825 

10 

2f 

If* 

5 

385 

" 

M 

" 

840 

" 

it 

390 

" 

" 

" 

M 

900 

10i 

" 

« 

400 

u 

«« 

" 

" 

1,000 

10J 

n 

2* 

51 

405 

8 

% 

\t 

4 

1,100 

10| 

420 

u 

M 

1,200 

ioa 

" 

" 

440 

" 

" . 

" 

" 

1,300 

11 

3 

n  ■ 

5i 

450 

81 

" 

u 

" 

1,400 

11* 

455 

" 

" 

" 

1,500 

ni 

" 

" 

480 

" 

" 

" 

M 

1,600 

n| 

H 

2| 

5f 

490 

" 

" 

" 

" 

1,700 

nf 

495 

8* 

21 

ij 

41 

1,800 

iif 

H 

2i 

9 

500 

" 

1,900 

n| 

525 

2,000 

12 

3| 

6 

412  The   Naval   Constructor 


NOTES    ON  ANCHOR   CRANES. 

The  most  suitable  radius  of  crane  to  efficiently  fish  the  anchor 
having  been  determined,  this  dimension  in  feet  multiplied  by  the 
weight  of  anchor  including  stock,  will  give  the  moment  in  foot- 
cwts. ,  to  which  reference  must  be  made  for  the  corresponding  sizes 
of  parts. 

N.B. — These  cranes  are  in  accordance  with  Lloyd's  require- 
ments per  Table  12,  but  for  convenience  the  moment  is  given, 
which  will  be  found  much  easier  of  application,  and  the  table  has 
been  extended  to  deal  with  the  heaviest  anchors. 

Of  course  where  the  ship  is  not  classed  to  Lloyd's,  the  crane 
should  be  figured  out  with  a  factor  of  safety  of  eight,  when  it  will 
be_  found  that  the  sizes  in  this  table,  being  empirical,  may  be  con- 
siderably reduced. 

The  heavier  sizes  of  cranes  may  with  economy  be  built  up  with 
structural  sections,  or  the  post  and  jib  may  be  formed  with  angle 
sections  having  lattice  bracing. 

It  will  also  be  found  more  economical  to  step  the  crane  post  or 
anchor  deck  in  preference  to  housing  it  and  making  it  revolve 
with  the  jib. 


Bronze  Ship's  Bell  413 

BRONZE    SHIP'S    BELL. 

Copper  13,  Tin  4  parts. 

Directions  for  Laying  Out.  —  Divide  diameter  of  bell  into 
24  parts. 

\ 

i   \ 
\\   SHIP'S  BELL. 


Fig.  226. 
Then        AD  —    6  parts.  6  — A  =11      parts. 

DB  - 14     "  A-4  =   4.         " 

B-S=U     "  P~Q=      TVdiam. 

B-R=U     "  Rad.  K=    3  J  parts. 

C-c  =      \  "  ^4-8=8        m 

c  — 6  =    5f  "  Thickness  at  8  =    1      part. 

6-s  =  11     " 
Arc  ^4  —  (t,  drawn  with  rad.  of  3£  parts  from  K,  wherever  that 
may  fall,  the  rest  of  curve  laid  in  by  hand. 

Rad.  of  crown  17  parts  may  be  16£  to  19;  thickness  of  bell  at  B, 
|  parts  =  waist,  sound  bow  =  -^  diam.  =  QP. 
Part  of  bell  above  bis.  laid  in  as  a  cylinder. 


41i 


The   Naval   Constructor 


WEIGHT    OF   BRONZE    SHIPS   BELLS. 


Diameter 

of  Mouth  in 

Inches. 

W'lKiHT  IN 
Poinds. 

Diameter 

of  Mouth  in 

Inches. 

Weight  i\ 

POUM.s. 

3 

7 

8 

9 

10 

11 

12 

13 

14 

6 
8 

10 
15 
18 
22 
26 
38 
55 

15 

16 

17 

18 

19 

20  • 

21 

22 

65 
75 
100 
125 
.  156 
178 
204 
231 

Note.  —  Weights  given  are  exclusive  of  hangers  or  belfry. 


BELAY   PINS. 


Fig.  227. 


Size 

of 

A. 

R. 

C. 

7). 

z:. 

.P. 

rp. 

Pin. 

n 

n 

n 

// 

// 

n 

a 

a 

\ 

4 

5 

I 

ItV 

ft 

\\ 

1 

1 

4* 

6 

H 

J* 

tt 

n 

1 

* 

5 

7 

l 

If 

H 

ifV 

H 

I 

H 

8 

*A 

*l 

*$ 

ItV 

H 

1 

6 

9 

n 

Hi 

lS 

n 

if 

n 

m 

10 

i* 

H 

ifV 

H 

2 

if 

3 

11 

jA 

2 

ItV 

if 

21 

i* 

8 

12 

If 

2* 

ItV 

i* 

«] 

i| 

8i 

13 

H 

2| 

IfV 

1H 

2| 

Balanced  Armor  Hatch 


415 


Scale  of  Diagram 
0  Iff. 


Scale  of  zlnche*     , 
Of      2-5    4      5    6     7     S     9     K>     II 


aftaaKKWfl 


BALANCED 
ARMOR   HATCH. 

Fig.  228. 


416  The   Naval   Constructor 

BALANCED    ARMORED    HATCH. 
Determination  of  Counterweight.  — 
Weight  of  hatch  and  fittings  complete  Wi  =  540  lbs. 
Center  of  gravity  of  hatch  from  hinge  pin  20  ins. 
Lift  applied  on  handle  to  start:  L  =  30  lbs. 
Moment  of  hatch  about  hinge  pin 

Wi  X  20  =  540  X  20  =  10,800  in.-lbs. 
Deduct:  applied  lifting  moment 

L  X  36*"  =  30  X  36*"  =    1,095  in.-lbs. 
Resulting  moment  about  hinge  =    9,705  in.-lbs. 

9705 
Pressure  on  roller  Pi  =  sr"  =  373  lbs. 
Jo 

Moments  about  centre  of  upper  gear  segment:  — 

373  X  24.8  =  P2  X  5.375  ins. 

*=;^8  -»■» 

+  15  per  cent  for  friction  in  teeth  and  bearings         258  lbs. 
Total  load  on  teeth  =  1980  lbs. 

Moments  about  centre  of  lower  gear  segment:  — 
1980  X  5.75"  =  W2  X  33.5", 

^2  =  oT^~ —  =  340  lbs.  =  weight  of  counterweight. 

oo.o 

Strength  of  Teeth  for  Gear  Segments.  —  Lewis  formula:  — 

W  =  s.  p.  f.  y.,  p  =  pitch, 

W  -  load  on  teeth  =  1980  lbs.,        /  =  face  =  2  p, 

s  =  8000  lbs.  per  sq.  in.  (man-        y  =  coefficient  =  0.1, 

ganese  bronze),  1980  =  8000  X  p  X  2  p  X  0.1, 


V 


=  1.13",  say  H"  pitch,  2\"  face. 


8000  X  2  X  0.1 


Strength    of   Upper    Shaft.  —  Distance   between  bearings 

ab0Ut  8"'                                       1730  X  8 
Maximum  bending  moment  Mb  =  5 =  1730  in.-lbs. 

o 

Maximum  twisting  moment  Mt  =  1730  X  5.375  =  9300  in.-lbs. 
Equivalent  bending  moment  M  =  0.35  Mb  +  0.65  Mt  =  0.35 

X  1730  +  0.65  X  9300  =  6650  in.-lbs. 
M  =  ^d*Xf;    /=  10,000  lbs.  per  sq.  in., 

..  1  n  nfm  =  1.9",  make  2"  to  allow  for  keyways,  etc. 

n"X  1U.UUU 


■7 


Ship's   Bollards  417 


SHIPS   BOLLARDS    (STANDARD). 

Bollards  are  invariably  made  of  cast  iron  of  good  quality,  and 
should  be  fairly  smooth  castings.  In  small  yacht  and  high  class 
work  they  are  sometimes  made  of  gunmetal,  and  in  battleships  of 
steel.  The  bolt  holes  should  not  be  cored  but  drilled  and  counter- 
sunk afterwards,  the  bolts  being  of  BB  iron  or  steel  with  full 
countersunk  heads. 

The  diameter  B  of  the  barrel  should  be  in  accordance  with 
the  sizes  given  in  the  table,  opposite  the  corresponding  length  of 
vessel,  and  with  this  dimension  as  a  unit  the  proportionate  sizes 
of  the  various  parts  calculated  from  the  appended  proportion 
table  and  diagram  : 

Diameter  of  bollard B=\. 

Centres C  =  2.83 

Height H=1.77 

Length £  =  5.22 

Width  of  base W=1.50 

Ends #=1.20 

Diameter  of  top D=1.16 

Depth  of  ridge R=    .33 

Thickness  of  base T=   .17 

Thickness  of  side S  =   .  12 

Moulding  at  top M=   .1(5 


418 


The   Naval   Constructor 


STANDARD  BOLLARDS 


3                   C 

r^ 

1 

i 

1         i 

r 

c 

J   i- 

! 

f 

—  UNIT 

V                     X 

1 

1 

) 

■\ 

: 1 — ^_ 

} 

K 1 

Pig.  229. 

*i 

TABLE   OF  BOLLARDS    (Cast  Iron). 

Length 

OF 

Ship. 

Dimen- 
sion B. 

Approxi- 
mate 
Weight. 

Length 

of 

Ship. 

Dimen- 
sion B. 

Appboxi- 

M  a  I  !•: 
Weight. 

Ft. 

Ins. 

Lbs. 

Ft. 

Jus. 

Lbs. 

60 

3 

40 

420 

13V 

1,710 

80 

3§ 

50 

440 

14 

1,900 

100 

4 

60 

460 

141 

2,100 

110 

H 

72 

480 

15 

2,310 

120 

5 

85 

500 

151 

2,525 

140 

5} 

110 

520 

16 

2,750 

160 

6 

145 

540 

161 

3,000 

170 

6} 

185 

560 

17 

3,250 

180 

7 

235 

580 

171 

3,540 

190 

n 

295 

600 

38 

3,850 

200 

8 

360 

620 

18} 

4,140 

210 

8| 

430 

640 

19 

4,440 

220 

9  • 

510 

660 

19V 

4,810 

240 

n 

605 

680 

20 

5,160 

280 

10 

700 

700 

20J 

5,560 

300 

10J 

815 

720 

21 

5,960 

320 

11 

935 

740 

211 

6,390 

340 

11* 

1,070 

760 

22 

6,780 

360 

12 

1,210 

780 

221 

7,240 

380 

12* 

1,375 

800 

23 

7,660 

400 

13 

1,530 

850 

24 

8,560 

N.B.  —The  extra  heavy  bollards  on  forecastle  head  and  quarters  should 
be  J  larger  than  given  in  table  for  the  corresponding  length  of  ship. 


Wire   Rope  Snatch    Blocks 


419 


Fig.  230. 


Size  of  Block. 


Sheave. 

Hinge  . . 
Hook.. 

Block.. 


Outside  diameter . 
Diameter  bottom 

of  groove 

Thickness 

Pin 

Wire 

Short  strap 

Long  strap 

Diameter 

Opening 

Length  over  all . . 

Width 

Thickness 

Weight 


10  INS. 


10 

8* 

H 

l 

H 

2Xi 
2X* 
If 
2 
24 
10i 
4 


12 
10 

ii 

H 
H 

2iXi 
2*X* 

n 

27 
12f 
34 

70  lbs. 


14  INS. 


14 

u* 

H 
H 

2*Xi 

2*X* 

1J 

2* 

30 

15 

3* 

104  lbs 


16  INS. 


16 
13* 

1! 
4 

1 

3*X* 

3*X* 

2 

n 

39 
17 

4 

140  lbs 


18  INS. 


18 

16} 
« 

li 
1 
3iXi 
3*X* 
2i 
3 

46 

19 

44 

175  lbs. 


420 


The  Naval  Constructor 


DIAMOND    ROPE    BLOCKS. 


,\1    I 


rs 

T 

<-H-> 

_L 



ii 

) 

V 

, s 

■J 

u 

/  „ 



-^       Ny 

t'  ,*' 

N        S 

<-F-> 

\ 

$ 

> 

! 
\ 

\ 

/ 

S.---N, 

•L  - 

.*-, 

\n  V-- 

□ 

>  I 


F-> 


Fig.  231. 


Diamond  Wire  Rope  Blocks  421 


1 

pq 

1 

Swoo 

(MOO 
N    M    OO 

81    O    H 
O0    CO    CO 

o  •*  o 

CO    •*    K5 
H    IN    CO 

Hl§ 

~      CM    «S    t^" 

CO    CO    00 

r<M    r-K.    <*• 

co   co  oo 

M    N    O) 

CO    t—    05 

j3 

*  aas 

r^  t-^  r^ 

sss 

CM    CM    CM 

"own: 

CM    CN    CM 

-        FH     ^H     (M 
*       CN    CN    CM 

io  is  e 

CM    CN    (M 

oo  oo  o 

CM    CM    CN 

■*   -ti   co 

CO     CO     CO 

w 

a 
B 

o 

1 

«  srsrs 

**s? 

**« 

CM    CN    CM 

CM    CM    CM 

He* 
5     f   «■* 

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15    lO    C9 

4* 

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eq  <n  <m 

arsar 

CO    CO    CO 

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ms? 

srw* 

CM    CM    CM 

CN    CM    CM 

4 

02 

mo   r*0    r>W> 

5    XXX 

N    N    N 

XX 
XXX 

?r  ?r  ?r 

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•  a 

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nh«  nw  o|« 

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» £  *  "s 

.*>.♦. 

— 

i 

n 

^ 

4i 

••       H-*   H*   -hW 

H«  «l«  -*• 

Hn  hk  -h 

•*«  «*•  oM 

«(■«  «!•*  rti* 

B. 
Diam. 
Bottom 
Groove. 

;      OO    00    00 

o  o  O 

SSS 

522 

ic  >o  >o 

• 

;  •   O    O   O 

CM    <M    <M 

■»f    ■*    "* 

co   co   co 

00    00    00 

S 

(  Single... 

10"  •!  Double.. 

'  Triple. . . 

(  Single... 

12"  )  Double.. 

1  Triple. . . 

(Single... 

14"  <  Double.. 

(  Triple. . . 

I  Single... 

16"  <  Double.. 

(  Triple... 

(  Single... 

18"  <  Double. . 

'  Triple. . . 

100 

t 


I  he   Naval   Constructor 


STANDARD   BLOCKS 

(Chaii 

i    Sheaves). 

Simuj:. 

Double. 

5     - 

10 

15 

20 

5 

10 

15 

20 

Tons. 

Tons. 

Tons. 

Tons. 

Tons. 

Tons. 

Tons. 

Tons. 

a 

it 

/'    . 

^ 

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// 

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A 

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if 
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21 
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2ft 

8ft 

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2ft 

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ift 

Hi 

1ft 

ItV 

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HI 

Standard   Blocks 

STANDARD  BLOCKS 


423 


Figs.  232-2o5. 


424 


The  Naval   Constructor 


Cast  Steel   Cleats 


425 


PROPORTIONS  OF  CLEATS 
("Cast.  Steel) 
Fig.  237. 

CAST    STEEL    CLEATS   SUITABLE    FOR    MANILA 
ROPE. 


Circumfer- 
ence 
of  Manila 
Rope. 

Corre- 
sponding 
Length  of 
Cleat. 
(Unit.) 

Weight 

in 
Pounds. 

Circumfer- 
ence 

of  Manila 
Rope. 

Corre- 
sponding 
Length  of 
Cleat. 

(Unit.) 

Weight 

IN 

Pounds. 

In. 
1 

n 

2 

n 

In. 
6 

8 

10 

12 

Lbs.  • 
2 

3 

6 

9    ' 

In. 
3 

3* 

4 

In. 
14 

16 

18 

20 

Lbs. 
12 

17 

22 

31 

426 


The  Naval   Constructor 

UNITED    STATES    STANDARD 


Bolt. 

Diameters. 

Tim  i 

NESS. 

Areas. 

u 

u 

i 

M 

/^ 

,  n 

"Sj 

B 
6 

3 

■ 

S 

•3  •*' 
I 

1 

& 

3 

eg 

I? 

.25 

20. 

.5 

.578 

.707 

.1850 

.25 

.25 

.0491 

.0269 

.3125 

18. 

.5938 

.686 

.840 

.2403 

.3125 

.2469 

.0767 

.0454 

.375 

16. 

.6875 

.794 

.972 

.2938 

.375 

.3438 

.1104 

.0678 

.4375 

14. 

.7813 

.902 

1.105 

.3447 

.4375 

.3906 

.1503 

.0933 

.5 

13. 

.875 

1.011 

1.237 

.4001 

.5 

.4375 

.1963 

.1257 

.5625 

12. 

.9688 

1.119 

1.370 

.4542 

.5625 

.4844 

.2485 

.1621 

.625 

11. 

1.0625 

1.227 

1.502 

.5069 

.625 

.5313 

.3068 

.2018 

.75 

10. 

1.25 

1.444 

1.768 

.6201 

.75 

.625 

.4418 

.3020 

.875 

9. 

1.4375 

1.660 

2.033 

.7307 

.875 

' .7188 

.6013 

.4193 

1. 

8. 

1.625 

1.877 

2.298 

.8376 

1. 

.8125 

.7854 

.5510 

1.125 

7. 

1.8125 

2.093 

2.563 

.9394 

1.125 

.9063 

.9940 

.6931 

1.25 

7. 

2. 

2.310 

2.828 

1.0644 

1.25 

1. 

1.2272 

.8899 

1.375 

6. 

2.1875 

2.527 

3.093 

1.1585 

1.375 

1.0938 

1.4849 

1.0541 

1.5 

6. 

2.375 

2.743 

3.358 

1.2835 

1.5 

1.1875 

1.7671 

1.2938 

1.625 

5.5 

2.5625 

2.960 

3.623 

1.3883 

1.625 

1.2813 

2.0739 

1.5149 

1.75 

5. 

2.75 

3.176 

3.889 

1.4902 

1.75 

1.375 

2.4053 

1.7441 

1.875 

5. 

2.9375 

3.398 

4.154 

1.6152 

1.875 

1.4688 

2.7612 

2.0490 

2. 

4.5 

3.125 

3.609 

4.419 

1.7113 

2. 

1.5625 

3.1416 

2.3001 

2.25 

4.5 

3.5 

4.043 

4.949 

1.9613 

2.25 

1.75 

3.9761 

3.0213 

2.5 

4. 

3.875 

4.476 

5.479 

2.1752 

2.5 

1.9375 

4.9087 

3.7163 

2.75 

4. 

4.25 

4.909 

6.010 

2.4252 

2.75 

2.125 

5.9396 

4.6196 

3. 

3.5 

4.625 

5.342 

6.540 

2.6288 

3. 

2.3125 

7.0686 

5.4277 

3.25 

3.5 

5. 

5.775 

7.070 

2.8788 

3.25 

2.5 

8.2958 

6.5092 

3.5 

3.25 

5.375 

6.208 

7.600 

3.1003 

3.5 

2.6875 

9.6211 

7.5491 

3.75 

3. 

5.75 

6.641 

8.131 

3.3170 

3.75 

2.875 

11.0447 

8.6412 

4. 

3. 

6.125 

7.074 

8.661 

3.5670 

4. 

3.0625 

12.5664 

9.9929 

4.25 

2.875 

6.5 

7.508 

9.191 

3.7982 

4.25 

3.25 

14.1863 

11.3302 

4.5 

2.75 

6.875 

7.941 

9.721 

4.0276 

4.5 

3.4375 

15.9043 

12.7405 

4.75 

2.625 

7.25 

8.374 

10.252 

4.255] 

4.75 

3.625 

17.7205 

14.2205 

5. 

2.5 

7.625 

8.807 

10.782 

4.4804 

5. 

3.8125 

19.6350 

15.7659 

5.25 

2.5 

8. 

9.240 

11.312 

4.7804 

5.25 

4. 

21.6475 

17.5745 

5.5 

2.375 

8.375 

9.673 

11.842 

4.9530 

5.5 

4.1875 

23.7583 

19.2678 

5.75 

2.375 

8.75 

10.106 

12.373 

5.2030 

5.75 

4.375 

25.9672 

21.2620 

6. 

2.25 

9.125 

10.539 

12.903 

5.4227 

6. 

4.5625 

28.2743 

23.0947 

Diameter -Li      fsbarP    V    of    60°    angle 
of  Thread. 


Diameter  bolt  less 


Sellers "    or   .75  depth  of  thread  =  Diameter  bolt    less 
t    (1.2990375  X  pitch  of  thread). 

Flats  of  (S)  or    ^  nuts  =  1.5  diameter  of  bolt  +  .125". 
Corners  of  {oj  nuts  =  1.155  flats, 


United  States  Standard   Bolts  and   Nuts     427 


BOLTS    AND    NUTS,   ETC. 


Tensile  Strength. 

Shearing 

Strength. 

ft  t» 

ft 

M 

CP 

ft 

u 

ft 

Full  Bolt. 

Bottom  of 
Thread. 

jd 

|a 

CO 

8    ^ 

J> 

©    a 

3*2 

3* 

$1  ^ 

©      fl 

ox  a" 

Q       fl 

©    ^ 

©*"  v  6* 

I6 

o 

2 

J** 

3 

< 

•< 

< 

^      ft 

< 

S        ft 

269 

336 

471 

368 

491 

202 

269 

No.  14 

454 

568 

795 

575 

767 

341 

454 

"    14 

678 

848 

1,187 

828 

1,104 

509 

678 

"    13 

933 

1,166 

1,633 

1,127 

1,503 

700 

933 

"    13 

1,257 

1,571 

2,200 

1,472 

1,963 

943 

257 

"    12 

1,621 

2,026 

2,837 

1,864 

2,485 

1,216 

1,621 

"    12 

2,018 

2,523 

3,532 

2,301 

3,068 

1,514 

2,018 

"    11 

3,020 

3,775 

5,285 

3,314 

4,418 

2,265 

3,020 

"    10 

4,193 

5,241 

7,338 

4,510 

6,013 

3,145 

4,193 

"      9 

5,510 

6,888 

9,643 

5,891 

7,854 

4,133 

5,510 

"      8 

6,931 

8,664 

12,129 

7,455 

9,940 

5,198 

6,931 

"      7 

8,899 

11,124 

15,573 

9,204 

12,272 

6,674 

8,899 

"      6 

10,541 

13,176 

18,447 

11,137 

14,849 

7,906 

10,541 

"      5 

12,938 

16,173 

22,642 

13,253 

17,671 

9,704 

12,938 

"      4 

15,149 

18,936 

26,511 

15,554 

20,739 

11,362 

15,149 

"      3 

17,441 

21,801 

30,522 

18,040 

24,053 

13,081 

17,441 

"      2 

20,490 

25,613 

35,858 

20,709 

27,612 

15,368 

20,490 

"       1 

23,001 

28,751 

40,252 

23,562 

31,416 

17,251 

23,001 

"      1 

30,213 

37,766 

52,873 

29,821 

38,761 

22,660 

30,213 

h" 

37,163 

46,454 

65,035 

36,815 

49,087 

27,872 

37,163 

6  // 

a 

46,196 

57,745 

80,843 

44,547 

59,396 

34,647 

46,196 

54,277 

67,846 

94,985 

53,015 

70,686 

40,708 

54,277 

i- 

65,092 

81,365 

113,911 

62,219 

82,958 

48,819 

65,092 

75,491 

94,364 

132,109 

72,158 

96,211 

56,618 

75,491 

h" 

86,412 

108,015 

151,221 

82,835 

110,447 

64,809 

86,412 

h" 

99,929 

124,911 

174,876 

94,248 

125,664 

74,947 

99,929 

t 

113,302 

141,628 

198,279 

106,397 

141,863 

84,977 

113,302 

127,405 

159,256 

222,959 

119,282 

159,043 

95,554 

127,405 

16 

142,205 

177,756 

248,859 

132,904 

177,205 

106,654 

142,205 

X" 

157,659 

197,074 

275,903 

147,263 

196,350 

118,244 

157,659 

f" 

175,745 

219,681 

307,554 

162,356 

216,475 

131,809 

175,745 

r 

192,678 

240,848 

337,187 

178,187 

237,583 

144,509 

192,678 

IS 

212,620 

265,775 

372,085 

194,754 

'259,672 

159,465 

212,620 

w 

230,947 

288,684 

404,157 

212,057 

282,743 

173,210 

230,947 

r 

Corners  of    jgj     nuts  =  1.414  flats. 

Thickness  of  nuts      =  diameter  of  bolt. 

Thickness  of  heads    =  flats  of  heads  and  nuts  —  2. 

Sizes  of  "  Sellers  "  or  Franklin  Institute  finished  heads  and  nuts  are 
(flats  and  thickness  of  U.S.  rough  and  finished  nuts)  —  ,0625//P.  Rough  heads, 
same  thickness  as  U.S.  nuts. 


428 


The   Naval  Constructor 


CHAIN   PLATES. 
-    -A J 


Fig.  238. 


Size  or 
Wire. 

A 

B 

c 

Z) 

£ 

F 

0 

H 

j 

x 

Z, 

// 

„ 

„ 

// 

II 

a 

// 

a 

a 

,i 

// 

n 

H 

3f 

* 

U 

1 

1* 

i 

i 

n 

1 

1 

H 

« 

I 

2 

1 

if 

f 

7 
8 

n 

If 

i 

2* 

6* 

3 

| 

2i 

1 

ll 

f 

H 

2f 

if 

I 

s 

7 

4* 

i 

2* 

H 

If 

* 

1A 

2f 

If 

1 

»i 

74 

4* 

ft 

3 

It 

lj 

I 

if 

2f 

if 

I 

3* 

7* 

5i 

J 

'A 

H 

if 

1 

if 

2f 

if 

i 

4* 

8* 

5* 

* 

2\ 

if 

n 

1 

if 

2f 

2f 

i 

5 

8* 

6i 

i 

2| 

H 

2 

1 

ii 

2§ 

2| 

u 

Proportions  of  Crane  Hooks  429 

TABLE   OF  DIMENSIONS. 

fXAXz 
z  +  AXa' 

f=W(i+z. 
A  =  Area  of  section, 
z=  Section  modulus, 
a=  Cr  of  hook  to  C.  G. 
of  section. 


A  =  J5a/W~ 


Fig.  239. 


Working 

A  — 

B  — 

c= 

D  — 

#  = 

^= 

<?  = 

zr= 

J  = 

Load 
in  Tons. 

1.00. 

1.00. 

1.80. 

.80. 

.40. 

1.00. 

3.00. 

1.60 

1.40 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

} 

1 

f 

1* 

\ 

i 

f 

H 

1 

1 

| 

\ 

f 

If 

f 

A 

I 

*l 

n 

If 

1 

\ 

J 

h\ 

« 

A 

i 

2A 

if 

if 

1* 

1 

1 

m 

H 

1 

3 

if 

1& 

2 

11 

n 

2 

il 

A 

If 

81 

m 

1A 

3 

If 

if 

2i 

A 

if 

4* 

2i 

HI 

5 

If 

it 

2}f 

}A 

f 

if 

*I 

2A 

2i 

7 

2| 

»| 

311 

if 

1 

21 

6f 

8A 

3 

10 

2| 

2f 

*} 

1J 

« 

2f 

7  { 

3H 

8| 

12 

2f 

2f 

4f 

*f 

ItV 

2f 

7| 

4i 

8 1 

15 

3 

3 

sA 

2A 

n 

3 

9 

*H 

*i 

18 

3i 

H 

5| 

2f 

}A 

H 

9f 

5i 

fi 

21 

H 

34 

6T5e 

m 

if 

81 

10  J 

&A 

fi 

25 

i 

3| 

s| 

61 

3 

ii 

3f 

111 

6 

b| 

430 


The   Naval   Constructor 


GATTING  HOOKS  FOR  ANCHOR  FALLS 

W*  WEIGHT   OF   ANCHOR  fT> 

DIA.  AT  "A"  ~  V4  VW. 


Fig.  240. 


Navy  Boat  Crane 


431 


LIST   OF   GEARS. 


Hoisting. 


Kind. 


Spur  pinion  (motor) . , 
Spur  gear , 


Worm , 

Worm  gear  (drum). 


Face. 


In. 

H 


Pitch 

Teeth. 

Pitch. 

Dia. 

In. 

In. 

14 

H  C.P. 

7.799 

40 

1J  C.P. 

22.282 

Triple 

3  pitch  I 

10 

R.H.  thrd. 

9  lead    \ 

34 

3  C.P. 

32.468 

Rev.  per 
Min. 


400 
140 

140 

12.35 


Mean  dia.  of  coil  of  rope  on  drum  =  31" 

8.12  X  12.35 
A  four  part  hoist  =  


12'  circum. 
25.07'  per  min.  hoist. 


Turning. 


Kind. 


Spur  pinion  (motor) . 
Spur  gear 

Worm 


Worm  gear .  . . 
Spur  pinion.  . 
Circular  rack. 


Face. 


Teeth. 

Pitch. 

Pitch 
Dia. 

In. 

In. 

15 

11  C.P. 

8.356 

43 

If  C.P. 

23.953 

Single 

4  pitch ) 
4  lead  ) 

10 

R.H.  thrd. 

20 

4    C.P. 

25.465 

15 

4   C.P. 

19.099 

96 

4    C.P. 

122.231 

Rev.  per 
Min. 


365 
127.3 

127.3 

6.366 
6.366 
0.S 


The  Naval   Constructor 

NAVY   BOAT   CRANE. 


Fiq.  241. 


Boat  Handling  Arrangement  433 

BOAT   HANDLING  ARRANGEMENT. 

lie  laws  of  the  principal  maritime  nations  require  that  not 
only  shall  a  stated  number  and  kind  of  boats,  lifeboat  and  work- 
ing, be  installed  on  board  ship,  varying  of  course  with  the  par- 
ticular requirements  of  the  vessel  itself  and  the  trade  in  which 
it  is  employed,  but  also  that  these  boats  shall  be  efficiently  in- 
stalled on  board  ship  and  conveniently  arranged  with  proper 
boat  handling  appliances.*  To  comply  with  these  enactments 
various  arrangements  are  adopted  suited  to  the  special  conditions 
which  obtain  in  the  particular  vessel,  ranging  from  the  simple 
single  davit  handling  a  10-foot  dinghy  slung  on  a  single  span, 
usual  in  harbor  tugs  and  similar  craft,  to  the  row  of  lifeboats  on 
a  modern  liner  handled  by  steam  or  electric  hoisters,  while  on  the 
larger  war  vessels  nests  of  boats  are  stowed  and  operated  by 
special  electric  driven  boat  cranes  or  large  derrick  booms,. 

Before  an  arrangement  of  boat  handling  appliances  can  be 
laid  out  the  special  requirements  governing  the  particular  case 
as  to  number  and  type  of  boats  must  be  considered  and  also 
the  kind  of  davit  decided  upon.  As  already  stated  the  rules 
and  regulations  of  the  hailing  country  and  the  trade  will  deter- 
mine the  former.  The  kind  of  davit  suitable  if  the  vessel  be  in 
the  ocean  passenger  trade  is  restricted  to  two  or  three  varieties 
as  shown  by  the  arrangements  in  the  figures,  these  consisting  of 
the  ordinary  rotating  davit,  the  Mallory  type  or  the  Welin 
quadrant  davit,  the  latter  being  an  excellent  davit  but  of  course 
slightly  more  costly  than  the  others,  the  cheapest  and  most 
convenient  where  there  is  room  to  install  being  that  known  as 
the  Mallory  davit. 

Rotating  Davits.  —  This  is  the  most  common  type  of  davit 
used  on  shipboard.  The  davit  and  method  of  installing  are  shown 
by  Fig.  242,  but,  of  course  the  heelstep  and  bearing  are  suscepti- 
ble of  many  variations  to  suit  individual  cases  or  local  conditions. 
The  required  diameter  suitable  for  a  given  weight  of  boat  may 

be  calculated  by  the  equation  W  X  a  =  ^r  D3f;    by  transpos- 
ed 
ing  we  get  diameter, 

D  ■ 


*  For  these  requirements  see  "  Inspectors  of  Steam  Vessels,  U.  S.,"  "  Board 
of  Trade  Rules  and  Regulations." 


434  The  Naval   Constructor 


ROTATING   DAVIT. 


Fia.  242. 


Boat  Handling  Arrangement  435 

the  lever  a,  or  outreach  of  davit,  being  measured  with  the  ship 
inclined  10  degrees.  Where  the  ship  is  intended  for  Lloyd's 
classification  the  formula  used  as  required  by  their  Rules  is 
practically  similar  to  the  foregoing,  but  is  differently  expressed  to 
make  it  more  convenient  of  application  where  actual  weights  of 
boats  are  not  at  hand  and  to  ensure  uniformity  of  requirements. 
Lloyd's  formula  is: 


V 


LXBXD(H  +  4S) 
C 


where  L,  B  and  D  are  the  length,  breadth  and  depth  respectively 
of  the  boat,  H  is  the  height  of  the  davit  above  its  uppermost 
point  of  support,  and  S  is  the  spread  of  the  davit;   each  of  these 
dimensions  being  in  feet. 
The  value  of  the  constant  term  C  is  to  be  as  follows:  — 

1.  When  the  davit  is  to  be  of  wrought  iron  and  of  sufficient 
strength  to  carry  the  boat,  its  equipment  and  a  sufficient  number 
of  men  to  launch  it,  the  value  of  C  is  to  be  144. 

2.  When  the  davit  referred  to  in  (1)  is  to  be  of  wrought  ingot 
steel  of  from  28  to  32  tons  per  square  inch  tensile  strength,  the 
value  of  C  is  to  be  174. 

3.  When  the  davit  is  to  be  of  wrought  iron  and  of  sufficient 
strength  to  safely  lower  the  boat  fully  equipped  and  carrying 
the  maximum  number  of  persons  for  which  it  is  intended,  the 
value  of  C  is  to  be  82. 

4.  When  the  davit  referred  to  in  (3)  is  to  be  of  wrought  ingot 
steel  of  from  28  to  32  tons  per  square  inch  tensile  strength,  the 
value  of  C  is  to  be  99. 

The  mountings  on  these  davits  comprise  belay  cleat,  fairlead 
sheave,  spectacles  for  span  and  guys,  the  span  being  clipped  with 
sister  hooks  at  one  end  and  shackle  on  the  other,  and  the  guys 
shackled  to  spectacle  and  set  up  on  deck  with  either  lanyard  or 
turnbuckle.  On  lifeboat  davits,  it  is  also  obligatory  to  secure 
to  davit  head,  lifelines  of  say  2-inch  manila,  long  enough  to 
reach  to  waterline  and  also  a  rope  ladder  from  span.  Where 
the  davits  operate  the  emergency  boat  (slung  outboard  at  sea), 
a  pudding  boom  should  be  lashed  to  davits  suitably  padded  in 
wake  of  chafe  to  which  the  boat  gripes  are  secured. 

Suitable  tackling  for  falls  are  readily  determined  from  the 
weight  of  boat.* 

In  first  class  practice  the  cast-steel  bearing  is  bushed  with 
composition  either  gun  metal  or  babbit  and  a  conical  disc  of 
hard  steel  is  inserted  in  the  heelstep,  these  additions  reducing 
the  friction  with  a  consequent  acquisition  to  the  ease  of  operation. 

*  For  tackles  see  Knight's  "  Seamanship"  or  "  The  Naval  Constructor." 


436  The   Naval   Constructor 


MALLORY    DAVIT. 


Fig.  243. 


Boat  Handling  Arrangement  437 

In  the  larger  classes  of  war  vessels,  as  battleships  and  cruisers, 
a  variation  of  this  davit  is  adopted  having  a  pivoting  bearing 
and  a  hinged  clamp  at  heelstep  to  permit  of  turning  down  the 
davits  when  clearing  the  deck  for  action.  The  -details  of  this 
type  are  various,  observing  that  the  bearing  is  cast  in  steel  and 
bronze  bushed,  the  swivel  pin  of  wrot  steel,  and  the  step  bearing 
of  cast  steel.  A  forged  operating  lever  about  four  feet  long  is 
furnished  for  turning  down  the  davit. 

Mallory  Davits.  —  These  davits  are  not  as  common  in 
practice  as  their  many  advantages  would  seem  to  warrant. 
They  are  not  proprietory  as  the  name  might  imply,  the  designat- 
ing title  being  derived  from  the  line  of  vessels  in  which  they  are 
most  often  fitted.  A  reference  to  Fig.  243  will  show  that  they 
may  be  formed  very  simply  from  ordinary  rectangular  universal 
roll  steel  of  a  section  at  bearing  step  derived  from  the  equation 

bh2 
W  x  a  =  —^  /,  as  in  the  case  of  the  swan-neck  davits  described 

on  this  page,  the  head  and  heel  dimension  being  approximately 
two-thirds  of  the  resulting  b  and  h.  Where  boats  are  stowed 
overhead  on  skid  beams  adjoining  deck  houses  Mullory  davits 
are  adaptable,,  take,  up  very  little  room,  and  cost  much  less  to 
install  than  the  more  common  rotating  davit,  in  addition  to 
which  they  are  much  more  quickly  and  conveniently  operated. 
It  will  be  seen  that  they  hinge  on  a  heel  pin  and  move  outboard 
between  guides  one  of  which  may  also  be  utilized  as  the  skid 
beams  and  a  positive  stop  inserted  between  them  to  limit  the 
outboard  range  of  the  davit. 

The  boat,  of  course,  is  handled  by  the  usual  falls,  but  the 
davits  are  operated  by  tackles,  the  maximum  pull  on  which  will 
W 

be  — :— ,  and  the  load  on  the  handling  part  will  equal  this  pull 

divided  by  the  number  of  parts  in  the  purchase. 

Swan-neck  Davits.  —  These  davits,  illustrated  by  Fig.  244, 
are  mostly  adopted  for  torpedo  boat  destroyers  and  similar  craft 
on  account  of  their  lightness  and  their  adaptability  to  the  re- 
stricted deck  area  associated  with  this  class  of  vessel  as  well  as 
on  account  of  their  speed  and  ease  of  operation.  It  will  be  noted 
that  the  boat  when  stowed  in  these  davits  is  entirely  within  the 
ship's  deck  line  and  that  no  actual  deck  space  is  occupied  as  the 
boat  is  carried  overhead  and  securely  griped  to  the  davits  and 
no  part  of  the  handling  gear  obtrudes  itself  beyond  the  side  of 
ship.  A  reference  to  the  figure  will  show  that  a  comparatively 
small  overhang  is  necessary  to  lower  the  boat  overboard.        • 


438  The   Naval   Constructor 


SWAN-NECK   DAVIT. 


Tig.  244. 


Boat  Handling  Arrangement  439 

Davits  of  this  type  are  usually  made  from  universal  roll  rec- 
tangular steel  bar  although  where  extreme  lightness  is  essential 
they  may  be  worked  from  structural  I  section. 

We  shall  assume,  then,  that  the  davits  required  are  intended 
to  handle  a  23-foot  whaleboat  commonly  carried  on  torpedo 
boat  destroyers,  and  that  the  weight  of  boat  plus  two  men  is 
1300  pounds  +  300  pounds  equal  to  a  total  load  of  1600  pounds 
or  800  pounds  per  davit.  It  is  sometimes  erroneously  assumed 
that  one  davit  may  be  subjected  to  the  entire  load  and  the  fibre 
stress  increased  to  15,000  pounds  accordingly  which  of  course  is 
just  the  same  as  the  more  correct  assumption  of  dividing  the  load 
between  the  davits  and  assuming  a  fibre  stress  of  7500  per  square 
inch  as  we  have  done  in  the  calculation. 


To  determine  the  section  of  the  davit  we  have  to  take  the 
bending  moment  at  A,  where  the  greatest  stress  comes,  with  the 
ship,  say  15  degrees,  heeled  over.     Let  us  assume  b  =  2\  inches. 

To  find  h  we  have 

bh2 
WXa=PXc=f°-^> 

where 

W  =  ~9  =  800  pounds, 

a  =  66  inches, 
c  =  27  inches, 
b  =  2 j  inches. 

In  this  case  we  will  set  the  fibre  stress  at  a  low  figure,  say 
7500  pounds  per  square  inch,  allowing  a  high  factor  of  safety. 


440 


The   Naval   Constructor 


MINE    DAVIT. 


4"        isiyd/j'rong 

Tapped  for  {Bolt     '*     8 
Fig.  246. 


Boat  Handling  Arrangement  441 


Then: 
and 


^X  66  =  7500^, 


,      t  /800  X  66  X  6  a  . 

A  =V  7500X2.25    =  4>33  ~  4°  mcheS- 
For  P  we  have: 

FXa  =  PXc,     or    800  X  66  =  P  X  27, 


where 


D      800X66       in_.  , 

P  =  — 27 =  1956  pounds. 


To  determine  the  diameter  at  bottom  of  operating  screw 
threads  it  would  seem  reasonable  to  derive  this  from  the  pull 
P  with  a  fibre  stress  of  7500  pounds  per  square  inch,  or, 


p  -  f wd2 

where 

P  =  1956  pounds, 

/  =  7500  pounds, 

where 

d2      1950      .  nQ 

—  =  1 =  0.26. 

4       7500             ' 

and 

d  =  0.58  inch. 

This,  however,  ignores  the  possibility  of  the  screw  being  sub- 
jected to  a  bending  stress  or  a  combination  of  bending  and  com- 
pressive stresses  caused  by  the  movement  of  the  vessel  swaying 
the  load.  As  the  intensity  of  these  is  problematical  we  can  only 
take  care  of  it  by  using  good  judgment  in  selecting  a  suitable 
diameter.  In  the  present  case  1^-inch  diameter  over  the  threads 
should  provide  an  ample  margin.  » 

The  thrust  R  on  pin  at  B  is  more  easily  determined  graphi- 
cally as  indicated  in  Fig.  1.     In  our  case  we  get 

R  =  3786  pounds.    • 

The  section  of  the  davit  should  be  gradually  tapered  down 
from  A  towards  B  and  C.  It  is  good  practice  to  make  the 
section  near  head  C  about  two-thirds  of  the  section  at  A.  For 
larger  davits  it  is  desirable  to  figure  the  strength  at  different 
sections  along  the  davit  in  order  to  make  it  as  light  as  possible. 

Pins  at  A,  B,  and  D  should  always  be  figured  for  bending  to 


442  The  Naval  Constructor 


insure  proper  strength.  In  many  cases,  especially  in  smaller 
davits  of  this  kind  as  illustrated  here,  it  will  be  found  that  the 
diameter  of  pin  thus  figured  is  too  small  to  be  practicable  and 
should,  therefore,  be  increased  properly. 

Besides  the  athwartship  screw-arm  stay,  an  additional  fore 
and  aft  stay  is  fitted  to  each  davit  to  steady  it  and  also  to  pro- 
vide support  against  collapsing  through  the  minor  axis  (espe- 
cially for  davits  of  rectangular  section) ;  this  latter  eventuality, 
however,  is  not  likely  to  occur  with  davits  of  such  small  sizes 
as  generally  fabricated  in  this  type. 

Where  occasion  suggests  it,  it  may  be  well  to  check  for  com- 
pression by  Euler's  formula: 

P_   2  EI 

where 

P  =  W  =  load  in  pounds, 

E  =  modulus  of  elasticity, 
I  =  moment  of  inertia  of  section, 
I  =  vertical  (projected  on  the   load   line) 
length  of  davit  in  inches. 

/  should  in  every  case  provide  a  sufficiently  large  factor  of  safety. 
As  the  illustration  shows,  the  davits  are  tied  longitudinally 
by  wire  rope  span  and  stay  to  the  deck,  a  turnbuckle  being  fitted 
to  set  up. 

Screw  Gear. — With  d  =  1|  inches.  For  square  threads 
the  following  proportions  are  generally  adopted:  — 

/i  =  - ,  say  in  this  case 

h=T&'>  ***  say32'- 

To  find  the  power  P  necessary  to  turn  the  hand- 
Fig.  247.  wheel,  we  have: 

PXr  =  QX^, 

where  r  =  radius  of  handwheel, 

in  this  case  =  7",  dl  =  1^~  =  1.34375". 


Boat  Handling  Arrangement  443 


WELIN   DAVIT. 


Fig.  248. 


444  The   Naval  Constructor 

To  find  Q  we  have : 

where  W  =  1956  pounds  (see  above), 

h  =  A-inch  =  0.3125, 

^  =  0.671875  inch, 


n  =  friction  —  coefficient, 


in  this  case  =  abt.  0.1. 
Then: 


and 


n      in_  0.3125  +  6.28X0.672X0.1      OAO  , 

Q  =  1956  6.28X0.672-0.3125X0.1  "  343  P°Unds 

p  =  ^1  =  343  X  0.672  =  33  pQunds< 


As  handwheels  usually  are  operated  by  both  hands  each  hand 
would  exert 

-q-  =  16£  pounds. 

Mountings.  —  The  mountings  or  fittings  on  these  davits 
comprise  the  span  and  stays  previously  mentioned  of  l^-inch 
circ.  galvanized  steel  or  iron  wire  rope  with  turnbuckle  and  eye- 
bolts  through  the  neutral  axis  of  davit  section  for  securing,  and 
lashing  pad  eyes,  say  TVmch  wire  by  lj-in°h  to  take  setting  up 
lanyards.  One  pair  of  blocks  per  davit  either  wood  or  iron 
suited  to  the  size  of  falls  rove  in  this  case  6-inch  iron  blocks  with 
phosphor  bronze  sheaves  for  2j-inch  circ.  manila  and  a  3|-inch 
fairlead  sheave  of  gun  metal  bolted  through  davit  where  shown. 
A  combined  belay  pin  and  slip  to  release  the  sword  matting 
gripe  which  is  secured  at  top  part  to  an  eye  in  davit  head  and  a 
chafing  pad  stuffed  with  oakum  and  covered  with  leather  to  pro- 
tect the  whaleboat. 


Board  of  Trade  Rules  for  Davits       445 


BOARD  OF  TRADE  RULES  FOR  ROUND  DAVITS  — 
SOLID    AND    HOLLOW. 

In  many  cases  the  regulations  require  the  davits  to  be  of 
sufficient  strength  to  safely  lower  the  boats  into  the  water, 
fully  equipped  and  carrying  the  maximum  number  of  persons 
for  which  they  measure. 

It  will  frequently  happen  that  the  same  set  of  davits  will  be 
used  for  launching  both  open  and  decked  lifeboats,  and  the 
diameter  of  the  davits  should  be  governed  by  the  weight  of 
the  boat  which  imposes  the  greatest  load  on  them  when  loaded 
with  the  maximum  number  of  persons  for  which  it  measures. 

The  weights  of  the  various  types  of  boat  should,  therefore, 
be  ascertained  from  time  to  time;  and,  in  estimating  the  weight 
of  the  persons  carried,  an  average  of  1£  cwts.  (140  lbs.)  should 
be  allowed  for  each  person. 

The  load  on  the  davits  includes  the  weight  of  the  boat,  equip- 
ments as  specified  in  General  Rules  8  and  9,  maximum  number 
of  persons  for  which  the  boat  measures  by  the  rule,  and  blocks 
and  falls.  As  the  blocks  are  frequently  made  of  metal  and 
fitted  with  metal  pulleys,  their  weight  is  considerable. 

A  wooden  boat  of  section  A,  about  28  feet  long,  complete 
with  equipments  and  gear  as  mentioned  above  and  carrying 
50  persons,  is  taken  as  imposing  a  load  of 
100  cwts.  on  the  davits,  or  2  cwts.  per  person 
for  which  the  boat  measures.  This  may  be 
stated  as  follows:  — 

W 

where  W  =  total  load  on  davits  in  cwts. : 

N  =  maximum  number  of  persons  for 
which  the  boat  measures; 

w  =  load  on  davits  in  cwts.  per  per- 
son carried. 

If  the  davits  proposed  are  found  to  be  equal 
in  diameter  to  the  dimensions  obtained  by 
the  following  rule  (2),  no  objection  need  be 
raised,  provided  that,  (a)  the  relative  strength 
along  the  tapered  parts  is  fully  maintained, 
and  (6)  the  total  weight  of  the  boat,  equip-  fig.  249. 

ments,  maximum  number  of  persons  for  which 
it  measures,  and  blocks  and  falls  does  not  exceed  2  cwts.  per  per- 
son, as  ascertained  by  rule  (1). 


446  The   Naval   Constructor 


\ 


X  D(H  +  4S)  m  d  (2) 

Where  L  =  length  of  boat,  in  feet; 

B  =  breadth  of  boat,  in  feet; 

D  =  depth  of  boat,  in  feet; 

H  =  height  of  davit,  in  feet,  above  upper  support; 

S  =  span  of  davit,  in  feet; 

C  m  constant,  to  be  taken  as  86  for  iron  davits,  and 
104  for  solid  ingot  steel  davits  of  from  27  to 
32  tons  tensile  strength,  and  for  hollow  welded 
davits  of  from  26  to  30  tons  tensile  strength; 

d  =  diameter,  in  inches,  of  solid  davit. 

In  dealing  with  hollow  davits  the  equivalent  sections  may  be 
found  by  the  usual  formula  after  the  cube  of  the  required  diam- 
eter of  solid  davit  has  been  ascertained  by  rule  (2),  as  follows:  — 

(3) 
or 

.3////3   v  mi\ 

(4) 

■         \     II  v      —    ±   I 

Where  d  =  diameter,  in  inches,  of  solid  davit; 

Dh  =  outside  diameter,  in  inches,  of  hollow  davit; 
dh  =  inside  diameter,  in  inches,  of  hollow  davit; 

m  =  the  ratio  -j-  • 
dh 

Boats  vary  considerably  in  weight,  small  ones  being  relatively 
heavier  than  large  ones,  and  weldless  steel  ones  heavier  than 
wooden  ones,  and  a  modification  of  the  constant  C,  rule  (2),  will 
sometimes  be  required.  This  can  easily  be  made  when  the 
maximum  weight  to  be  imposed  on  the  davits  is  known  and  the 
quantity  w  has  been  found  by  rule  (1).  In  the  case  of  weldless 
steel  boats  w  may  be  about  2.1  cwts.,  in  which  case  the  modi- 
fication of  the  constant  C  in  rule  (2)  will  be:  — 

C  X  2 

— J-: —  ■"  modified  constant. 


Dh< 

- 

Dh* 

Dh 

x3/ 

1  d* 

X  m4\ 

Board  of  Trade  Rules  for  Davits       447 


In  the  case  of  solid  iron  davits,  the  constant,  modified  as 
above,  will  be:  — 

86X2      82, 


and  for  steel  davits 


2.1 

104X2 
2.1 


Formula  (2)  applies  to  boats  of  sections  A,  B,  or  D,  in  which 
the  entire  cubic  capacity  is  measured  for  the  persons  carried, 
the  constant  C  being  reduced  or  increased  as  w  is  shown  to  be 
greater  or  less  than  2  cwts.  It  also  applies  to  boats  of  section  C 
when  the  weight  of  the  boat,  equipments,  and  persons  allowed, 


ivv— —  —  =  =  — 

t                       KK 

C                                                                 *S 

35  70                                        A 

-s                                                             V- 

°  An                                                     5        • 

t£  bU                                                                h 

~50                                                           A 

1                                                               \ 

"fcW                                                                 ~T 

c-30  ■                                          Y 

-20                                                                  j 

£m                                                             t 

o                                                         3 

0      10    20    30    40     50    60     70    80    90  100 
Dia,  of  Core  or  Hole  in  Percentage  of  Rod.Dia. 
Fig.  250. 


does  not  exceed  that  of  an  ordinary  wooden  boat  of  similar  size 
of  Section  A,  B,  or  D. 

In  the  case  of  davits  which  are  only  required  to  be  strong 
enough  to  carry  the  boat  and  equipments  and  a  sufficient  num- 
ber of  men  to  launch  it,  no  objection  need  be  raised  if  the  diam- 
eter is  not  less  than  that  found  by  formula  (2),  but  using  a 
constant,  C,  of  144  for  davits  of  untested  material. 

The  constants  given  for  steel  davits  are  on  the  understanding 
that  the  material  is  tested  and  found  to  be  within  the  limits 
given. 


448 


The   Naval   Constructor 
DAVIT   HEADS. 


HQ|«-!H 


Tons. 

A 

B 

c 

D 

g 

F 

G 

// 

j 

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L 

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0.9 
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2.3 
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if 
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11 

if 

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If 
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if 

if 
if 

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if 
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If 

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1  i 

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s 

Weights  of  Boats  and  Davit  Diameters    449 


WEIGHTS    OP    BOATS    AND    DAVIT   DIAMETERS. 


Diameter 


Dimensions 

*a 

h 

of  Boats. 

5Sx 

Build 

Ss3 
3g 

MS 

BE 

of 
Boat. 

Desckiption. 

L. 

B. 

D. 

fi« 

10 

4    3 

1    7 

670 

3  2 

£ 

Wood  clench 

Dinghy. 

12 

4    6 

1    9 

900 

3  4 

2| 

" 

14 

4    8 

1  11 

1,120 

3  6 

3 

" 

16 

4  10 

2    0 

1,350 

38 

11 

" 

18 

5    0 

2    0£ 

1,550 

3  9 

Cutter. 

20 

5    4 

2    2 

1,800 

40 

4 

M 

20 

5  10 

2    4 

2,000 

4  4 

4J 

"     carvel 

Yacht's  launch. 

22 

5  10 

2    4 

2,240 

4  4 

4£ 

"     clench 

Cutter. 

22 

6    0 

2   4 

2,450 

4  6 

4.1 

"     carvel 

Yacht's  launch. 

24 

7    3 

3   0 

2,450 

5  5 

4! 

"     clench 

Lifeboat. 

24 

6-  0 

2   9 

2,800 

4  6 

4| 

"     carvel 

Yacht's  launch. 

26 

7    6 

3   3 

2,700 

5  7 

.6§ 

M     clench 

Lifeboat. 

27 

5    9 

3    0 

5,600 

4  4 

3 

"     diagonal 

Steam  pinnace. 

28 

8    6 

3   8 

2,900 

6  4 

"      clench 

Lifeboat. 

30 

8    6 

3    8 

3,000 

64 

6 

II             u 

Lifeboat. 

30 

7    0 

3  10 

7,600 

5  3 

7I 

"     diagonal 

Steam  navy  pinnace. 

32 

7    4 

4   0 

7,850 

5  6 

7f 

M                II                   II 

36 

8    0 

4   3 

13,500 

60 

9 

II                II                   M 

40 

8    6 

4   9 

18,500 

6  4 

8   (3) 

M                II                   14 

42 

8    2 

4    6 

14,000 

6  2 

71(3) 
8|(3) 

Royal  barge. 

45 

8    6 

4    6 

21,300 

6  4 

Steam  navy  pinnace. 

47 

9    0 

4    6 

22,400 

69 

9    (3) 

"                M                   " 

50 

9    3 

5   8 

23,500 

7  0 

Crane 

II                II                   II 

56 

9    9 

4  10 

27,500 

7  4 

Crane 

II                  U                      II 

60 

9    6 

410 

28,500 

7  2 

Crane 

These  davit  diameters  are  figured  for  the  moment  exerted  with  the  shii 
inclined,  and  are  taken  for  a  fibre  stress  of  12,000  lbs.  per  square  inch,  witl 
one  davit  taking  the  entire  load. 


450 


The  Naval  Constructor 


NAVY    STANDARD. 
Hinged  Watertight  Doors. 


Size  of  Opening  in 
the  Clear. 

Dimensions  over 
Door  Frame. 

Breadth  of 
Frame. 

5  6x30 

i       ii            in 

6  lj  x  3  7 

5  6x22 
5  0x3  0 

6  lg  x  2  9 

5  7J  X  3  7 

3$  inches  each 
side  and  end  with 

5  0x20 
4  0x20 

5  7j  X  2  7 
4  1\  x  2  7 

I  inch   extra  on 
one  side  for  hinge 
pads. 

3  6x20 

4  lg  x  2  7 

2  6x16 

3  If  x  2:1 

Sliding  Watertight  Doors. 


/    //         /    // 

in           i     ii 

4  9x20 

5  6J  x  2  8 

4"  V.S.W.T.D. 

3  3x20 

4  0J  x  2  8 

4"  V.S.W.T.D. 

Sliding  Watertight  Doors 

SLIDING  WATERTIGHT  DOOR. 


451 


CAST  IRON  DOOR 


O 


WROT.IRON    FACING    BAR8 


"ITT 
JUL 


<w       O      O      O      O     /Cj""X\     o      o      o      o 


SECTION  AT  A.B. 


VWROT.IRON   FACING    BARS 


Pig.  252. 


452  The  Naval  Constructor 

HINGED    WATERTIGHT   DOOR. 


® 


te® 


m 


—^0 

Fig.  253. 


Details  of  W.  T.   Doors 

i 


453 


DETAIL  OF   DOGS 
Fig.  254. 


DETAIL  OF  HINGES 
Fig.  255. 


i:>4 


The  Naval   Constructor 


STANDARD    EYEBOLTS 


Fig.  256. 


A. 

5. 

c. 

D. 

E. 

i^. 

o. 

Breae 

AT 

Tons 

* 

A 

II 

H 

A 

H 

A 

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1 

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1A 

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if 

50 

Table  of  Fairleads 


455 


TABLE   OF  FAIRLEADS  (Cast  Iron). 
Single  Eoller. 


Fig.  257. 


Length 

of 

Ship  (Ft.). 

Unit 
Dimen- 
sion IN 
Inches. 
d. 

Approxi- 
mate 
"Weight  in 
Pounds. 

Length 

of 

Ship  (Ft.). 

Unit  Di- 
mension 

in 
Inches. 

d. 

Approxi- 
mate 
Weight  in 
Pounds. 

100 

3 

34 

470 

11 

1,670 

110    " 

H 

54 

490 

11$ 

1,907 

120 

4 

80 

520 

12 

2,167 

150 

H 

115 

550 

m 

2,450 

170 

5 

156 

570 

13 

2,750 

190 

H 

208 

600 

13* 

3,085 

200 

6 

271 

620 

14 

3,435 

215 

H 

345 

650 

U\ 

3,820 

240 

7 

430 

680 

15 

4,230 

280 

n 

530 

710 

15£ 

4,670 

300 

8 

644 

740 

16 

5,140 

330 

8* 

770 

760 

16£ 

5,635 

360 

9 

915 

780 

17 

6,165 

390 

n 

1,073 

800 

17* 

6,720 

410 

10 

1,253 

850 

18 

7,315 

440 

10£ 

1,452 

.... 

Weight  without  roller     =  ds  X  .6  =  lba. 
Weight  with  one  roller    =  d3  X  125. 
Weight  with  two  rollers  =  d3  X  1.5. 


456 


The  Naval  Constructor 


STANDARD   FLANGES   FOR   LEAD    PIPES. 

k-  -L- »| 


Bolt  Holes  Drilled 


note:  no  finish  on  ca8t  iron  flanges 
Fig.  258. 


Fbom  0  to  100  Pounds  Pressure. 

N 

s 

A. 

£. 

c. 

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Standard  Pipe  Flanges 


PIPE   FLANGES,  STANDARD. 


457 


Fig.  259. 


J 

From  0 

to  100  Pounds  Pressure  per  Square  Inch. 

1H 

&£ 

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The  Naval  Constructor 


STANDARD   FLANGES    FOR   VENTILATION. 


ft—  -Vi — * 


T" 

.to 


r 
i 


- 


I* 

B  ^ 


m;^ 


^ 


L 


Figs.  260  to  262. 


Inside 
Diameter 

OF 


Pipe. 


Flange. 


Bolts. 


No. 


Size 


Inside 

Diameter 

or 


Pipe. 


8* 

9 

9* 
10 
10* 
11 

Hi 

12 

12* 

13 

13* 

14 

14* 
15 
15* 
16 


Flange. 


Bolts. 


No. 


Size, 


a 


Inside 

Diameter 

of 


Pipe. 


16* 

17 

17* 

18 

18* 

19 

19* 

20 

20* 

21 

21* 

22 

22* 

23 

23* 

24 


Flange. 


Bolts. 


No. 


Size. 


Hand  Wheels 


459 


HAND   WHEELS    (Iron). 


Fig.  263. 


Diameter. 

No. 

A. 

B. 

a 

x>. 

E. 

F. 

G. 

H. 

.  JC 

Arms. 

2 

" 

i 

1 

A 

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460 


The  Naval  Constructor 


HAND    WHEELS    (Brass). 


Fig.  2<&. 


DlAM., 
A. 

B. 

a 

2).   • 

J?. 

<?. 

H. 

JT. 

No.  OF 
Arms. 

n 

i 

A 

A 

1 

i 

n 

A 

i 

4 

2 

A 

1 

1 

i 

i 

A 

4 
4 

3 

A 

1 

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A 

A 

4 

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if 

A 

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f 

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4 

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A 

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ft 

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4 

8 

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A 

6 

f 

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it 

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Keys  and  Keyways. 


KEYS    AND    KEYWAYS. 


461 


D 
W- 

T 
Taper  = 
t- 
T-t- 


diameter  of  shaft  in  inches. 

width  of  key  and  key  way  in  inches, 

thickness  of  key  =  ¥3^  D  +  \". 
\"  per  foot. 

depth  in  shaft  )  measured  at  the 
depth  in  hub    )      side. 


Fig.  265. 


D. 

fT. 

T. 

t. 

r— *. 

D. 

w. 

T. 

t. 

T-t. 

\ 

6 

A 

tV 

i 

5 

4 

ii 

f 

i 

t 

f 

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A 

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1* 

f 

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f 

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l 

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462 


The  Naval  Constructor 


HAWSE  PIPE  PROPORTIONS 

(8EE  TABLE  OF  WEIQHT8) 


CHAIN  CABLE  =  UNIT. 


-4  =  9.0,  B=.6,  C  =  .7,  D=.5,  J?  =  3.6,  F=5.0,  £  =  4.7. 


Hawse  Pipe   Weight 


463 


HAWSE   PIPE    WEIGHT   FOR    STOCKLESS 
ANCHORS. 

{Including  Pipe,  Lips,  and  Deck  Ring.) 


Cable 

Weight  of 

Cable 

Weight  op 

(Stud  Link). 

Hawse  Pipe. 

(Stud  Link). 

Hawse  Pipe. 

Ins. 

Lbs. 

Ins. 

Lbs. 

1 

1,000 

m 

4,400 

h\ 

1,030 

2| 

4,700 

n 

1,060 

2yV 

5,100 

h\ 

1,100 

2i 

5,500 

n 

1,200 

2A 

6,000 

4 

1,300 

2f 

6,500 

ii 

1,400 

w 

7,100 

h\ 

1,500 

2| 

7,700 

M 

1,560 

m 

8,500 

H9* 

1,700 

21 

9,300 

If 

1,800 

2}f 

10,200 

Hi     • 

2,000 

3 

11,400 

if 

2,100 

StV 

12,750 

HI 

2,300 

31 

14,000 

if 

2,500 

SA 

15,500 

HI 

2,700 

3i 

16,500 

2 

3,000 

8A 

18,000 

2TV 

3,200 

3f 

19,500 

2J 

3,400 

3TV 

21,000 

2A 

3,750 

3i 

22,500 

21 

4,000 

.    .   . 

.... 

M.B.  —  Weights  given  are  for  one  pipe. 


4G4 


The   Naval   Constructor 


HOOKS,   VARIOUS. 


Barrel  Hook. 


Bale  Hook. 


Figs.  267  to  271. 


Cargo  Hooks 

CARGO    HOOKS. 


465 


Fig.  272. 


Load. 

A 

B 

c 

D 

E 

F 

G 

# 

J 

K 

Tons. 

// 

„ 

// 

,i 

,, 

„ 

„ 

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3 

4 

1 

3 

4 

7 
8 

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If 

2 

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21 

2 

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7 
8 

14 

7 
8 

1 

ii 

14 

3 

6 

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2| 

2i 

U 

X\ 

H 

14 

14 

14 

4 

74 

34 

3* 

21 

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If 

l 

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2* 

5 

8* 

4J 

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2| 

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14 

14 

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2f 

Load. 

L 

M 

AT 

0 

p 

Q 

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a 

T 

u 

7 

Tons. 

// 

a 

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// 

„ 

„ 

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1 
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1 

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8 

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7 
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3 

4 

H 

5 

14 

2| 

44 

l 

34 

4 

5 

8 

H 

1 

1 

H 

hili 


The   Naval   Constructor 


SWIVEL   HOOKS. 


Fig.  273.    QJ 


Unit 
D. 

Working 
Load,  Lbs. 

Dimensions  of  Hook,  in  Inches. 

Weight 
in  Lbs. 

A 

5 

C 

E 

F 

(? 

tf 

/ 

t" 

700 

2H 

H 

n 

hi 

A 

H 

U 

* 

0.4 

H 

880 

m 

J  A 

K 

H 

1 

H 

* 

0.55 

R 

1100 

3a 

1A 

ii 

£ 

H 

r 

A 

* 

0.8 

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1320 

W 

ia 

ift 

A 

H 

H 

A 

1.01 

1 

1720 

3HI 

H 

X 

8 

H 

1A 

K 

A 

1.45 

1A 

2160 

*M 

\h 

y 

§i 

r- 

if 

f! 

A 

2.2 

If 

2820 

5A 

ill 

i» 

& 

A 

3.3 

lU 

3530 

5HA 

2* 

til 

1ft 

H 

If 

H 

P 

4.2 

1  » 

4450 

«A 

2h 

4 

H 

H 

l 

7.0 

5500 

7A 

$ 

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H 

m 

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9.3 

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l|{ 

1A 

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11.7 

2A 

8380 

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1A 

2 

Hi 

A 

13.3 

Unit 

Working 
Load,  Lbs. 

Dimensions  of  Swivel,  in  Inc 

HES. 

Weight 
in  Lbs. 

K 

L 

11 

M 
i 

O 
h 

P 

M 

R 

A 

T 

V 

1  " 

700 

M 

A 

ti 

0.4 

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880 

H 

1H 

H 

H 

H 

| 

ft 

t 

A 

0.55 

1' 

1100 

H 

H* 

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f 

A 

M 

Is 

0.8 

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A 

W 

IA 

(S 

1 

H 

1.01 

l 

1720 

U 

2A 

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H 

H* 

I A 

'4* 

1.45 

if- 

2160 
2820 

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2A 

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if 

1? 

1A 

P 

If 

P 

2.2 
3.3 

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1H 

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A 

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5500 

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if 

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11.7 

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8380 

4M 

>A 

1» 

Hi 

2* 

l 

H 

L| 

13.3 

Trip   Hooks 


467 


TRIP   HOOKS. 


Fig.  274. 


A 

B 

c 

D 

E 

f 

G 

H 

j 

A' 

L 

M 

N 

0 

p 

fi 

s 

1 

2 

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8 

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H 

8 

1 

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8 

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8 

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8 

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4 

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3 
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8 

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7 
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H 

8 

4| 

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The  Naval   Constructor 


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Fig.  275. 


3S.i. 


Fig.  276. 


470 


The   Naval   Constructor 


REVERSIBLE   PAD-EYE. 


5U.S.S.ThnperInch 


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^FT~?* — =^=^ — **  / 

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Fig.  277. 


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471 


LEWIS  BOLT. 
->*- 3f--->, 


f w~** 


1  >i  j  C-  %ts    ,  J —  Note.  Cover  to  be  Carefully 

.*-,/■.,  IT       Fitted  toSocket 


Fig.  278. 


472 


The   Naval   Constructor 


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The   Naval   Constructor 


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o 

0 

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2° 

to 

a 

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I 

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h  9^C  9  «  M 

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r* 


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11 
II 


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Si 

§t 


Strength  of  W.   I.   Pipe 


475- 


+38J  U|  Sdy  }QlijBu3-\ 


476 


The  Naval   Constructor 


PLUG    COCK   KEYS. 


Fig.  282. 


A. 

-B. 

a 

2). 

E. 

.F. 

G. 

L. 

•/ 

// 

// 

// 

// 

// 

" 

// 

| 

I 

f 

I 

H 

A 

A 

5 

1 

I 

1 

f 

I 

A 

A 

6 

! 

l 

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1 

1 

7 

11 

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H 

| 

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1 

1 

8 

n 

A 

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1 

l 

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1 

8J 

it 

A 

H 

1 

l 

A 

4 

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if 

s 

if 

11 

n 

I 

10* 

it 

A 

if 

H 

if 

I 

♦ 

11 

if 

j 

l| 

if 

if 

1 

A 

12 

ij 

f 

1} 

if 

if 

A 

A 

13 

2 

f 

if 

H 

if 

A 

14 

21 

1 

if 

}$ 

i* 

A 

A 

15 

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a 

2 

if 

if 

f 

i 

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f 

i 

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if 

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s 

17J 

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lj 

if 

1 

18 

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A 

2| 

if 

If 

I 

1 

19 

2J 

1 

2| 

If 

11 

1 

1 

20 

3 

I 

2i 

l| 

2 

f 

A 

21 

Strength  of  Rings 


477 


ggg; 


UJ00P3O0CI*«NO>«iO00 
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Si 


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478 


The  Naval  Constructor 


3UIM  JO  U3X3WVIQ 


Proportions  of  Rings 


479 


TABLE  II. — Proportions  of  Rings  for  Standard 
Short-link  Chains. 


!5B"  Chain. 

!" 

Chain. 

IB 

Chain. 

\" 

Chain. 

P.L.  1*  Tons. 

P.L. 

|  Tons. 

P.L. 

2\  Tons. 

P.L. 

3  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

T6 

1 

A 

i\ 

5 

8 

13- 

H 

1A 

4 

1ft 

5 

8 

z-k 

44 

2 

f 

If 

ft 

2A 

H 

3 

3 
4 

2} 

}t 

24 

5 

3A 

f 

4A 

if 

3| 

8 

3A 

4 

4*4 

If 

5& 

7 
8 

4H 

44 

4& 

&4 

8 

61 

fl 

5M 

1 

64 

1 

7A 

IA 

6A 



14 

71 

iV  Chain. 

1" 

Chain. 

H" 

Chain. 

\"K 

2hain. 

P.L.  3|  Tons. 

P.L.  < 

If  Tons. 

P.L.  5|  Tons. 

P.L. 

3f  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

H 

U 

1 

8 

W 

it 

i! 

IA 

2i 

I 

2^ 

1* 

2| 

1 

2& 

14 

2H 

H 

3^ 

1 

3A 

IA 

m 

1A 

3A 

l 

4 

IA 

3H 

1* 

3| 

14 

4| 

1A 

4^ 

14 

4f 

IA 

4& 

1A 

4f« 

}4 

5f| 

IA 

5& 

14 

64 

H 

5H 

iA 

74 

H 

6f 

IA 

6& 

1A 

6f 

i| 

»A 

IA 

7M 

if 

74 

14 

7| 

if 

9| 

IA 

8f 

1A 

9 

li 

9|      • 

if 

10i 

480 


The  Naval  Constructor 


TABLE  II. 

—  (Con 

tinued.) 

\i"  Chain. 

i"  Chain. 

H"  Chain. 

1"  Chain. 

P.L.  7ft  Tons. 

P.L.  9J  Tons. 

P.L.  10§  Tons. 

P.L.  12  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

1* 

i 

H 

21 

lft 

2H 

1* 

2f 

lft 

If 

3& 

If 

31 

lft 

3& 

H 

a| 

3tf 

lft 

31 

n 

3| 

1ft 

4 

lft 

4H 

1* 

4 

lft 

4ft 

it 

4f 

14 

5A 

lft 

51 

if 

5 

1ft 

5& 

lft 

gj 

1  5 

Is 

6 

IH 

5} 

1| 

6^ 

ll 

7& 

IH 

61 

If 

6* 

lft 

71 

If 

8& 

If 

7\ 

Iff 

7A 

If 

8* 

91 

if* 

8f 

U 

8f 

l» 

9H 

1*1 

10| 

9tf 

iff 

2 

9f 
10ft 

1A" 

Dhain. 

H"  Chain. 

i&" 

Chain. 

1J"  Chain. 

P.L.  K 

}  Tons. 

P.L.  15*  Tons. 

P.L.  1 

3/(,  Tons. 

P.L.  181  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

3& 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

H 

3& 

lft 

If 

3^ 

If 

3A 

lft 

m 

If 

m 

IH 

3& 

IH 

41 

11 

4A 

1« 

U 

If 

41 

H 

4ft 

lh 

4M 

If 

41 

ih 

4tt 

i+f 

6ft 

1! 

51 

ill 

5& 

u 

5f 

2 

6 

Iff 

6A 

u 

6A 

ill 

6^ 

2V* 

6^ 

u 

7& 

W 

7^ 

2 

6H 

21 

7A 

in 

81 

2 

7ii 

2tV 

7& 

2^ 

8 

2 

9 

2^ 

88 

2| 

8| 

21 

91 

2^ 

10 

2| 

9f 

2A 

9A 

2ft 

10 

2* 

m 

2ft 

10H 

21 

101 

2f 

11 

21 

HI 

2A 

HI 

2^ 

12 

2f 

12f 

24 

13ft 

Proportions  of  Rings 


481 


TABLE  II.  —  (Continued.) 


1TV'  Chain. 

If"  Chain. 

1T7B"  Chain. 

li"  Chain. 

P.L.  20|  Tons. 

P.L.  22f  Tons. 

P.L.  24f  Tons. 

P.L.  27  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

11 

1*1 

2 

2^ 

2| 

2& 

2j 

2^ 

2f 

2A 

2} 

2A 

2| 

4& 

4| 

5| 

5| 
6& 

8« 

9f 
10tt 
HI 
12H 
13f 

lit 

2 

2& 

2| 

2^ 

2J 

2| 

2^ 

2£ 

2& 

2f 

2H 

2| 

4& 

4f 

5^ 

5| 

6| 

7| 

m 

9^ 
10A 
111 
12} 

13A 

14| 

2 

2A 

2| 

2^ 

2| 

2A 

2| 

2A 

2* 

2& 

2| 

2ft 

2i 

2H 

21 

4& 

4& 
6* 

5| 
6f 

m 

7f 
8& 
9& 
10J 

11 

12« 
13*1 
15* 

2 

2A 

2J 

2A 

2| 

2^ 

2£ 

2& 

2| 

2ft 

2! 
24i 

21 

2ft 
3 

H 

4& 

e* 

61 

7* 

81 

9^ 

91 

ioU 

in 

12ft 

13£ 
MA 

15| 

M.S.  =  Minimum  size  of  iron  in  ring. 
M.I.D.  =  Maximum  internal  diameter  of  ring. 
(P 


P.L.  -  Proof  load  -  18.7  ^  , 
d  =  dia.  of  iron  in  ring, 

where 

and 

D  m  mean  dia.  of  ring. 

Safe  load  =  One  half  the  proof  load. 

482 


The  Naval  Constructor 


TABLE  III.  —  Proportions  of  Rings  for  Double-leg 
Sling-Chains. 


ft"  Chain. 

|"  Chain. 

/a"  Chain. 

1"  Chain. 

P.L.  21  Tons. 

P.L.  31  Tons. 

P.L.  4J  Tons. 

P.L.  6  Tons 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

5 
8 

U 

4 

If* 

$ 

Iff 

1 

24 

1* 

2 

H 

2J 

H 

n 

1* 

2*4 

2f 

i 

3 

l 

3A 

ll 

3& 

tt 

3* 

ft 

3J| 

1* 

3$ 

1* 

4^ 

i 

4ft 

l 

4| 

14 

4|i 

5| 

If 

41 

$ 

m 

1* 

j>4f 

1* 

Iff 

5! 

i 

7« 

1* 

7A 

H 

61 

If 

6| 

1* 

8« 

1* 

8^ 

1* 

8& 

1* 

7A 

l* 

10| 

if 

10 

if 

9T7s 

ll 

9 

1* 

10| 

1* 

10f 

/B"  Chain. 

f  "  Chain. 

U"  Chain. 

I"  Chain. 

P.L.  7J  Tons. 

P.L. 

91  Tons. 

P.L.  Hi  Tons. 

P.L.  131  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

1* 

JA 

i'i 

f 

11 

2*f 

11 

3& 

1* 

3 

l* 

1* 

3i 

1* 

m 

H 

3f 

if 

3| 

11 

4i 

If 

4  *■ 

1* 

4* 

i* 

4& 

1* 

4H 

1*4 

4# 

11 

6| 

i* 

5& 

14 

51 

if 

6f 

1* 

5« 

l* 

6& 

m 

6* 

m 

6^ 

ll 

erf 

it 

7A 

if 

7| 

if 

7H 

l* 

7^ 

m 

8 

ill 

8^ 

i*f 

84 

If 

9& 

if 

9& 

ii 

9^ 

2 

9 

1 

10* 

m 

10* 

i« 

10| 

2tV 

10 

U* 

ii 

11* 

2 

n! 

2f 

114 

2^ 

12| 

2A 

124 

Proportions  of  Rings 

TABLE  III.  —  (Continued.) 


483 


ijj"  Chain. 

J"  Chain. 

tt" 

Chain.    • 

1"  Chain. 

P.L.  15$  Toi 

18. 

D. 

P.L.  18i  Tons. 

P.L. 

21  Tons. 

P.L.  24  Tons. 

M.S. 

M.I. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

n 

aft 

n 

3! 

If 

4 

2 

4 

i« 

4 

in 

a 

ltf 

4£ 

2ft 

a 

i| 

4ft 

i* 

4| 

2 

51 

2| 

5| 

ifc 

5ft 

m 

5| 

2ft 

5f 

2ft 

6 

n 

51 

2 

6| 

2* 

6ft 

2| 

6| 

m 

8 

2ft 

Sff 

2ft 

7f 

2}| 

7ft 

2 

7ft 

2£ 

7H 

% 

71 

2* 

8ft 

2ft 

8ft 

2ft 

8| 

2ft 

8H 

2ft 

8| 

2* 

9ft 

2J 

91 

2| 

9ft 

2* 

9H 

2ft 

10ft 

2ft 

10ft 

2ft 

10ft 

2ft 

10ft 

2i 

lift 

2* 

lift 

2* 

lift 

2| 

HI 

2A 

12ft 

2ft 

12ft 

•2ft 

12ft 
13| 

2H 

12ft 

n 

13ft 

2* 

13± 

2| 

2! 

13| 

2H 

14ft 

2il 

14ft 

W»"C 

HAIN. 

li"  Chain. 

P.L.  27 

Tons. 

P.L.  30J  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

2i 

4£ 

2i 

4^ 

1 

* 

5 

2^ 

r 

5| 

5f 

2* 

5^ 

I 

2ft 

6ft 

2^ 
2i 

6t 

V 

2* 

6| 

7t 

* 

2ft 

n 

2t* 

T 

7^ 

4 

81 

n 

8| 

2ft 

9ft 

2f 

r 

9, 

% 

4 

9| 

2f 

idj 

24* 

1QH 

2f 

1 

11 

2f 

HI 

n 

llj 

2H 

12ft 

2f 

i 

m 

1 

2f 

13J 

3 

m 

2^ 

14ft 

3^ 

14| 

3 

15f 

3i 

15i 

1 

484 


The   Naval  Constructor 


TABLE  IV.  — Proportions  of  Rings  for  Three-leg 
Sling-Chains. 


A"  Chain. 

I"  Chain. 

/B"  Chain. 

P.L.  3|  Tons. 

P.L.  4J  Tons. 

P.L.  6f  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

It 

1ft 

3f 

4# 
5& 

6f 

8& 

if 

1ft 

If 
1ft 

a 

7f 
8f 

m 

}ft 

If 

If 

|ft 

If 

i| 

4M 

i 

7| 

9 

10* 
111 

13f 

i"  Chain. 

TV'  Chain. 

f  "  Chain. 

P.L.  9  Tons. 

P.L.  11 J  Tons. 

P.L.  13J  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

a 

1* 
1ft 

If 
ltt 
If 
1« 

lit 

6| 

6f 
7& 
8& 
91 

10ft 

Hi 

13ft 

11* 
iji 
if 
lit 

2 

2^ 

2f 

2& 

6i 

n 

8^ 
9& 

10* 

Hi 

m 

13« 
15ft 

If 

1.U 

2 

2^ 

2f 

2^ 

21 

Jft 

2f 

7^ 
7| 

8tf 
9H 

ioi| 
n« 

13* 

14f 
15f 

Proportions  of  Rings 

TABLE   IV.  —  (Continued.) 


485 


\l"  Chain. 

J"  Chain. 

J|"  Chain. 

P.L.  161  Tons. 

P.L.  20J  Tons. 

P.L.  23/s  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

2& 

7& 

2* 

81 

2^ 

9 

21 

8£ 

2ft 

8*f 

24 

m 

2ft 

9^ 

2f 

9M 

2& 

ioi 

2} 

10f 

2^ 

io|§ 

2| 

ntt 

2ft 

lift 

2* 

m 

2tt 

12| 

2f 

12| 

2& 

13 

2| 

13H 

2^ 

13f 

2f 

14 

2M 

ii| 

2| 

14H 

2H 

ISA 

21 

151 

2& 

16* 

21 

16| 

2« 

17ft 

2f 

17ft 

2H 

17f 

3 
3ft 

18ft 

19tt 

J"  Chain. 

H"c 

HAIN. 

P.L.  27|  Tons. 

P.L.  31 

i  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

21 

9H 

2*§ 

10f 

2H 

101 

21 

m 

2! 

Hf 

m 

12ft 

2M 

12ft 

3 

13 

21 

13i 

3A 

14 

2H 

l4 

31 

15 

3 

15f 

3& 

16 

3A 

16ft 

H 

171 

31 

171 

3A 

181 

3& 

181 

3f 

19ft 

si 

20| 

3A 

20H 

486 


The   Naval   Constructor 


TABLE   V.  -  Proportions  of  Rings  for  Four-leg 
Sling-Chains. 


A"  Chain. 

I"  Chain. 

XV'  Chain. 

P.L.  4|  Tons. 

P.L.  6J  Tons. 

P.L.  9  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

1* 

n 

\t 

61 
8& 

1ft 

If 

1ft 

If 

1ft 

71 
8| 
9ft 

1ft 
U 

m 

H 

5* 

6f 
7ft 
8ft 
9f 

10ft 

HI 

i"  Chain. 

A"  Chain. 

f "  Chain. 

P.L.  12  Tons. 

P.L.  15  Tons. 

P.L.  18*  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

U 

lji 
if 

2 
21 

6* 

7ft 

Si 

9f 
10ft 
lift 
12^ 

l4 
If 

2 

2| 
2A 
2§ 
2A 

2f 

5ft 
gA 

7ft 
8 
81 
9f 

ion 

HI 

13ft 

14i 

2 

2ft 

21 

2A 

2i 

2ft 

21 

2ft 

2i 

2ft 

2f 

2H 

6ft 

m 

h\ 

8§ 

9i 
10^ 
HI 
12A 
13i 
14ft 
15H 
16M 

Lengths  of  Countersink  Point  Rivets     487 

TABLE    V.— (Continued.) 


W  Chain. 

J"  Chain. 

il"  Chain. 

P.L.  22*  Tons. 

P.L.  27  Tons. 

P.L.  31  f  Tons. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

M.S. 

M.I.D. 

2t3s 

21 

2A 

2f 

2^ 

2* 

2A 

2| 

2H 

2f 

2tt 

2| 

2M 

6* 

7il 

8f 

9& 

10A 

Hf 
12f 

13ft 
14J 

15| 
161 

ISA 

2^ 

2£ 

2& 

2f 

2& 

2f 

2H 

2| 

2*| 

3 

3A 

3| 

3A 

3| 

7h 
81 

9A 
9£ 

io« 

Hi 
12ft 
13} 
14ft 

15f 

16ff 

18 

19i 

20ft 

2f 
2H 

2| 

2tf 

2* 

2M 

3 

3^ 

3|s 

3tI 

31 

3ft 

3| 

3^ 

3* 

8| 

9f 

10$ 

.  1U 

12^ 

13 

14 

15 

16 

TO 
181 

19^ 
20H 
22 

THE   ORDERED   LENGTHS    OF   COUNTERSINK 
POINT  RIVETS. 

1.  The  following  curves  for  ordering  countersink  point  rivets 
are  based  on  the  U.  S.  Navy  standard  rivets  and  countersink. 
Curves  should  be  read  to  the  longest  "ordered  length." 

2.  Where  more  than  two  thicknesses  are  connected,  add  \" 
to  each  extra  thickness. 

3.  Length  of  snap  point  rivets  use  the  rule:  total  thickness 
of  plates  +  one  diam.  -+-  }"j    except   for   excessive   thickness, 

add  \" . 

4.  For  hydraulic  riveting  add  1"  to  the  length  required  for 
hand  or  machine  work. 

5.  The  curves  for  f"  to  f"  rivets  are  computed  -fa",  and  f" 
to  1"  rivets,  \"  longer  than  required  to  theoretically  fill  the  hole. 

6.  The  type  of  head  has  no  bearing  on  the  ordered  length. 


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FIG.  290. 


Standard  Shackles 


497 


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Anchor  Shackles. 


Fig.  291. 


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STANDARD    SHACKLES    (As   Manufactured). 

(Continued.) 

Chain  Shackles. 


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Iron 

Iron 

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The   Naval  Constructor 


SCREW  STEERING  GEARS.  —  (Continued.) 


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509 


,       Fil/mg  Piece  above  Flai Bar 


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Fig.  301. 


510 


The   Naval   Constructor 

DECK    SEATS. 


Fig.  302. 


Deck  Seats 


511 


DECK    SEATS. 


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Fig.  303. 


512 


The   Naval  Constructor 


WEIGHTS    OF   BRASS    FRAMED    SIDELIGHTS. 


Diameter 
(Clear  Glass). 

Description. 

Brass. 

Glass. 

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In. 

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Proportions  of  Chain  Slips 


513 


PROPORTIONS    OF    CHAIN    SLIPS. 


Fig.  304. 


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514 


The   Naval   Constructor 

BOOM   MOUNTINGS. 


Boom  Mountings 


515 


BOOM  MOUNTINGS. 


Diameter  of 

Shoe. 

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1 

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1 

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n 

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(From  Middendorf'a  "Bemastung  und  Takelung  der  Schiffe,"  by  permission 
of  the  Publishers.) 


516 


The  Naval  Constructor 

BOOM   MOUNTINGS. 


Fia.  306. 


Spider  Bands 


517 


SPIDER    BANDS. 


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Approx.  Rule 


Breadth 


"  =  .8  "^diam.  of  spar 


Thickness  "b"  =  .17  v'diam.  of  spar 


518 


The  Naval   Constructor 


TORPEDO   NET   DETAILS. 

Roebling'8  System. 

,-  I ^'DiaTurn  buckle 


I'Dia.  6'x7  Wire  /(ope  bah.PfoW, 


Net 


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^tfte/Catfi/iy 


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V'Dict  Bronze  Pins 


<33I 


Figs.  307-309. 


Gaff  Mountings 

GAFF  MOUNTINGS. 


519 


Fig.  310. 


520 


The   Naval   Constructor 


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521 


Fig.  311. 


522 


The  Naval   Constructor 


GAFF   MOUNTINGS. 


Fig.  312. 


Stuffing  Boxes  and  Glands 


523 


Fig.  313. 


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524 


The  Naval  Constructor 


THIMBLES   FOR   WIRE   ROPE. 


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525 


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Fig.  315 


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526 


The  Naval   Constructor 


Fig.  316. 


Admiralty  Turnbuckles 


527 


ADMIRALTY   TURNBUCKLES,   ETC. 
Steel  "Wire  Rigging. 


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121 

45 

H 

35 

31 

if 

21 

1           i 

?2 

4 

31 

u 

71 

5 

2f 

5 

31 

u 

6 

21 

If    3 

2| 

4j 

u 

35 

31 

2 

24 

U      s 

52i 

4 

31 

If 

71 

55 

21 

1 

31 

m 

65 

21 

2A3 

2f 

45 

15 

35 

31  2 

24 

11  * 

9  21 

4 

35 

If 

71 

51 

2f 

1 

31 

m 

H 

21 

2A3 

2f 

S 

If 

35 

3f  2 

24 

U        3 

*2* 

4 

31 

2 

71 

55 

3 

l 

31 

121 

61 

n 

2A3 

b  2f 

5.1 

11 

41 

3|  2 
i 

24 

H    i 

5  2i 

4 

31 

2 

8 

H 

3 

1 

31 

13 

71 

2f 

2A3 

b  21 

542 


The  Naval  Constructor 


FRICTION   BRAKE   FOR   CRANES. 

The  crane  brake  is  solely  for  the  purpose  of  preventing  the 
load  from  falling  when  there  is  no  other  sustaining  force  and 
preventing  the  load  from  falling  faster  than  desired  when  lower- 
ing. Incorrect  disposition  of  the  friction  of  a  brake  in  relation 
to  the  load  and  power  makes  its  purpose  unattainable,  and  an 
improper  proportion  of  friction  to  load  makes  its  operation  doubt- 
ful and  unsatisfactory,  causing  it  to  either  slip  or  stall  the  motor 
when  trying  to  lower.  The  general  features  of  brake  friction 
brakes  are  as  follows:  A  cam  in  some  part  of  the  transmission 
mechanism  is  so  designed  that  the  downward  pressure  of  the 
load  causes  an  axial  pull  in  the  shaft  which  presses  friction 


Fia.  323,— Cone  Brake  "  Naval  "  Boat  Crane  Full  Load  Torque  =  7880 In- Lbs. 

surfaces  together.  The  outer  casing  or  barrel  is  allowed  to 
rotate  with  the  other  parts  when  hoisting,  but  prevented  from 
rotating  when  lowering  by  ratchet  and  pawls  or  band  brake. 
Lowering,  then,  is  always  accompanied  by  relative  motion  between 
the  friction  discs  or  cones  and  whatever  friction  is  developed 
between  these  tends  to  prevent  the  load  from  lowering  and  must 
necessarily  be  overcome  or  relieved.  The  proper  arrangement 
of  friction  brakes  is  obtained  by  dividing  the  friction  between 
the  power  and  load  ends  of  brake,  half  being  on  the  motor  side 
and  half  on  the  load  side  of  the  cam.  Examples  of  this  type 
are  shown  in  the  cone  brake  for  a  gantry  crane  and  in  the 
Seller's  type  of  disc  friction  brake  supplied  for  naval  boat  cranes. 
The  reasons  for  this  arrangement  will  be  developed  in  the  follow- 
ing discussion. 


. 


Friction   Brake  for  Cranes 


543 


Fig.  324. 


Case  I.  —  Two  friction  brakes  designed  with  all  the  friction 
on  the  load  side  of  cam  as  shown  on  accompanying  sketches, 
Figs.  323  and  325,  one  taken  from  the  automatic  brake  for  boat 
crane  of  battleship  and  the  other  being  the  brake  supplied 
by  the  builders  of  the  gantry  crane.  This  arrangement  of 
friction  is  entirely  erroneous,  as  the  motor  must  always  keep 
some  force  on  the  cam  to  prevent  the  friction  surfaces  from 
separating,  and  allowing  the  load  to  slip.  Suppose  AO,  Fig.  324, 
to  represent  the  force  required  to  overcome  the  load,  applied  at 
mean  radius  on  the  cam,  OB  represents  the  axis  of  the  shaft. 
If  in  a  given  design  we  assume  that  an  axial  pull  of  OC  is  required 

to  cause  sufficient  friction  to 
overcome  the  load,  GG  will 
represent  the  slope  of  a  cam 
which  will  just  supply  the 
requisite  pull.  OD  is  its 
normal  pressure,  and  AD  = 
OC  is  the  axial  component. 
With  cam  GG  the  friction 
of  the  brake  just  balances 
the  load  supported  by  AO. 
When  this  brake  is  lowering 
and  the  motor  withdraws  its  pressure  against  the  cam,  the  load  will 
drop  until  it  overtakes  the  power  side  of  the  cam  and  causes  a 
normal  pressure  with  an  axial  component  sufficient  to  again  set  up 
the  frictions.  This  same  normal  pressure  always  tends  to  drive 
the  motor  downward  and  it  will  thus  be  seen  that  even  when  the 
load  is  being  lowered  the  motor  must  exercise  a  force  against  the 
cam  in  the  direction  tending  to  lift  the  load.  Thus,  with  the 
above  cam  GG  and  axial  component  OC,  we  find  by  drawing 
the  balance  diagonal  AC,  that  in  lowering  at  constant  speed, 
one-half  of  the  load  is  overcome  by  the  friction  of  the  brake, 
see  AL,  and  the  other  half  has  to  be  overcome  by  an  upward 
pressure  of  the  motor,  see  OL.  Suppose  we  represent  by  R  the 
ratio  of  the  axial  pull  in  the  shaft  due  to  hoisting  full  load  to 
the  axial  pull  required  to  just  balance  the  load.  In  the  case 
above,  R  =  1.  Suppose  R  =  2,  the  axial  component  being 
AE  =  2  OC,  we  find  that  when  lowering  at  constant  speed 
the  friction  of  the  brake  overcomes  AM  =  f  of  the  load,  and 
the  motor  has  to  supply  OM  =  f  of  the  load  in  the  direction 
tending  to  lift  the  load.  Again,  if  R  =  3,  the  axial  component 
=  AF  =  3  OC,  and  the  motor  lowers  with  \  load  supported  by 
the  motor,  ON,  and  f  load  supported  by  the  friction  of  the  brake, 

AN.     Thus,  if  R  =  n,  the  lowering  will  take  place  with  — — :  of 

the  load  overcome  by  friction  in  the  brake  and  — t-^c  supported 

n  +  1 


r,4i 


The  Naval  Constructor 


by  a  raising  pressure  on  the  motor  side  of  the  cam.  In  a  brake, 
with  all  of  the  friction  on  the  load  side  of  the  cam  it  is  obvi- 
ously impossible  to  check  the  tendency  of  the  load  to  drop 
without  maintaining  an  upward  pressure  on  the  motor  side  of 
the  cam  so  as  to  keep  the  friction  set.  The  main  object  of  an 
automatic  brake  is  therefore  impossible  to  obtain  with  this 
arrangement,  and  the  motor  is  run  backward  against  the  force 
which  it  has  to  apply  on  the  cam  in  order  to  keep  the  friction 
surfaces  operative.  The  best  that  can  be  done  with  this  arrange- 
ment is  to  make  the  value  of  R  as  large  as  possible,  by  using 
say  8  to  10  degrees  angle  of  cones  and  as  small  a  lead  of  cam  as 

the  shaft  will  stand,  thereby  reducing  the  value  — — -.  to  be 

supported  by  the  motor.  A  magnetic  clutch  on  the  motor,  or 
great  friction  of  bearings  is  necessary  to  hold  the  cam  in  such  an 
arrangement  when  power  is  cut  off  from  motor. 

Calculation  of  Cone  Brake  for  Gantry  Crane. 

The  full-load  force  on  25,^-inch  pitch  diameter  gear  is   2400 

25  l 
pounds.     The  torque  then  is  2400  X  -=*  =  30,400  inch-pounds. 

m 

fleshts  with  Motor  Pinion 
Load 1400 Lbs 


ZO'Slopt 


Fig.  325.  —Cone  Brake  for  Gantry  Crane  Full  Load  Torque  =  30,400  In-Lbs. 


Taking  the  mean  radius  of  the  brake  cones  as  9^  inches,  the  force 

of  friction  required  at  this  radius  is    •   '  _     =  3200  pounds. 

Then  if  we  assume  a  coefficient  of  friction  of  0.1  between  the 
friction  surfaces,  the  normal  pressure  required  on  the  cones  will 


Friction   Brake  for  Cranes 


545 


be  32,000  pounds.  This  has  to  be  obtained  by  a  suitable  angle 
of  cam  in  combination  with  the  slope  of  the  friction  cones.  Tak- 
ing the  mean  radius  of  the  cam  as  3  inches  we  get  — '-x —  =  10,133 

o 

pounds  tangential  pressure. 

Referring  to  diagram,  Fig.  327,  OB  represents  the  axis  of  brake 
shaft.  Laying  down  this  cam  pressure  to  the  scale  of  10,000 
pounds  =  1  inch  we  obtain  OA  normal  to  OB.  If  we  use  12-inch 
pitch  for  the  cam  its  slope  is  represented  by  CD,  and  we  find 
from  the  normal  OE  that  the  axial  pull  will  be  ON,  friction  not 
considered.  Allowing  for  0.15  coefficient  of  friction  on  the  cam 
we  lay  off  FOE  an  angle  whose  tangent  is  0.15  and  obtain  OM 
as  the  axial  pull.  Extend  MF  and  intersect  same  by  OG  the 
required  normal  pressure  32,000  pounds  to  scale.     Perpendicular 


Fig.  326.  —Original  Disc  Brake  on  Gantry  Crane. 

to  this  we  get  the  slope  of  the  cones  OH,  which  will  obtain  the 
above  normal  pressure  with  the  given  axial  pull.  By  measure- 
ment BOH  is  found  to  be  21  j  degrees.  If  we  use  a  cone  angle 
of  20  degrees  and  return  through  the  construction  from  H-G-F- 
E-CD  we  find  that  the  necessary  axial  pull  will  be  given  by  a 
cam  whose  lead  is  12|  inches.  The  use  of  12-inch  lead  on  cam 
with  20-degree  cones  will,  therefore,  furnish  a  friction  slightly 
in  excess  of  that  required  under  the  conditions  mentioned.  Prob- 
ably the  friction  between  the  cones  will  never  reach  a  lower 
coefficient  than  the  0.1  assumed,  but  in  case  this  should  occur 
the  first  motion  will  produce  vibration  destroying  the  friction 
on  the  cam  surface  and  produce  additional  axial  pull  approaching 
ON.  The  construction  of  point  K  shows  that  brake  will  operate 
on  a  coefficient  of  0.08  or  less  when  cam  friction  is  destroyed. 
The  width  of  the  cones  is  determined  by  the  pressure  desired. 

Using  50  pounds  per  square  inch  we  need — -^ —  =  640  square 


inches  area  and 
of  each  cone. 


640 


9.5  X  2ir 


50 
lOf  inches  width,  say  b\  inches  width 


546 


The  Naval  Constructor 


The  oiling  system  is  designed  to  pick  up  oil  outside  of  cones 
and  deposit  same  between  cones  when  lowering,  so  that  the  oil 
must  pass  continually  from  small  to  large  ends  of  both  cones. 

There  are,  as  seen  by  the  above,  and  by  reference  to  Fig.  324, 
three  quantities  inter-related  in  brakes  of  the  class  just  designed 
for  the  gantry  crane.  The  normal  pressure  required  on  the 
friction  surfaces,  the  angle  of  the  cones,  and,  the  lead  of  the 
cam. 

With  given  materials  the  pressure  per  square  inch  can  be 
decided  upon  and  the  diameter  and  breadth  of  cones  chosen  to 
take  the  total  pressure  which  is  the  frictional  torque  needed 
divided  by  the  mean  radius  of  cones 
and  by  the  coefficient  of  friction.  This 
quantity  arranged,  we  can  assume  a 
value  for  one  of  the  other  variables 
and  determine  the  remaining  quan- 
tity, a  couple  of  trials  being  needed 
to  obtain  a  suitable  set  of  values. 

If,  instead  of  50  pounds  per  square 
inch,  we  had  used  materials  allowing 
200  pounds  per  square  inch  as  in 
Fig.  324,  the  brake,  Fig.  327,  could 
have  been  much  smaller,  and  a  design 
with  6-inch  mean  radius  of  cones 
would  have  15-degree  cones  each  3| 
inches  wide  with  a  10-inch  lead  on 
cam  of  3-inch  radius. 

The  axial  pull  is  least  affected  by 
friction  on  the  cam  when  the  lead  is 
such  as  to  give  a  cam  angle  of  about 
40  degrees,  and  angles  between  25 
and  40  degrees  are  therefore  prefer- 
able. Lubrication  of  the  cam  should 
be  arranged  or  the  operator  instructed  to  keep  cam  well  greased. 
Pawls  should  be  designed  carefully,  as  light  as  possible  and  nearly- 
balanced;  and  their  friction  levers  should  be  long  enough  to  posi- 
tively operate  the  pawls.  Wood  friction  pieces  slip  when  wet  and 
metal  pieces  when  oily  so  corks  are  used  since  they  have  0.30  to 
0.36  coefficient  of  friction  under  varying  conditions  and,  with 
relatively  smaller  pressure,  have  3  to  6  times  the  life  of  wood  for 
friction  blocks. 


Fig.  327. 


Case  II.  —  Taking  the  second  case,  where  all  of  the  friction 
is  gathered  on  the  motor  side  of  the  cam,  we  get  a  brake  the  re- 
verse of  the  above  arrangement  in  which  all  of  the  purposes  are 
obtainable  but  liable  to  be  unsatisfactory  if  for  any  reason, 


Friction   Brake  Cranes 


547 


such  as  lack  of  attention  to  lubrication,  the  coefficients  of  friction 
on  the  working  surfaces  should  vary  greatly  from  those  expected. 
Let  OA,  Fig.  324,  again  represent  the  lifting  force  of  the  motor 
on  the  cam,  GG  the  slope  of  the  cam  and  OC  the  axial  compo- 
nent required  to  just  balance  the  load.  If  all  power  be 
turned  off  the  motor  or  even  if  the  motor  pinion  or  couplings 
be  removed,  the  lowering  tendency  of  the  load  will  cause  the 
normal  pressure  OD  whose  axial  component  OC  locks  the  fric- 
tions and  prevents  dropping.  Now  suppose  this  brake  to  be 
designed  for  0.1  coefficient  of  friction,  the  friction  on  the  cam 
not  being  considered.  If  for  some  reason  this  coefficient  of 
friction  should  drop  to  0.08  or  the  friction  between  the  sliding 


Fig.  328.  —  Sellers  Type  Disc  Friction  Brake  for  Boat  Crane 
Full  Load  Torque  =  21,900  In.  Lbs. 

surfaces  of  the  cam  should  become  apparent,  this  normal  pres- 
sure OD  will  be  insufficient  to  lock  the  load.  We  must  then  design 
for  the  worst  conditions  allowing,  say,  0.15  coefficient  of  friction 
on  the  cam.  If  this  brake  were  allowed  to  run  dry  and  the  co- 
efficient of  friction  between  the  working  surfaces  rose  to,  say  0.15, 
and  the  friction  between  the  cam  surfaces  was  overcome  by 
the  vibration  of  the  machinery,  then  the  pressure  of  the  load 
on  the  cam  would  cause  an  axial  component  supplying  more 
than  twice  the  necessary  friction,  and  the  motor  to  lower  must 
exert  more  than  its  normal  power,  i.e.,  run  overloaded  to  force 
the  load  down. 

Case  III.  —  This  state  of  affairs  can  be  overcome  by  the 
arrangement  of  brakes  shown  in  Figs.  325  and  328,  in  which  the 
friction  is  divided  between  the  motor  and  load  ends.     In  these 


548  The  Naval   Constructor 


brakes  the  cones  or  discs  will  have  the  same  total  area  as  in  the 
foregoing  case,  but  with  a  marked  difference  in  operation.  Take 
the  case  when  R  =  1,  the  axial  component  OC,  Fig.  324,  will  cause 
just  enough  friction  to  balance  the  load  when  starting  to  lower. 
The  motor  must  overcome  the  difference  between  the  resistance 
of  the  friction  on  its  side  of  the  cam  and  the  turning  effect  of  the 
load  pressure  against  the  cam.  As  soon  as  this  is  overcome  the 
pressure  betweeen  the  cam  surfaces  drops  to  \  of  its  hoisting 
value,  that  is,  \  of  load  AL  will  be  overcome  by  friction  on  load 
side  and  other  half  Oh  by  friction  on  the  motor  side,  so  that  in 
lowering  this  brake  the  motor  must  give  downward  direction,' 
but  no  power  is  required  to  lower  unless  R  exceeds  1.  This 
brake  must  be  designed  also  for  minimum  conditions  expected, 
say  coefficient  of  friction  =  0.1  on  sliding  surfaces  and  =  0.15 
on  cam  surfaces.  It  locks  to  an  equal  extent  as  the  brake  just 
discussed  with  friction  entirely  on  the  power  side  of  cam,  but 
instead  of  using  full  power  or  overload  on  the  motor  when  lower- 
ing under  adverse  conditions,  on  this  brake  it  would  only  require 
a  large  force  to  overcome  the  first  frictional  set  of  the  brake  when 
starting  to  lower  and  would  lower  thereafter  with  never  more 
than  one-half  of  the  motor's  normal  load,  as  can  be  seen  by  the 
discussion  of  Fig.  324.  Even  if  this  brake  were  designed  well  on 
the  safe  side,  say  R  =  \\,  to  provide  a  margin  when  locking  the 
load  and  should  double  its  coefficient  of  friction  the  force  of 
\\  normal  load  which  would  stall  the  motor  in  Case  II  could  be 
easily  furnished  for  the  instant  necessary  in  starting  by  a  series 
wound  motor,  and  the  brake  thereafter  would  lower  easily  with 
some  small  downward  force  exerted  by  the  motor.  This  last 
arrangement  with  frictions  divided  between  motor  and  load  ends, 
in  addition  to  being  effectively  self-locking  and  unapt  to  stall, 
has  the  further  advantage  of  being  the  least  complicated  of  all 
cases  as  can  be  seen  by  comparison  of  Figs.  325  and  328. 

VENTILATION. 

The  accompanying  sketch  shows  a  complete  system  of  ventila- 
tion designed  and  calculated  according  to  results  of  experiments 
relative  to  deliveries  of  ventilation  systems  on  board  ship  made 
by  D.  W.  Taylor,  Naval  Constructor,  U.  S.  N.,  at  the  Experi- 
mental Model  Basin,  Navy  Yard,  Washington,  D.  C. 

The  first  point  to  be  determined  in  laying  out  any  system 
of  ship  ventilation  is  the  amount  of  air  that  is  required  in 
each  compartment  to  be  ventilated,  assuming  that  the  number 
of  cubic  feet  of  air  to  be  delivered  per  minute  as  marked  on 
sketch  at  each  terminal  is  the  amount  required  at  that  special 
point  for  the  efficient  ventilation  of  any  compartment  or  com- 


Ventilation  System 


549 


VENTILATION    SYSTEM. 


6{'0la: 


\i'D/a.-Ye/'/50Z 

IS'Dia.-V<MS4S 
*-BB 
<-li'Dia-V*/.Z007 


VellSIZ  8      *--rity>&>-  C'  '    ptrrvn. 

'<-Steel  Plate  Electric  Fan  ^^£&s-. 

Capacity  1500  Cub- Ft  "%  r* 

perMinAtMaxe.Speed 

Fia.  329. 


550  The  Naval  Constructor 

partments,  such  as  engine  rooms,  water  closets,  cabin  spaces, 
storerooms,  magazines,  etc.;  the  fan  is  then  placed  in  the  most 
convenient  location  for  economy  in  piping.  The  next  step  is 
the  head  of  the  main  or  mains  which  should  be  as  straight  as 
possible  with  the  number  of  bends  reduced  to  a  minimum.  Then 
make  the  standard  conditions  at  the  first  outlet  5  pounds  pres- 
sure, and  about  2000  feet  per  minute  velocity.  "This  pressure 
of  5  pounds  per  square  foot  is  for  standard  conditions  of  air, 
density  corresponding  to  a  barometric  height  of  30  inches,  a 
temperature  of  70  degrees  Fahrenheit  and  a  relative  humidity 
of  70  per  cent.  Under  these  standard  conditions  a  cubic  foot  of 
air  weighs  0.07465  pound.  The  pressure  of  5  pounds  is  equiva- 
lent to  a  pressure  head  of  67  feet  of  standard  density  air.  A 
velocity  of  2000  feet  per  minute  corresponds  to  a  velocity  head 
of  17.27  feet.  The  total  head  then  against  which  air  is  delivered 
to  the  supply  main  is  84.27  feet." 

As  the  branches  lead  off  do  not  change  the  size  of  the  main 
until  sufficient  air  has  been  removed  to  reduce  the  velocity  to  a 
value  between  1200  and  1500  feet  per  minute.  Then  contract 
the  mains  with  a  taper  of  1£  inches  to  the  foot  until  the  area  is 
so  reduced  that  the  velocity  again  becomes  about  2000  feet  per 
minute.  Repeat  the  contraction  wherever  necessary,  but  do 
not  reduce  the  final  diameter  of  the  main  to  less  than  twice  the 
diameter  of  the  last  branch. 

A  15j-inch  diameter  pipe  is  selected  for  the  first  section  of 
the  main,  on  account  of  giving  the  nearest  velocity  to  2000  feet 
per  minute.  After  branches  A,  B,  and  C  have  been  taken  off  the 
velocity  is  reduced  to  1458  feet  per  minute.  Being  below  1500  feet 
per  minute  the  main  is  reduced  in  size  with  a  taper  of  1^  inches 
to  the  foot  to  13-inch  diameter  which  increases  the  velocity  to 
2007  feet  per  minute.  At  the  beginning  of  the  13-inch  diameter 
or  B.B.  section  of  the  main,  the  direction  is  changed  90  degrees 
which  should  be  done  with  an  elbow  having  a  radius  of  throat 
not  less  than  diameter  of  pipe.  When  branches  D  and  E  have 
been  taken  off  the  velocity  becomes  1302  feet  per  minute;  the 
main  is  again  reduced  in  size  with  a  taper  1  \  inches  to  the  foot 
to  10§-inch  diameter  increasing  the  velocity  to  1995,  and 
again  branches  F  and  G  reduce  the  velocity  to  1247  feet  per 
minute,  which  necessitates  changing  the  size  of  the  main  to 
8j-inch  diameter,  bringing  the  velocity  up  to  2020  feet  per  min- 
ute. Branches  H  and  /  again  reduce  it  to  1212  feet  per  minute 
as  the  main  should  never  be  reduced  to  less  than  twice  the 
diameter  of  the  last  branch  but  it  can  now  only  be  reduced  to 
about  7-inch  diameter  to  be  settled  definitely  later  when  sizes  of 
branches  are  determined. 


Chart  for  Ventilation  Pipes 


551 


84nuiu 
j  ad -4 j -no 
uisaoiniOA 


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552  The  Naval  Constructor 

The  formula  for  velocity  in  ventilation  pipes  is 
.        _  Volume 
—  Velocity 

Knowing  everywhere  the  size  and  the  lead  of  the  main,  the  next 
point  to  be  considered  is  the  size  of  the  branches  which  is  governed 
largely  by  the  distance  of  the  point  of  intersection  of  the  branch 
with  the  main  from  the  fan.  This  is  due  to  the  loss  in  delivery 
of  air  due  to  friction  in  the  main  up  to  this  point. 

The  formula  for  loss  of  head  in  a  round  or  square  pipe  is 

Hf  =  4  F-j  TV,  where  Hf  is  loss  of  head  in  feet  of  air  due  to 

friction,  F  is  the  coefficient  of  friction,  L  and  d  are  length  and 
diameter  of  the  pipe,  respectively,  both  expressed  in  feet  or  both  in 
inches,  and  V\  is  the  velocity  of  flow  through  the  pipe  in  feet  per 
second.  If  we  change  V\  to  V  or  velocity  in  feet  per  minute  and 
give  F  its  proper  value  for  first  class  piping,  namely,  0.00008, 
we  have  upon  substituting  and  reducing 

F     d  11,250,000* 

For  practical  purposes  it  is  only  necessary  to  figure  the 
loss  of  head  in  feet  of  air  due  to  friction  for  each  section  of  the 
main,  and  the  size  of  all  branches  leading  off  from  that  section 
of  the  main  should  be  governed  by  the  loss  of  head  figured 
for  the  entire  section.     Such  being  the  case  we  should  substitute 

for  V  in  the  formula  for  loss  of  head  given  above    y  — ^ — » 

where  V  is  the  velocity  in  feet  per  minute  at  the  beginning 
of  any  section  of  the  main  and  F2  is  the  velocity  in  feet  per  min- 
ute at  the  end  of  the  same  section.  This  velocity  is  called  the 
mean  velocity  for  that  section  of  the  main.  The  main  velocities 
for  the  different  sections  of  the  main  on  the  accompanying  sketch 
are  as  follows:  — 

Section  A.A. 


M.V.  =  \/<1970)'  +  (1655)'  =  1819. 


Section  B.B. 

M 
Section  C.C. 

M 


Vt  =  v/(2007)2  +  (1845)a==1928j 
V.  -  y/(1"5)2  +  (1787)2  =  1894. 


Ventilation 


553 


Section  D.D. 

M.V. 


\f- 


(2020)2  +  (1616)2 
2 


1829. 


Section  E.E. 


M.V. 


\fl 


=  1331. 


r(1684)  +  (842)- 

From  the  experiments  above  mentioned  it  was  concluded  that 
each  foot  of  head  lost  means  an  approximate  loss  of  about  0.6 
of  one  per  cent  of  delivery  as  compared  with  standard  condi- 
tions. In  consideration  of  this  fact  the  percentage  of  loss  in 
deliveries  of  air  due  to  friction  for  the  different  sections  of  the 
main  on  the  accompanying  sketch  is  as  follows:  — 


Remarks. 

Each 
Section. 

Total  from 
Fan. 

Section  A. A. 
Diam.=15i",  length  =  183",  M.V.  =  1819 

183XU819)'         „„XOfi_              « 
^~  15.25X11,250,000 -3-53X0-6- 

Per  cent. 
2.12 

Per  cent. 
2.12 

Section  B.B. 
Diam.  =  13",  length=134",  M.V.  =  1928 
_    134X (1928)2    _,,vnfi 
Hp~  13X11,250,000  -3-4X0-6- 

2.04 

4.16 

Section  C.C. 
Diam.  =  10|",  length =88",  M.V.  =  1894 
_      88X  (1894)2          ' 
HF~  10.5X11,250,000  -2-67X0-6- 

1.6 

5.76 

Section  D.D. 

Diam.=8i",  length  =  101",  M.V.  =  1829 
_     101X(1829)»        -fl.vn- 
^"8.25X11,250,000     3-64X0-6- 

2.18 

7.94 

Section  E.E. 
Diam.=7",  length=48",  M.V.  =  1331 
_    48X(1331)2   _    ftoVOfi_ 
^-7X11,250,000     108X0-6- 

0.65 

8.59 

For  general  run  of  branches  make  the  angle  anything  less  than 
45  degrees;  30  degrees  is  a  very  good  angle,  but  it  is  not  neces- 
sary to  adhere  to  it  rigidly.  For  the  branches  at  the  extreme  end 
of  the  main,  where  the  velocity  is  very  much  reduced,  the  angle 
should  be  increased  and  the  last  branch  should  generally  lead 
off  at  90  degrees. 

In  determining  the  inside  diameter  of  the  branches  an  allow- 
ance should  be  added  to  the  length  of  the  branch  along  centre 
line   for    elbow,    as   follows:  —  for    one    90-degree  elbow  add 


554 


The  Naval   Constructor 


3  feet,  for  two  add  7  feet,  for  three  add  7  feet.     For  elbows  less 

than   90  degrees  add  in  proportion.     This  applies  to  elbows 

whose  radius  to  the  center  of  the  pipe  is  li  diameters.     A  smaller 

radius   should  never   be  used.     Take  branch  J   for   instance, 

where  225  cubic  feet  per  minute  are  needed;  the  loss  of  delivery 

in  the  main  up  to  this  point  is  8.59  per  cent  and  the  actual 

delivery  to  be  expected  will  be  only  0.9141  of  the  standard 

225 
delivery;    the  standard  delivery  then  would  be  =  246 

cubic  feet  per  minute.  As  branch  J  is  about  17j  feet  long 
and  has  two  90-degree  elbows  and  one  45-degree  elbow,  we 
should  add  about  8  J  feet  to  the  length,  which  would  make  it 
26  feet  long.  Now  if  the  inside  diameter  of  branch  J  is  made 
of  a  size  (see  Fig.  330)  to  pass  246  cubic  feet  length  26  feet  under 
standard  conditions,  it  may  be  expected  to  give  the  required 
225  cubic  feet  under  actual  conditions.  The  sizes  of  all  branches 
are  determined  by  the  same  method. 

The  length  and  size  of  branches  being  determined,  connect 
these  with  their  outlet  fittings  by  a  cone  expanding  \\  inches 
to  the  foot  to  the  desired  diameter  for  the  velocity  required  on 
the  accompanying  sketch.  The  outlet  fittings  are  all  shown  ad- 
justable elbows  which  are  usually  fitted  on  all  supply  systems  on 
government  vessels.    Any  style  terminal  may  be  used. 

FIXED   TERMINALS    FOR   EXHAUST   FIPES. 


$K 

A. 

B. 

c. 

D. 

E. 

F. 

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Adjustable  Terminals 


556 


ADJUSTABLE   TERMINAL. 


Seamed andSo/dere, 

not  Movable 
.  Brass  I 
20$Lti 
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^Movable  Joint 


Adjustable  Terminal 
for  Supply  Pipes 
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556 


The  Naval  Constructor 


ADJUSTABLE   TERMINALS    WITH    DAMPERS. 


Fia.  333. 


Note.  Terminals  to  be  Nichel  Plated  in 
Officers  Quarters}el$ewheretobe  6alvanized 


Size. 

A. 

N.P. 

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D. 

N.P. 

N.P. 

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//. 

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Standard  Sizes  of  Ventilators 


557 


The  air  is  to  be  renewed  in  the  various  spaces  approximately 
as  follows,  based  on  the  gross  capacity  of  the  compartments, 
and  on  the  above  pressure: 

Quarters  on  orlop  deck,  in  from  ten  to  twelve  minutes. 

Water  closets,  in  from  four  to  six  minutes. 

Storerooms,  in  from  eight  to  twelve  minutes. 

Magazines,  in  from  six  to  eight  minutes. 

Engine  rooms  and  steering  compartments,  in  about  two 
minutes. 

Ice-machine  room,  in  about  three  minutes. 

Dynamo  rooms,  in  about  three-fourths  of  a  minute. 


r.  — 

600  cubic  feet. 

5,000  cubic  feet 

1,000       " 

it 

6,000       "       " 

1,600       " 

it 

8,000       "       " 

2,500      " 

a 

10,000       "       " 

4,000      " 

it 

12,000      "      " 

STANDARD    SIZES    OF   VENTILATORS    AND 
COWLS  —  .U.  S.  N. 


DlAM.   OF 

Ventilators. 

DiaM.  of 

Cowl,  Large 

Opening. 

Material  for 
Ventilator 

Trunk, 
Hull  Steel. 

Material  for  Ventilators 
and  Cowls. 

Sheet  Iron 
or  Steel, 
U.S.S.G. 

Soft  Rolled 

Copper,  Stubs 

Gauge. 

10 

20 

U.  S.  S.  G.  13 

20"  gauge 

16"  gauge 

12 

24 

13 

20"      " 

16"      " 

15 

30 

13 

20"      " 

16"      " 

18 

36 

13 

20"      " 

16"      " 

21 

42 

5  lbs. 

16"      " 

14"      " 

24 

48 

5    " 

16"      " 

14"      " 

27 

54 

5    " 

16"      " 

14"      M 

30 

60 

5    " 

16"      " 

14"      " 

36 

72 

7*  " 

14"      " 

12"      " 

42 

84 

7i  " 

14"      " 

12"      " 

48 

96 

7i  " 

12"      " 

12"      " 

54 

108 

7*  " 

12"      " 

12"      '* 

558 


The  Naval   Constructor 


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Weight  of  Standard  Ventilator  Cowls       559 


WEIGHT   OP   STANDARD    VENTDLATOR    COWLS. 


Diameter 

of 

Ventilator 

Trunk. 


In. 
10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

33 

36 

42 

48 


Length  of 

Parallel 

Neck  below 

Centre 
of  Throat 

Radius. 

Area  in 

Square 

Feet  Plus 

Laps. 

Weight 
of  Cowl  in 

Pounds, 

Exclusive 

of 

Fittings. 

In. 

Sq.  Ft. 

Lbs. 

*\ 

5.5 

11.25 

3 

7.5 

15.50 

3$ 

10.5 

21.50 

4 

13.75 

28.00 

*l 

17.50 

35.75 

5 

22.00 

45.00 

H 

27.00 

55.00 

6 

32.50 

66.25 

H 

39.00 

79.50 

7 

45.50 

93.00 

n 

53.75 

172.00 

8i 

64.50 

205.00 

9 

77.50 

247.00 

101 

105.00 

335.00 

12 

135.00 

430.00 

Thickness 

in 
U.S.  Gauge. 


No.  18  U.S.  G. 


No 


14 


560 


The  Naval  Constructor 


ELS  WICK 


Diam.  of  bore,  ins 

Diam.  of  bore,  mm 

Len.  of  bore,  cals 

Wt.  of  gun 

1.46 

37 

25 

Lbs. 

79 

Oz. 
1.125 

1540 
18 
1.9 

1.46 

37 

45 

Lbs. 

268 

1.5 

Oz. 

4.5 

2300 
55 
4.3 
25 

1.85 

47 

40 

Lbs. 

506 

3.3 

Oz. 

7.94 

2132 
104 
5.2 
25 

1.85 

47 

50 

Lbs. 

1067 

3.3 

Lbs.oz. 

1      4f 

1    6 

2800 

179 

7.8 

25 

1.85 

47 

50 

Lbs. 

852 

3.3 

Oz. 
15.0 

2700 
166 
7.4 
25 

1.85 

47 

46 

Lbs. 

560 

3.3 

Oz. 

10.0 

2300 

121 

5.7 

25 

2.24 

57 

40 

Lbs. 

840 

6 

Oz. 

9.2 

1968 
161 
5.6 
25 

Wt.  of  proj.,  lbs 

Wt.  of  Cord.,  ch 

Wt.  ofM.D.,  ch 

Muz.  vel.  f.  a 

Muz.  ener.  f.  t 

Pen.  at  muz.,  ins 

Rds.  per  min 

How- 
itzer. 

How- 
itzer. 

How- 
itzer. 

Diam.  of  bore,  ins 

Diam.  of  bore,  mm 

Len.  of  bore,  cals 

Wt.  of  gun 

4 

102 

8.75 

Lbs. 

220 

20 

Oz. 

n 

950 
125 

4 
102 
40 
Cwt. 
26 
31 

Lbs. 

5* 
2300 
1137 

12 

4 
102 
50 
Cwt. 
42 
31 

Lbs. 
11 

3000 

1934 

16.0 

12 

4.3 

109.2 

12.5 

Cwt. 

7 

40 
Oz. 
15.75 

980 
266 

4.7 
120 
12 
Cwt. 
8 
35 

Lbs.oz. 
1    4* 
1150 
321 

4.7 

120 

40 

Cwt. 

42 

45 

Lbs.oz 

5    5 

2200 

1510 

11.6 

12 

4.7 
120 
45 
Cwt. 
53 
45 
Lbs.  oz 

8  2J 

9  4 
2570 
2061 
15.2 

12 

Wt.  of  proj.,  lbs.... 

Wt.  of  Cord.,  ch 

Wt.  of  M.D.,ch.... 

Muz.  vel.  f.  a 

Muz.  ener.  f.  t 

Pen.  at  muz.,  ins 

Elswick  Guns 


561 


GUNS. 


Jointed 
Gun. 

Field. 

House 
Artil- 
lery. 

Field. 

2.24 

2.953 

3 

3 

3 

3 

3 

3.3 

57 

75 

76 

76 

76 

76 

76 

84 

50 

14.13 

40 

50 

19.2 

28 

23 

28 

Cwt. 

Lbs. 

Cwt. 

Cwt. 

Cwt. 

Cwt. 

Cwt. 

Cwt. 

10| 

210 

12 

18* 

4 

n 

6 

9 

6 

11.75 

w 

12.5 

12.5 

14.3 

12.5 

18.5 

Oz. 

Lbs.  oz. 

Lbs.  oz. 

Lbs.  oz. 

71 

1   10 

3   4 

1   3| 

Lbs.  oz. 

Oz. 

Oz. 

Lbs.  oz. 

1   3 

2   0 

4   0 

131 

1204 

1   4 

1   8 

2400 

1100 

2210 

2800 

1458 

1755 

1700 

1635 

240 

98 

423 

680 

185 

305 

250 

336 

8.0 

8.8 

11.6 

25 

20 

20 

20 

15 

15 

20 

20 

4.7 

5 

5 

6 

6 

6 

6 

7.5 

120 

127 

127 

152 

152 

152 

152 

190 

50 

32 

8.4 

12.2 

40 

45 

50 

45 

Cwt. 

Tons. 

Cwt. 

Cwt. 

Tons. 

Tons. 

Tons. 

Tons. 

66 

2 

9 

20 

6.6 

7.35 

8.75 

13.8 

45 

60 

50 

100 

100 

100 

100 

200 

Lbs. 

Oz. 

Lbs. 

Lbs. 

Lbs. 

8.5 

11.5 

18.3 

26 

36 

Lbs.  oz. 

Lbs.  oz. 

Lbs. 

15   0 
3000 

9   8 
2115 

782 

3   5 

1000 

22 

31 

34 

75 

2500 

2800 

2930 

2850 

2808 

1861 

212 

693 

4334 

5436 

5952 

11,264 

19.4 

13.0 

-  19.5 

23.1 

24.8 

30.4 

12 

10 

9 

9 

9 

6 

562 


The  Naval   Constructor 


ELS  WICK   GUNS.  —  (Continued.) 


I  )ia in .  of  bore,  ins. . 
Diam.  of  bore,  mm. 
Len.  of  bore,  cals 


Wt.  of  gun 

Wt.  of  proj.,  lbs. 


Wt.  of  Cord.,  ch. 


Wt.ofM.D.,  ch.. 

Muz.  vel.  f.  a 

Muz.  ener.  f .  t 

Pen.  at  muz.,  ins. 
Rds.  per  min 


7.5 
190 

50 

Tons. 

15 

200 


Lbs. 
77,5 
2,950 
12,068 
32.0 
6 


45 

Tons. 
18.0 
250 


Lbs. 

80 

2,800 

10,872 

32.2 

5 


203 

50 

Tons. 

21 

250 


Lbs. 

85 

2,950 

12,069 

34.8 

5 


210 

44 

Tons. 

18.1 

308.6 

Lbs. 

47 

Lbs. 

52 

2,300 

11,320 

27.0 

5 


Jointed 
Gun 


9.2 

234 

45 

Tons. 

26.75 

380 


Lbs. 

122 

2,750 

19,926 

35.9 

4 


Field 


9.2 
234 

50 
Tons. 

28 


Lbs. 

136 

3,000 

23,712 

39.8 

4 


Diam.  of  bore,  ins. . 
Diam.  of  bore,  mm. 
Len.  of  bore,  cals. . . . 


Wt.  of  gun 

Wt.  of  proj.,  lbs. 


Wt.  of  Cord.,  ch. 

Wt.  ofM.D.,  ch. 
Muz.  vel.  f.  a. .  . . 

Muz.  ener.  f .  t 

Pen.  at  muz.,  ins. 
Rds.  per  min. . .  . 


Field. 

How- 
itzer. 

How- 
itzer. 

10 

10 

12 

12 

12 

254 

254 

305 

305 

305 

45 

50 

40 

40 

45 

Tons. 

Tons. 

Tons. 

Tons. 

Tons. 

36.25 

36 

48.5 

51 

59.3 

500 

500 

850 

Lbs. 

141 

850 

850 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

167 

180 

155 

260 

286 

2,800 

2,900 

2,400 

2,650 

2,800 

27,181 

29,157 

33,949 

41,386 

46,208 

40.9 

42.95 

38.4 

44.6 

48.5 

3 

3 

2 

2 

2 

38  rds.  in  1  min.  45  sec.  from  4  guns;  35  rds.  in  1  min.  45  sec.  from 

min.  from  10  guns. 


7.5"  gun 
4  guns. 

6"  gun  —  74  rds.  in  1  min.  from  10  guns;  78  rds.  in 

4.7"  gun  —  79  rds.  in  1  min.  from  8  guns. 

4"  gun  —  59  rds.  in  45  sec.  from  8  guns. 

12  pr.  gun  — 10  rds.  in  31  sec.  from  1  gun. 

Some  results  actually  obtained  under  service  conditions  at  a  target. 

12"  gun  —  8  rds.  in  2  min.  10  sec.  from  1  turret  (pr.  of  guns);   16  rds.  in  2  min. 
45  sec.  from  2  turrets  (4  guns). 

9.2"  gun  —  57  rds.  in  2  min.  from  6  guns;  44  rds.  in  2  min.  from  6  guns;  13  rds. 
in  2  min.  from  2  guns. 


Vickers   Guns  and   Mountings  563 

VICKERS    GUNS    AND    MOUNTINGS. 


Wt.    of  mounting   com 

plete  with  shield 

Theory  of  shield,  ins. . . 

Wt.  of  shield 

Angle  of  elevation 

Angle  of  depression 

Wt.    of   mounting   com 

plete  with  shield 

Theory  of  shield,  ins 

Wt.  of  shield 

Angle  of  elevation 

Angle  of  depression 

Wt.  of  mounting  compl. 

with  shield 

Theory  of  shield,  ins. . . 

Wt.  of  shield 

Angle  of  elevation , 

Angle  of  depression 


37  MM. 
30  Cal. 


c.    q.   1. 

4    1     10 
0.1875 
q.      1. 
3      11 
16° 
25° 


37   MM. 

42.5  Cal. 


c.    q.    1. 

4    3    20 

0.16 
q.  1. 
1      22 

15° 

20° 


3-PDR. 

50  Cal. 


c.    q.   1. 

11    3    0 

0.25 
c.    q.    1. 
1    0    0 

20° 

20° 


6-PDR. 

50  Cal. 


c.    q.   1. 

14    2    0 
no 

shield 
20° 
10° 


Moun- 
tain 

3  Ins. 
12*  Ph. 
14.3  Cal. 


c.    q.     1. 

7      3    0 

0.1 

q.      1. 
1      17 

25° 

15° 


Weight  of 
Carb. 

WITHOUT 

Limber. 


11      3      0 

0.125 

q.        1. 

2         0 

16° 

6° 


Weight  of 

Carr.  and 

Limber 

with  24 

Rounds. 


t.     c.     q. 

1      5      1 

0.144 
c.    q.      1. 
1      0      15 

16° 

10° 


3  In. 

Semi-Aut. 
50  Cal. 


t.  c.  q.  1. 

10    2    0 
no 

shield 
20° 
10° 


4  Ins. 
50  Cal. 


t.    c.  q.  1 

2    4    2    0 
no 

shield 
15° 
10° 


Weight  of 

Carr. 

without 

Limber. 


4.7  Ins. 
45  Cal. 


c.     q,    1. 


17     3      0 
no 


shield 

50° 
5° 


t.    c.    q.    1. 

3  13  3  0 
2  and  0.313 
c.    q.    1. 

(17    0     0 
(110 
20° 
7° 


4.7  Ins. 
48.4  Cal. 


Weight  of 
Carr. 

WITHOUT 

Limber. 


t.  c.  q.  1. 

5    9    2    0 

3 
t.    c.    q.    1. 

1     12    2    0 

20° 
10° 


t.    c.  q.   1. 

2    14    3    0 

0.23 

c.       q. 

3        3 

50° 
0° 


564 


The   Naval  Constructor 


VICKERS,    SONS   AND   MAXIMS 


3  Pdr. 
50  Cal. 

6  Pdr. 
50  Cal. 

3  Ins. 
12*  Pr. 
14.3  C. 

37  mm. 
30  Cal. 

37  MM. 

49.5  Cal. 

Diam.  of  bore,  ins 

1.457 
43.5 
73.75 

13 

0.0782 

c.   q.    1. 
3    2    24 

1800 
22.5 

1.9 

1.5 

1.457 
62 
94 

14 
0.1875 
1.25 
c.  q.    1. 

5    1    19 

2300 

45.85 

3.3 

2.6 

300 

1.85 
92.5 
98.9 

17 
1.066 
3.3 
c.    q.   1. 
5    2    4 
2800 
79.4 

6.7 

5.1 

30 

2.244 
112.2 
118.6 

16 

.    1.55 

6 

c.  q.    1. 

9    1     5 

2600 

281 

7.5 

5.4 

28 

3 

42.94 
47.23 

12 
0.5 
12.5 
c.    q.    1. 
2    12    3 
1150 
115 

20 

Max.   pr.   in   chamber, 

Wt.  of  charge,  lbs 

Wt.  of  proj.,  lbs 

Wt.  of  gun 

Muz.  vel.  f.  s 

Pen.  of  W.  I.  pi.  at  muz. 

Gavre  form.,  ins 

Pen.   of  M.   st.   pi.  at 

muz.  Gavre  form.,  ins. 
Pen.  of  hard  st.  pi.  at 

3000  yds.  Gavre  form., 

Rds.  per  minute 

300 

6  In. 
Howit. 

6  Ins. 
45  Cal. 

6  Ins. 
50  Cal. 

7.5  Ins. 
45  Cal. 

7.5  Ins. 
50  Cal. 

Diam.  of  bore,  ins 

6 
94.5 
102.8 

9.85 

5.3 
90.3 
c.      q. 
18      3 

1285 

1035 

6 
269.5 
279.2 

17.75 

35.25 

100 

t.    c.   q. 

7     8    2 

3012 

6290 

23.65 

18.4 

6.3 
10 

6 

300 

310.07 

18 

43 

100 

t.    c.   q. 

7    16    0 

3190 

7056 

25.8 

20 

7.2 
10 

7.5 
337.5 
349.2 

18 
78.25 
200 
t.    c.  q. 
14    0    2 
2,875 
11,465 

28.75 

22.25 

7.5 
375 

386.7 

17.5 
80.03 
200 
t.     c.  q. 
16    0    0 
3,007 
12,540 

30.75 

23.7 

Max.  pr.    in    chamber, 

Wt.  of  charge,  lbs 

Wt.  of  gun 

Muz.  vel.  f.  s 

Pen.  of  W.  I.  pi.  at  muz. 

Gavre  form.,  ins 

Pen.  of  M.  st.  pi.  at  muz. 

Gavre  form.,  ins 

Pen.  of  hard  st.  pi.  at 

3000  yds.  Gavre  form., 

8.9 

■    8 

9.35 

8 

Rds.  per  min 

Vickers   Guns  and  Mountings 


565 


GUNS   AND   MOUNTINGS. 

Field. 

3  In.  S. 

Aut. 
50  Cal. 

4  Ins. 
50  Cal. 

4.33  In. 
Howit. 
13.5  C. 

4.7  Ins. 
45  Cal. 

4.7  Ins. 
48.4  Cal. 

Lt.  3  Ins. 

22  Cal. 

Hvy 

2.95  Ins. 
30  Cal. 

3 

64.96 
69.3 

2.95 
99.46 
103.8 

3 

150 
159.995 

4 
201 . 15 
208.45 

4.33 
58.45 
63.55 

4.724 
212.6 
220 

4.724 
228.45 
236.2 

16 
1 
12.5 

16.0 
1.032 
14.33 

17 

3.625 
12.5 

18 

11.25 

31 

12.5 

1.0 

35.27 

17 
19 
45 

18 
17 
45.14 

c.    q.    1. 

4    2     0 

1600 

220 

c.  q.  1. 

7    2   6 
1660 
274 

c.  q.  1. 

19    0   0 

2700 

632 

t.   c.   q. 

2    1    3 
3030 
1975 

c.     q. 

7      1 
1045 
267 

t.     c.     q. 
3      3      3 

2925 

2670 

t.  c.   q. 

3    2    0 
3050 
2910 

9.65 

16.0 

16.65 

17.8 

7.5 

12.4 

12.9 

13.8 

25 

20 

25 

15 

12 

12 

8  Ins. 
48.5  Cal. 

9.2  Ins. 
47  Cal. 

9.2  Ins. 
50  Cal. 

10  Ins. 
45  Cal. 

10  Ins. 
48.6  Cal. 

12  Ins. 
45  Cal. 

12  Ins. 
50  Cal. 

8 
388.75 
400 

9.2 
429.3 
442.35 

9.2 
460 
473 

10 
450 
464.6 

10 
486 

500 

12 
540 
557.55 

12 
600 
617.7 

18 
90 

216.7 

t.    c.   q. 

14    3    0 

3,090 

14,350 

18 

170.5 
380 

t.    c.   q. 

28    1    0 

3,025 

24,110 

18 
184 
380 
t.   c.    q. 
27  16   1 
3,070 
24,835 

18 

190.5 

478.4 
t.    c.   q. 
34  17    0 

18 

172 

496.6 

t.  c.   q. 

27  17    0 

18 

356 

850 
t.     c.     q. 
57    14     0 

18.5 

344 

850 
t.     c.    q. 
65    17    0 

2,850 
26,945 

2,863 

28,225 

2,950 
51,290 

3,010 
53,400 

31.5 

39.25 

39.95 

38.9 

40.2 

50.65 

52.1 

24.4 

30.45 

31.0 

30.1 

31.15 

39.25 

40.4 

9.8 
6 

13.35 
4 

13.75 

4 

13.8 
3 

14.65 
3 

19.5 

2 

20.0 
2 

566 


The  Naval   Constructor 


SCHNEIDER 


305 

274.4 

240 

12.0 
45 
52.9 
826 

2,952 

50,007 

38.3 

29.3 

12.0 
50 
57.3 
826 

3,116 

55,717 

41.6 

31.9 

10.9 
45 
38.5 
606 

2,952 

36,670 

34.6 

25.5 

10.9 
50 
41.7 
606 

3,116 

40,859 

37.4 

27.8 

9.4 
45 
25.8 

407 

2,952 

24,667 

30.1 

21.2 

9.4 
50 
27.9 

407 

3,116 

27,487 
32.3 

23.1 

Wt.  of  A.P.  proj.,  lbs 

Wt.  of  charge* 

Muz.  vel.,  ft.  see 

Muz.  energy,  ft.  tons 

Perf  .of  steel  at  muz.  (ins.) 
Perf .  of  steel  at  3000  yds. 

120 

100 

75 

4.7 
45 

3.2 
48 

2952 

2932 

13.9 

6.4 

4.7 
50 
3.5 

48 

3116 
3268 
15.0 

6.9 

3.3 
45 

1.9 
28.6 

2952 
1734 
11.6 

4.6 

3.9 
50 

2.0 
28.6 

3116 
1931 
12.5 

4.9 

2.9 
50 

0.85 
14.3 

2871 
820 
9.3 

2.9 
60 

1.2 
14.3 

3035 
917 
10.0 

Wt.  of  A.P.  proj.,  lbs 

Wt.  of  charge  * 

Muz.  vel.,  ft.  sec 

Muz.  energy,  ft.  tons 

Perf .  of  steel  at  muz.  (ins.) 
Perf.  of  steel  at  3000  yds. 

Not 


Schneider  Guns 

567 

GUNS 

210 

200 

175 

150 

8.3 

8.3 

7.9 

7.9 

6.9 

6.9 

5.9 

5.9 

45 

50 

45 

50 

45 

50 

45 

50 

17.3 

18.6 

14.9 

16.2 

10.0 

10.8 

6.3 

6.8 

275 
2,952 

275 
3,116 

231 
2,952 

231 
3,116 

165 
2,952 

165 

9 

9 

99 
3116 

3,116 

2952 

16,667 

18,572 

14,002 

15,601 

10,000 

11,143 

6001 

6886 

26.2 

28.3 

24.3 

26.3 

22.1 

23.9 

18.2 

20.1 

17.5 

19.2 

16.1 

17.3 

13.8 

15.2 

10.2 

11.8 

65 

57 

47 

37 

2.5 

2.5 

2.21 

2.21 

1 

.8 

1.4 

50 

60 

50 

60 

60 

60 

0.5 

5 

0.76 

0.45 

0.55 

0 

.30 

0.17 

8.8 

8.8 

6 

6 

3 

.3 

1.76 

2952 

3116 

2952 

3116 

3 

116 

3116 

533 

594 

362 

400 

223 

119 

7.9 

9.1 

7.1 

7.5 

5 

.9 

5.0 

stated. 

568 


The  Naval  Constructor 


03 


24.44 

76.78 

3,558 

6.03 

90.39 

12.4 

39.47 

3196 

2858 

6389 

18.98 

26.84 
5.66 

a 

c 

W    ^H                       »■* 

1        » 

22.00 
47.49 
2.015 
5.34 
90.39 
12.4 
34.40 
3008 
2697 
5680 
17.41 

24.52 
5.29 

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len.  of  gun 
of  bore,  ins 

of  gun,  lbs. . 

of  gun,  tons 

of  st.  proj.  i 
of  ch.  in  lbs 
.  vel.  in  ft.-s 
.  energy  tot 

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«®  **"  «® 

570 


The  Naval  Constructor 


BETHLEHEM 


ORDNANCE. 


Cal. 

Len. 

or 
Bore 

in 
Cal. 

Cal. 

Wt. 

OF 

Gun. 

Wt. 

OF 

Proj. 

At  Muzzle. 

Per. 

of  W.I. 

Gavre 
Form- 
ula. 

At  3000  Yds 

.  Range. 

Veloc- 
ity. 

En- 
ergy. 

Dan- 
gerous 
Space 
for 

Tar- 
get 25' 
High. 

En- 
ergy. 

Ft.- 
tons. 

Per.  of  B. 

Hard-faced 

Arm. 

Pierc. 

Proj.  with 

Normal 

Impact. 

Ins. 
1.457 

Cals. 
50 

Cms. 
3.7 

Lbs. 
120 

Lbs. 

Ft.-lb. 
sec. 

2150 

Ft.- 

tons. 
37 

Ins. 

Yds. 

Ins. 

1.831 

50 

4.7 

550 

3 

2400 

119 

2.244 

50 

5.7 

960 

6 

2400 

240 

3 

50 

7.62 

1900 
Tons. 

13 

2800 

707 

4 

45 

10.16 

2.3 

33 

2600 

1545 

9.8 

240 

755 

4 

50 

10.16 

2.6 

33 

3000 

2060 

12.1 

315 

1,000 

5 

45 

12.7 

3.4 

60 

2600 

2810 

12.8 

255 

1,575 

5 

50 

12.7 

4.75 

60 

3000 

3745 

15.8 

340 

2,035 

6 

45 

15.24 

7.2 

105 

2600 

4965 

16.9 

275 

2,970 

6.9 

6 

50 

15.24 

8.4 

105 

3000 

6550 

20.0 

365 

3,950 

8.3 

7 

45 

17.78 

12.7 

165 

2800 

8965 

23.2 

330 

5,790 

9.5 

7 

50 

17.78 

14.5 

165 

3000 

10,300 

25.5 

385 

6,640 

10.4 

8 

35 

20.32 

15.2 

316 

2250 

10,500 

28.3 

235 

8,240 

11.0 

8 

45 

20.32 

18.6 

260 

2800 

14,230 

29.1 

350 

9,860 

12.3 

8 

50 

20.32 

22.3 

260 

3000 

16,220 

32.2 

405 

11,350 

13.4 

10 

35 

25.4 

30.0 

604 

2250 

21,200 

38.6 

245 

16,580 

14.8 

10 

45 

25.4 

35.4 

515 

2800 

27,990 

40.8 

370 

21,080 

17.2 

10 

50 

25.4 

43.9 

515 

3000 

32,110 

44.7 

430 

24,070 

18.7 

12 

35 

30.48 

52.0 

1046 

2250 

36,700 

50.1 

250 

29,880 

19.1 

12 

45 

30.48 

53.8 

870 

2800 

47,290 

51.7 

380 

36,790 

21.7 

12 

50 

30.48 

66 

870 

3000 

54,280 

57.1 

435 

42,350 

23.7 

14 

35 

35.56 

57.4 

1660 

2150 

53,190 

50.4 

230 

44,660 

22.3 

14 

45 

35.56 

70.3 

1350 

2450 

56,170 

52.4 

295 

45,090 

22.4 

18 

30 

45.72 

60.0 

2075 

2150 

66,490 

49.2 

225 

52,750 

21.1 

Guns  less  than  3"  cals.  are  chambered  for  fixed  ammunition  with  the  powder 
and  projectiles  in  brass  cartridge  cases.  Guns  from  3"  cals.  upwards,  and  includ- 
ing the  6"  L  45  gun,  can  be  chambered  to  use  either  fixed  ammunition,  or  loose 
ammunition  with  the  powder  in  cartridge  bags  and  the  projectile  separate  from  the 
powder.  Guns  above  6"  cal.  and  including  the  6"  L  45  gun  are  chambered  for 
loose  ammunition.    The  breech  mechanisms  of  all  guns  up  to  10"  are  operated  by 


Bethlehem   Steel  Company 

STEEL   COMPANY. 


571 


ORDNANCE. 


At  8000  Yds.  Range. 

Limiting  Ranges  beyond 

Cal. 

Dangerous 
Space  for 
Target 
25'  high. 

Energy. 

Perf.  of  B. 

Hard-faced 

Arm.  by 

Capped 

Arm.  Pierc. 

Proj.  with 

Norm. 

Impact. 

Proj.  will  not  perforate 

Krupp  Hard-faced  Arm.  of 

12"  and  7"  thickness. 

12"  plate. 

7"  plate. 

Yds. 

Ft.-tons 

Ins. 

Yds. 

Yds. 

Ins. 

1.457 
1.851 
2.244 
3 

4 

55 

1,307 

4  1 

2,870 

4 
5 
5 
6 

75 

1,749 

4  9 

4,500 

6 

70 

2,285 

6.1 

6,350 

7 

85 

3,267 

6.7 

7,310 

7 

60 

5  060 

8  1 

10,230 

8 

85 

5,457 

8.6 

3,240 

10,420 

8 

95 

6,235 

9.0 

4,420 

11,610 

8 

65 

11,120 

11.5 

7,300 

Max.  range 

10 

95 

13,160 

12.8 

9,075 

"        " 

10 

115 

15,150 

13.9 

10,560 

"        " 

10 

70 

21,700 

15.6 

14,180 

"        " 

12 

105 

24,615 

16.9 

14,560 

"        " 

12 

120 

28,135 

18.3 

16,330 

"        " 

12 

70 

33,650 

18.7 

Max.  range 

"        " 

14 

85 

32,030 

18.1 

"        " 

"        " 

14 

65 

36,360 

16.7 

15,100 

18 

the  single  motion  of  a  hand-lever.    Those  of  the  larger  guns  are  operated  by  the 
revolution  (3  to  5  turns)  of  a  crank. 

The  8",  Wand  12"  L  50  guns,  and  the  14"  L  45  gun  are  for  use  in  turrets,  and  are 
of  great  weight  at  the  breech  in  order  to  balance  the  long  muzzles,  so  that  a  com- 
paratively small  barbette  may  be  used. 


572 


The  Naval  Constructor 


UNITED    STATES 


Gun. 

Mark. 

6 
2 
A 

H 

Tot. 
Len. 

Cap.  of 
Cham- 
ber in 
Ins. 

Travel 

of 
Proj. 
in  Ins. 

Wt. 
of 

Cl   N. 

Wt. 

OF 

Proj. 

© 
« 

o 
S 

H 

Ins. 

Tons. 

Lbs. 

Lbs. 

3"  R.F.G. 

II,  III 

50 

154 

219 

128.3 

0.9 

13 

3.85 

3"  S.A. 

V,  VI 

50 

159 

219 

128.3 

1.0 

13 

3.85 

4"  R.F.G. 

III,  IV,  V,  VI 

•40 

164 

331 

134.5 

1.5 

33 

4.85 

4" 

VII 

50 

205 

652 

168.3 

2.6 

33 

9.0 

4» 

VIII 

50 

205 

652 

168.3 

2.9 

33 

12.3 

5" 

II,  III,  IV 

40 

206 

656 

167.8 

3.1 

50 

10.0 

5"  B.L.R. 

V,  VI 

50 

256 

1,200 

215.6 

4.6 

60 

19.2 

5" 

VI 

50 

256 

1,200 

215.6 

4.6 

50 

20.5 

5"  R.F.G. 

VII 

51 

261 

1,165 

215.6 

5.0 

50 

23.8 

6"  R.F.G. 

II,  III 

30 

196 

1,318 

145.4 

4.8 

105 

18.8 

6" 

IV,  VII 

40 

256 

1,320 

205.8 

6.0 

105 

18.8 

6" 

IX 

45 

270 

1,320 

221.7 

7.0 

105 

18.8 

6"  B.L.R. 

VI 

50 

300 

2,101 

247.5 

8.3 

105 

30.0 

6" 

VIII 

50 

300 

2,101 

247.5 

8.6 

105 

37.0 

7"  B.L.R. 

II 

45 

323 

3,643 

259.8 

12.7 

165 

58.0 

8"  B.L.R. 

III,  IV 

35 

305 

3,170 

245.8 

13.1 

260 

43.8 

8" 

V 

40 

343 

5,243 

273.1 

18.1 

260 

78.0 

8" 

VI 

45 

369 

5,243 

299.1 

18.7 

260 

98.5 

10" 

I,  II 

30 

329 

6,779 

251.1 

25.1 

510 

90.0 

10" 

III 

40 

413 

7,222 

327.0 

34.6 

510 

207.5 

12" 

I,  II 

35 

441 

11,991 

345.2 

45.3 

870 

160.0 

12" 

III,  IV 

40 

493 

17,096 

392.2 

52.1 

870 

237.5 

12" 

III,  IV 

40 

493 

17,096 

392.2 

52.1 

870 

305.0 

12" 

V 

45 

553 

16,974 

452.0 

52.9 

870 

305.0 

12" 

VI 

45 

553 

14,970 

452.0 

53.6 

870 

340.0 

12" 

VII 

50 

607 

14,296 

506.3 

56.1 

870 

340.0 

13" 

1,11 

35 

479 

15,068 

374.9 

61.4 

1130 

180.0 

14" 

II 

45 

642 

63.1 

1400 

365.0 

United  States  Naval  Ordnance 


573 


NAVAL   ORDNANCE. 


Muz. 
Vbl. 

Muz. 
Energy 

Pen.  at  Muz. 

Krupp  Arm. 

Using  Capped 

Proj. 

At  3000  Yds. 

At  6000  Yds. 

At  9000  Yds. 

Remain- 
ing 
Vel. 

Pene- 
tration. 

Remain- 
ing 
Vel. 

Pene- 
tration. 

Remain- 
.Vef. 

Pene- 
tration. 

Ft.-sec. 

Ft.-tons. 

Ins. 

Ft.-sec. 

Ins. 

Ft.-sec. 

Ins. 

Ft.-sec. 

Ins. 

2700 

658 

3.3 

1230 

1.2 

848 

0.8 

2700 

658 

3.3 

1230 

1.2 

848 

0.8 

2000 

915 

3.4 

1156 

1.7 

897 

1.2 

2500 

1,430 

4.6 

1432 

2.2 

979 

1.4 

853 

1.2 

2800 

1,794 

5.3 

1627 

2.6 

1033 

1.5 

878 

1.2 

2300 

1,834 

5.3 

1286 

2.6 

934 

1.7 

829 

1.4 

2700 

3,032 

6.2 

1692 

3.5 

1102 

2.0 

928 

1.6 

3000 

3,122 

6.4 

1732 

3.2 

1057 

1.7 

877 

1.4 

3150 

3,439 

6.8 

1835 

3.5 

1091 

1.8 

895 

1.4 

1950 

2,768 

5.3 

1305 

3.2 

1009 

2.3 

909 

2.0 

2150 

3,365 

6.0 

1440 

3.6 

1058 

2.4 

934 

2.1 

2250 

3,685 

6.3 

1511 

3.8 

1086 

2.5 

948 

2.1 

2600 

4,920 

7.6 

1770 

4.7 

1207 

2.9 

996 

2.2 

2800 

5,707 

8.3 

1923 

5.2 

1297 

3.2 

1026 

2.3 

2700 

8,338 

9.6 

1948 

6.4 

1382 

4.2 

1083 

3.0 

2100 

7,948 

8.6 

1576 

6.0 

1206 

4.2 

1040 

3.6 

2500 

11,264 

10.6 

1898 

7.5 

1428 

5.3 

1141 

4.0 

2750 

13,360 

12.0 

2106 

8.6 

1589 

6.1 

1227 

4.4 

2000 

14,141 

10.7 

1590 

8.0 

1274 

6.1 

1103 

5.0 

2700 

25,772 

15.6 

2184 

11.9 

1747 

9.0 

1406 

6.9 

2100 

26,596 

14.2 

1733 

11.2 

1433 

8.8 

1219 

7.2 

2400 

34,738 

16.8 

1994 

13.3 

1649 

10.5 

1396 

8.3 

2600 

40,768 

18.5 

2171 

14.8 

1801 

11.7 

1500 

9.3 

2700 

43,964 

19.4 

2259 

15.5 

1877 

12.3 

1561 

9.8 

2850 

48,984 

20.8 

2393 

16.6 

1991 

13.3 

1553 

10.6 

2950 

52,483 

21.7 

2483 

17.5 

2071 

13.9 

1719 

11.0 

2000 

31,333 

15.0 

1679 

12.0 

1413 

9.7 

1221 

8.1 

2600 

65,606 

28.3* 

23.4* 

Section  IY. 

RIGGING  AND   ROPES. 


CHAPTER   I. 

The  rigging  and  ropes  of  a  modern  steamship  still  constitute  a 
very  important  part  of  the  vessel's  equipment,  notwithstanding 
the  almost  total  abolition  of  sail  area,  and  its  extinction  as  a 
propelling  agent  in  the  present  day  steamer. 

Generally  too  little  attention  is  devoted  to  what  are  considered 
the  minor  details  of  a  steamship's  rigging,  by  those  best  qualified 
to  determine  the  sizes  of  ropes  and  blocks,  and  the  arrangement 
of  tackles  on  a  mechanical  basis.  The  array  of  derricks  around 
the  masts  and  kingposts  of  a  freighter,  with  their  varying  loads  of 
from  2 \  to  50  tons,  exemplify  the  necessity  for  a  closer  acquaintance 
with  the  staying,  guying  and  tackling  of  these  appliances,  to  en- 
sure that  the  whole  of  the  system  shall  be  designed  throughout  on 
an  uniform  basis. 

RIGGING. 

By  the  term  "  rigging"  is  generally  denoted  the  standing  rigging, 
or  that  part  whose  function  is  to  stay  or  support  the  masts,  spars 
and  funnels,  and  comprises  the  shrouds,  guys,  pendants,  bowsprit 
shrouds,  jib-boom  guys,  stays  and  backstays.  These  supports  are 
now  invariably  made  of  galvanized  wire  rope,  either  iron  or  mild 
steel,  the  latter  being  employed  where  strength  and  lightness  are 
desired,  or  where  heavy  working  derricks  are  fitted.  A  special 
quality  called  plough  steel,  is  sometimes  used  when  exceptionally 
great  loads  have  to  be  lifted.  Indeed,  it  will  often  be  found 
cheaper  to  employ  plough  steel  in  these  cases,  as  the  number  of 
shrouds  or  stays  may  thereby  be  reduced,  thus  effecting  a  greater 
saving  in  the  quantity  required  than  the  extra  cost  in  quality  has 
involved. 

Wire  Rope.  —  As  its  name  implies,  wire  rope  is  manufactured 
from  small  steel  or  iron  wires,  twisted  into  strands,  six  of  which 
(usually)  are  laid  up  around  a  tarred  hemp  centre,  the  strands 
having  a  wire  heart  where  strength  is  more  important  than  flexi- 

575 


576  The  Naval  Constructor 


bility,  otherwise  where  used  as  running  gear  and  flexibility  is  a 
necessity  they  also  have  a  hempen  centre.  The  number  of  wires 
constituting  a  strand  varies  with  the  degree  of  flexibility  required, 
19  wires  to  a  strand  being  ordinary  flexible  rope,  and  37  wires 
extra  flexible,  such  as  would  be  used  for  derrick  topping  lifts. 
Steel  wire  rope  for  ship  rigging  should  always  be  galvanized, 
otherwise  it  deteriorates  rapidly,  and  where  it  is  used  for  running 
gear,  it  should  be  soaked  in  boiling  tallow  and  linseed  oil,  a 
process  which  will  add  much  to  its  life. 

Great  care  must  be  used  at  all  times  in  handling  it  so  as  to  avoid 
sharp  nips  or  kinks,  either  of  which  is  fatal.  For  this  reason 
when  used  as  hawsers,  wire  rope  must  be  stowed  on  a  reel  having 
a  core  of  suitable  diameter,  and  in  the  case  of  running  rigging,  the 
proper  diameter  of  sheave  for  a  given  size  of  wire  is  important. 
An  undersized  sheave  shortens  the  life  of  the  best  rope,  and  by 
distorting  the  fibres,  weakens  its  strength. 

Approximate  diameters  of  sheaves  for  extra  flexible  steel  wire 
rope,  are  given  in  the  table  on  page  381. 

Splices.  —  Splices  in  wire  rope,  such  as  are  necessary  around 
thimbles  and  elsewhere,  weaken  its  strength  from  10  to  15  per  cent. 
It  is  necessary,  therefore,  to  take  account  of  this  in  fixing  on  the 
safe  working  load.  Likewise  in  ordering  the  lengths  of  rope, 
allowance  must  be  made  on  net  sizes  for  the  number  of  splices 
worked. 

Thimbles.  —  In  working  eyes  in  the  ends  of  wire  rope,  it  is 
necessary  that  the  fibres  forming  the  inside  of  eye  should  be 
protected  from  the  destructive  effect  of  a  link  or  shackle  pin 
bearing  on  same.  To  guard  against  this,  the  splice  is  worked 
around  heart  shaped  eyes  or  thimbles.  These,  like  the  sheaves, 
must  be  of  a  suitable  size  for  a  given  circumference  of  rope. 


Sheaves  and  Splices 


577 


SHEAVES   FOR   EXTRA   FLEXIBLE 
V/IRE  ROPE. 


STEEL 


For  Steering  Leads,  Topping  Lifts  and  Purchases. 


Circum- 

Diameter 

Weight 

Circum- 

Diameter 

Weight 

ference 

of 

in 

ference 

of 

in 

of  Rope. 

Sheave. 

•  Brass.* 

of  Rope. 

Sheave. 

Brass.* 

In. 

In. 

Lbs. 

In. 

In. 

Lbs. 

1 

4* 

2* 

8* 

16 

46 

H 

6 

5* 

H 

17 

54 

if 

7 

8* 

4 

18 

66 

if 

8 

11 

H 

19 

78 

2 

9 

15 

H 

20£ 

107 

H 

10| 

20 

4f 

2H 

120 

*t 

12 

26 

5 

23 

138 

H 

13 

29 

S| 

25 

163 

3 

14 

34 

6 

27 

190 

H 

14* 

37 

H 

30 

235 

*  Weight  in  cast  iron  =  Brass  X 


LENGTH  OF  WIRE  ROPE  REQUIRED  FOR 
SPLICES. 


Circum- 

Allowance 

Allowance 

ference  OF 

for  Iron  Wire 

for  Steel  Wire 

Manila. 

Rope. 

Rope. 

Rope. 

In. 

In. 

In. 

1 

9 

12 

li 

12 

18 

2 

15 

21 

2i 

18 

24 

An     average 

3 

20 

30 

allowance  of  15 

n 

22 

33 

inches  is  made 

4 

24 

36 

for  Manila. 

4* 

27 

39 

5 

30 

42 

6 

35 

48 

7 

40 

54 

578 


The  Naval  Constructor 


GALVANIZED    IRON    AND    STEEL    WIRE 
RIGGING   ROPES. 


To  Admiralty  or  Li 

.oyp's  Requirements. 

Sizes. 

Breaking  Stress. 

Weight 
per 

Best  Best 

(ialvan- 

('.alv.uiiy.fd 

-   Circum. 

Diameter. 

Fathom. 

Galvanized 

ized  Mild 

Patent 

Iron. 

Steel. 

Steel. 

Inches. 

Inches. 

Lbs. 

Tons. 

Tons. 

Tons. 

1 

.318 

0.96 

1.2 

1.75 

2.8 

11 

.397 

1.2 

1.5 

2.25 

3.6 

If 

.397 

1.5 

1.87 

3 

4.5 

If 

.437 

1.8 

2.25 

3.25 

5.4 

n 

.477 

2.1 

2.62 

4 

6.3 

if 

.517 

2.5 

3.12 

5 

7.5 

if 

.557 

2.9 

3.62 

6.5 

8.7 

if 

.596 

3.3 

4.12 

6 

9.9 

2 

.636 

3.8 

4.7 

7 

11.4 

2* 

.676 

4.3 

5.3 

8 

12.9 

*§ 

.716 

4.8 

6.0 

9 

14.4 

n 

.755 

5.3 

6.6 

10 

15.9 

H 

.795 

5.9 

7.3 

11 

17.7 

2f 

.835 

6.6 

8.2 

12 

19.8 

n 

.875 

7.1 

8.8 

13 

21.3 

n 

.915 

7.8 

9.7 

14.5 

23.4 

3 

.954 

8.5 

10.6 

16 

25.5 

81 

.994 

9.2 

11.5 

17.5 

27.6 

8f 

1.03 

9.9 

12.3 

19 

29.7 

a 

1.07 

10.7 

13.3 

20.5 

32.1 

3* 

1.11 

11.5 

14.3 

22 

34.5 

3f 

1.15 

12.3 

15.3 

24 

36.9 

8f 

1.19 

13.2 

16.5 

26 

39.6 

8| 

1.23 

14.1 

17.6 

28 

42.3 

4 

1.27 

15.0 

18.7 

30 

45.0 

if 

1.31 

16.0 

20.0 

32 

48.0 

4* 

1.35 

17.0 

21.2 

34 

51.0 

4| 

1.39 

18.0 

22.5 

36 

54.0 

4§ 

1.43 

19.0 

23.7 

38 

57.0 

*f 

1.47 

20.1 

25.1 

40 

63.3 

if 

1.51 

21.2 

26.5 

42 

63.6 

4| 

1.55 

22.4 

28.0 

44 

67.2 

5 

1.59 

23.5 

29.3 

48 

70.5 

5f 

1.67 

26.0 

32.5 

53 

78.0 

6] 

1.75 

28.5 

35.6 

58 

85.5 

6 

1.9         1 

34.0 

42.5 

68 

102.0 

Standard   Hoisting  Rope 


579 


STANDARD    HOISTING     ROPE.  — SWEDISH    IRON. 

(Roebling.) 
Composed  of  6  Strands  and  a  Hemp  Center,  19  Wires  to  the  Strand. 


Approx. 

Proper 

Diameter 

Approx. 

Approx. 

Strength 

Working 

of  Drum 

Diameter 

ClRCUM.  IN 

Weight  per 

in  Tons 

Load  in 

or  Sheave 

in  Inches. 

Inches. 

Foot. 

of  2000 

Tons  op 

in  Feet 

Lbs. 

2000  Lbs. 

Advised. 

2f 

8f 

11.95 

Ill 

22.2 

17 

21 

7| 

9.85 

92 

18.4 

15 

21 

71 

8.0 

72 

14.4 

14 

2 

61 

6.30 

55 

11.0 

12 

H 

H 

5.55 

50 

10.0 

12 

H 

51 

4.85 

44 

8.8 

11 

H 

5 

4.15 

38 

7.6 

10 

1} 

4J 

3.55 

33 

6.6 

9 

H 

41 

3.00 

28 

5.6 

81 

U 

4 

2.45 

22.8 

4.56 

71 

H 

31 

2.00 

'    18.6 

3.72 

7 

3 

1.58 

14.5 

2.90 

6 

i 

2f 

1.20 

11.8 

2.36 

51      • 

f 

21 

0.89 

8.5 

1.70 

41 

I 

2 

0.62 

6.0 

1.20 

4 

A 

U 

0.50 

4.7 

0.94 

31 

1 

H 

0.39 

3.9 

0.78 

3 

A 

H 

0.30 

2.9 

0.58 

21 

! 

H 

0.22 

2.4 

0.48 

21 

A 

1 

0.15 

1.5 

0.30 

2 

1 

1 

0.10 

1.1 

0.22 

H 

Cast  Steel. 

21 

8f 

11.95 

211 

42.2 

11 

21 

n 

9.85 

170 

34.0 

10 

21 

71 

8.00 

133 

26.6 

9 

2 

61 

6.30 

106 

21.2 

8 

U 

H 

5.55 

96 

19.0 

8 

if 

51 

4.85 

85 

17.0 

7 

H 

5 

4.15 

72 

14.4 

61 

l* 

4f 

3.55 

64 

12.8 

6 

if 

41 

3.00 

56 

11.2 

51 

H 

4 

2.45 

47 

9.4 

5 

11 

31 

2.00 

38 

7.6 

41 

l 

3 

1.58 

30 

6.0 

4 

J 

H 

1.20 

23 

4.6 

31 

i 

21 

0.89 

17.5 

3.5 

3 

f 

2 

0.62 

12.5 

2.5 

21 

A 

U 

0.50 

10.0 

2.0 

21 

1 

U 

0.39 

8.4 

1.68 

2 

A 

H 

0.30 

6.5 

1.30 

If 

I 

H 

0.22 

4.8 

0.96 

H 

A 

1 

0.15 

3.1 

0.62 

H 

1 

! 

0.10 

2.2 

0.44 

1 

:,so 


The   Naval   Constructor 


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Mild  Steel  Open  Thimbles 


581 


TABLE   OF   MILD    STEEL   OPEN  THIMBLES. 

For  Steel  Wire  Rope  or  Hawsers. 

(British  Admiralty.) 


Circum- 
ference 

of 
Rope  or 
Hawser. 

Score. 

Size  in  Clear. 

Weight 
Each. 

Width. 

Depth. 

Width. 

Length. 

In. 

In. 

In. 

In. 

In. 

Lbs. 

1 

.4 

.2 

.87 

1.50 

i 

n&n 

.6 

.3 

1.31 

2.25 

ft 

If  &  2 

.8 

.4 

1.75 

3.00 

4 

2i  &2J 

1.0 

.5 

2.18 

3.75 

2A 

2f  &3 

1.2 

.6 

2.62 

4.50 

3Tf 

•    3J 

1.4 

.7 

3.06 

5.25 

6 

4 

1.6 

.8 

3.50 

6.00 

9 

41 

1.8 

.9 

3.93 

6.75 

HI 

5 

2.0 

1.0 

4.37 

7.50 

16  1 

51 

2.2 

1.1 

4.81 

8.25 

231 

6 

2.4 

1.2 

5.25 

9.00 

26  i 

61 

2.6 

1.3 

5.68 

9.75 

37  1 

7 

2.8 

1.4 

6.12 

10.50 

44  1 

8 

3.2 

1.6 

7.00 

12.00 

661 

582 


The   Naval   Constructor 


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584  The   Naval  Constructor 

WIRE    ROPE   END-FITTINGS. 


TyiMBLLftNpHOM. 
Figs.  337-344. 


Rope  Fittings  585 

Rope  End  Fittings.  —  Another  method  of  forming  an  eye  on 
the  end  of  wire  rope,  is  to  work  an  open  eye  with  groove-shaped 
ends,  to  enclose  the  rope,  and  through  which  they  are  riveted  as 
shown  in  the  plate.  This  "  shoe,"  however,  is  rarely  resorted  to 
unless  on  the  bowsprit  shrouds,  and  similar  rigging  on  yachts, 
where  small  close-fitting  eyes  are  desired  for  neat  appearance. 

Some  of  the  more  common  forms  of  wire  rope  end  fittings  are 
illustrated  on  the  preceding  page.  Their  various  uses  will  suggest 
themselves  to  the  observant. 

Parcelling  and  Serving. —  In  ordinary  merchant  work,  the 
lower  ends  of  shrouds  and  stays  for  6  or  7  feet  are  wormed  and 
parcelled  with  two  overlapping  layers  of  cotton  sheeting,  painted 
and  thereafter  served.  Where  stays  are  subjected  to  much 
chafing,  they  should  be  doubly  served  and  covered  with  leather 
in  the  collars. 

,    No  serving  must  be  fitted  on  stays  which  carry  sails,  as  it  would 
only  be  cut  to  pieces  by  the  chafe  of  the  hanks. 

Turnbuckles.  —  Standing  rigging  is  invariably  set  up  with 
turnbuckles,  or  rigging  screws  to  enable  the  wire  to  be  tautened, 
as  quite  an  appreciable  amount  of  "stretch"  takes  place,  more 
particularly  in  new  rope. 

These  screws  are  proportioned  to  the  breaking  strength  of  the 
wire,  which  should  be  spliced  around  a  solid  heart-shaped  core 
for  the  heavier  sizes,  or  an  open  thimble  in  the  case  of  light  wire. 
Where  used  for  shrouds,  the  lower  end  must  be  arranged  to  swivel 
freely,  and  the  pad-eye  riveted  to  sheerstrake,  the  connection 
developing  the  same  strength  as  the  screw.  Where,  however,  they 
are  set  up  fore  and  aft  on  stays,  the  pad  should  have  a  shackle-eye 
for  pin,  as  'thwartship  movement  is  not  then  desirable,  and  the 
shackle-eye  will  permit  of  a  smaller  diameter  pin  being  used. 

In  proportioning  screws  under  one  inch  in  diameter,  an  allow- 
ance of  about  20  per  cent  must  be  added  to  the  area  of  metal  at 
root  of  thread,  as  compensation  for  the  loss  of  strength  sustained 
in  cutting  the  screw.  Screws  should  be  smeared  with  tallow  and 
coated  with  a  canvas  cover. 

Sheerpoles.  —  It  is  usual  to  fit  a  rod  to  the  heads  of  turn- 
buckles to  shrouds  connecting  and  supporting  the  heads  in  their 
relative  position,  and  preventing  the  screws  from  slacking  back. 
In  small  vessels  it  may  be  from  g"  to  § "  diameter,  seized  to  each 
head  with  seizing  wire.  Where  heavy  rigging  is  dealt  with,  the 
sheerpole  is  bolted  through  the  heart  of  turnbuckle,  and  bosses 
jumped  on  to  form  receptacles  tor  belay  pins. 

Ratlines — Are  commonly  made  of  hemp  or  wire  rope,  seized 
at  outer  shrouds  and  passing  around  the  others  in  a  clove  hitch, 


586  The  Naval   Constructor 


and  spaced  about  24  inches  apart.    Rope,  however,  is  being  fast 
displaced  by  iron  rod  ratlines,  seized  with  wire  to  shrouds. 

ROPES. 

Manila  and  hemp,  tarred  and  white,  are  the  materials  from 
which  most  ship's  ropes  are  made.  As  its  name  indicates, 
"Manila"  hails  from  the  Philippines,  and  is  made  from  the 
fibre  of  the  wild  banana.  Hemp  rope  is  made  from  the  fibre  of 
the  hemp  plant,  the  Russian  variety  being  most  generally  used. 
Tow  lines  are  sometimes  made  of  coir,  which  is  manufactured 
from  the  tough  fibrous  husk  of  the  cocoanut.  In  referring  to 
ropes,  the  circumference  always  denotes  the  size. 

Manila.  —  All  running  ropes  and  those  used  for  sundry  work 
on  shipboard  are  made  of  Manila,  as  hemp,  though  stronger 
when  white,  is  not  pliable  enough.  It  is  usual  to  make  it  of  3 
strands,  although  4-stranded  or  shroud-laid  rope  is  also  made ;  and 
for  yacht  work,  4-strand  Manila  is  best,  as  it  is  smaller  in 
diameter  for  a  given  strength,  besides  being  neater. 

Manila  is  of  greater  strength  than  tarred  hemp,  and  stands  the 
weather  much  better  than  the  untarred  or  white  hemp,  although 
not  so  strong  as  the  latter. 

The  following  tables  give  strengths  and  weights  of  Manila, 
hemp,  and  coir  ropes  :  — 


Manila  Rope 


587 


MANILA   ROPE. 


go? 
5£§ 

Diam- 
eter 

OF 

Rope. 

Wt. 

per 

Foot. 

Break- 
ing 
Stress. 

i  w  a 

£  *  O 

Diame- 
ter of 
Rope. 

Wt. 

PER 

Foot. 

Break- 
ing 
Stress. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

i 

A 

.035 

405 

H 

11 

.640 

16,200 

I 

i 

.045 

585 

5 

If 

.720 

20,000 

1 

A 

.055 

700 

H 

If 

.835 

23,650 

n 

1 

.065 

900 

6 

11 

1.05 

27,000 

n 

A 

.075 

1,170 

61 

2 

1.15 

29,250 

H 

i 

.085 

1,800 

6| 

n 

1.25 

31,690 

n 

A 

.110 

2,295 

7 

21 

1.42 

33,800 

2 

1 

.140 

3,200 

?! 

21 

1.70 

36,750 

21 

I 

..170 

3,750 

8 

2A 

2.00 

39,200 

2* 

if 

.200 

4,050 

B* 

2| 

2.30 

50,000 

2| 

I 

.240 

6,050 

9 

21 

2.65 

54,190 

3 

i 

.275 

7,200 

n 

3 

3.00 

57,800 

31 

*A 

.325 

7,875 

10 

»A 

3.40 

75,000 

3| 

M 

.360 

9,800 

11 

pi 

4.00 

96,000 

Si 

1A 

.410 

10,500 

12 

81 

4.70 

101,000 

4 

n 

.460 

11,250 

13 

41 

5.65 

117,000 

*i 

if 

.510 

13,500 

14 

41 

6  50     ' 

158,300 

4 

iA 

.585 

14,450 

15 

M 

7.50 

172,500 

:>ss 


The   Naval   Constructor 


HEMP    CORDAGE. 


.5 

fa 

a    g 

*     H 

£2^ 

WO  w 

Mb 

0 

0 

fc  05 

»  W 

Kind. 

In. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

| 

6 

.018 

336 

.015 

476 

1 

12 

.037 

672 

.031 

1,008 

40  Thread 

1 

15 

.047 

896 

.039 

1,344 

Yarn  Hemp. 

H 

21 

.062 

1,120 

.052 

1,680 

i| 

33 

.098 

1,680 

.083 

2,352 

Tarred  is 

l| 

42 

.125 

2,240 

.105 

3,136 

Riga. 

2 

54 

.161 

3,024 

.134 

4,144 

2* 

66 

.196 

3,808 

.160 

5,162 

White  is 

2J 

84 

.250 

4,480 

.208 

6,496 

Italian. 

2} 

102 

.302 

5,600 

.240 

7,800 

3 

120 

.355 

6,720 

.296 

9,408 

3i 

105 

.414 

7,840 

.331 

11,000 

30  Thread 

H 

123 

.485 

8,512 

.403 

12,544 

"  Yarn  Hemp. 

4 

159 

.626 

11,200 

.522 

16,240 

.     Tarred  is 

*i 

201 

.791 

14,448 

.661 

20,720 

Riga. 

5 

249 

.995 

17,696 

.816 

25,760 

White  is 

6 

360 

1.40 

25,760 

1.18 

36,960 

J        Italian. 

6* 

351 

1.66 

28,672 

1.40 

43,200 

25  Thread 

7 

408 

1.92 

33,152 

1.61 

47,000 

Yarn  Hemp. 

n 

468 

2.07 

38,000 

1.85 

51,520 

Tarred  is  St. 

8 

534 

2.52 

43,456 

2.11 

58,240 

Petersburg. 

9 

675 

3.18 

53,760 

2.66 

73,920 

White  is 

12 

1,200 

5.65 

96,500 

4.72 

131,040 

Italian. 

Hemp.  —  Hemp  rope  deteriorates  rapidly  when  exposed  to 
wind  and  weather,  and  for  this  reason,  when  practicable,  it  is 
tarred,  although  doing  so  weakens  it.  Hemp  should  only  be  used 
for  warps  and  bolt  ropes  of  sails,  as  it  is  much  too  hard  for  other 
purposes,  more  especially  when  wet. 

The  following  rules  give  the  equivalent  circumference  of  tarred 
and  white  hemp  rope  for  a  working  load  in  tons  of  one  third  the 
breaking  stress  :  — 


*sfl  X  load  =  circumference  of  white  rope. 
V9  x  load  =  circumference  of  tarred  rope. 


Length  of  Reel 


589 


Other  Rope.  —  A  variety  of  small  stuff  is  used  in  ship  work 
for  sundry  purposes,  the  principal  kinds  of  which,  and  their 
purposes,  follow  :  — 

Cotton  Rope  is  only  used  for  halliards  and  sheets  in  small  craft, 
being  much  softer  than  Manila. 

Houseline  is  used  for  lacing  sails,  etc. 

Marline  is  a  small  kind  of  tarred  hemp,  used  for  serving  ropes 
and  splices. 

Serving  twine  (tarred  or  waxed)  is  used  for  whipping  the  ends 
of  ropes  and  other  small  jobs. 

COIR   ROPE. 


fa 

tf 

a 

fa 

ri 

<S 

9  w  2 

V  fa 

fa 

fa 

H       fa 

fa  fa  fa 

?°* 
A 

fa  kg 

is 

R  «  £ 

« 
Pa 

5 

rt  P5  ^ 
m  Ed  © 

5* 

Si 

In. 

In. 

Lbs. 

Lbs. 

In. 

In. 

Lbs. 

Lbs. 

H 

if 

.100 

1,064 

6 

M 

.568 

6,384 

3 

l 

.142 

1,568 

7 

2* 

.775 

8,512 

3* 

1A 

.193 

2,072 

8 

8* 

1.003 

10,864 

4 

n 

.251 

2,856 

9 

»* 

1.280 

14,336 

5 

it 

.392 

4,480 

LENGTH    OF   REEL 

For  100  Fathoms  of  Manila. 


(Cores  4£" 

Diameter.) 

fa 
,  0 

^'A  fa 

S  ^03 

wfa 
fa 

fa  fa  fa 
S  0  w 

fa 
0  if 

w    3 

H       O 

go 

,  0 

hi 

«§3 

fa 

u 

H       O 
O  far> 

3   tf 

ft 

a  I 

fa 

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H 

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8* 

24 

20 

34  0 

6 

24 

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22  0 

8* 

30 

13 

55  6 

6 

30 

43 

25  0 

4 

24 

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30  0 

6$ 

24 

63 

19  0 

4 

30 

16 

49  0 

6i 

30 

46 

27  0 

** 

24 

35 

25  0 

7 

24 

70 

18  0 

H 

30 

20 

43  0 

7 

30 

50 

26  0 

5 

24 

43 

23  0 

a 

24 

75 

18  0 

5 

30 

27 

38  4 

n 

30 

53 

26  0 

&! 

24 

51 

22  6 

8 

24 

80 

17  9 

5* 

30 

35 

31  6 

8 

30 

55 

27  0 

590  The  Naval   Constructor 

CHAPTER   II. 

BLOCKS. 

Blocks  are  divided  broadly  into  two  varieties,  wood  and  iron, 
the  former  being  used  when  reeving  falls  or  tackles  of  Manila,  and 
the  latter  for  wire  rope.  Wood  blocks  are  either  "  made  "  or 
"  mortised,"  and  may  have  metal  or  lignum-vitae  sheaves.  The 
space  in  the  block  between  the  wood  and  the  sheave  is  called  the 
"  swallow,1'  the  opposite  end  of  the  block  being  named  the 
"  breech,"  and  the  sides  the  "  cheeks."  The  frame  of  the  block 
may  be  strapped  with  iron  or  rope,  a  score  being  cut  to  form  a 
housing  for  same. 

All  good  blocks  should  be  fitted  with  patent  roller  sheaves, 
especially  for  halliards  and  sheets,  or  for  any  heavy  work.  For 
topsail,  sheet,  throat  and  peak  halliard  purchases,  etc.,  ash  blocks, 
rope  stopped,  should  be  used.  For  derricks  on  freighters,  where 
wire  rope  is  used  for  heavy  loads,  iron  blocks  are  best ;  where 
Manila  falls  and  topping  lifts  are  fitted,  wood  blocks  are  most 
suitable. 

It  will  be  evident  that  a  good  deal  of  power  can  be  wasted  by 
friction  of  the  sheave  on  pin,  and  also  by  the  rope  chafing,  through 
insufficient  "swallow."  To  minimize  the  loss  due  to  friction 
through  the  former  cause,  the  pins  should  be  bushed.  Various 
bushings  are  employed  for  this  purpose,  probably  the  most 
efficient  being  a  gunmetal  or  bronze  sheave  with  spotted  graphite 
next  the  pin. 

The  loss  due  to  friction  is  10  per  cent  for  each  sheave. 

Blocks  are  designated  "single,"  "double,"  or  "treble,"  in 
accordance  with  the  number  of  sheaves  fitted,  and  are  variously 
named  to  denote  either  a  particular  shape  or  as  indicating  the 
purpose  for  which  they  are  intended.  Some  of  the  more  common 
ones  are  :  — 

Snatch  Blocks  are  used  to  divert  the  lead  on  the  hauling  part 
of  a  fall  or  tackle,  having  for  this  purpose  a  hinged  part  on  one  of 
the  cheeks,  to  permit  of  placing  the  rope  in,  which  would  other- 
wise require  reeving  —  a  tedious  and  often  impracticable  process. 
They  are  usually  fitted  at  heels  of  derricks,  and  on  deck,  to  take 
warping  and  other  leads,  and  are  mostly  made  of  iron,  the  old- 
fashioned  wood  snatch  block  being  clumsy  and  cumbersome. 

Fiddle  Blocks  take  the  name  from  their  resemblance  to  the 
instrument,  being  constructed  with  two  sheaves  placed  tandem,  to 
permit  of  reeving  separate  halliards  leading  in  opposite  directions. 


Blocks  591 


They  are  to  be  found  on  peak-halliards,  at  preventer  stay  tackles, 
etc.,  and  are  made  in  wood  where  Manila  is  rove,  and  in  iron  for 
wire  rope. 

Gin  Blocks  are  used  on  derrick  heads  and  spans  in  conjunc- 
tion with  a  whip  for  handling  cargo,  and  comprise  a  skeleton  frame 
and  sheave  of  iron. 

Cat  and  Fish  Blocks  are  fitted  to  the  anchor  davit,  or  crane, 
and  consist  of  a  pair  of  blocks  with  double  or  treble  sheaves,  hav- 
ing a  large  swallow.  The  fish  (or  lower)  block  has  a  large  hook, 
sometimes  made  to  trip,  for  fishing  the  anchor  by  the  gravity  band 
on  the  stock.  These  blocks  are  made  in  both  wood  and  iron,  the 
latter  being  often  fitted  with  Manila  falls. 

Clump  Blocks  are  made  short  and  thick,  as  their  name  im- 
plies. They  are  used  for  tacks  and  sheets,  and  for  this  reason  are 
extra  large  in  the  swallow.     Made  iu  wood  and  iron. 

Wrecking  Blocks  are  large,  extra  heavy  iron  strapped  blocks, 
with  lashing  shackles,  and  are  used  for  rigging  up  special  derricks 
for  temporary  use  with  heavy  loads. 

Cheek-Blocks  have  only  one  side,  the  other  cheek  being 
formed  by  fitting  against  a  spar. 

The  size  of  a  block  is  designated  by  the  length  of  the  shell,  and 
this  is  determined  from  the  circumference  of  the  rope  which  it 
reeves,  as  a  unit.  For  most  purposes  three  times  the  size  of  rope 
gives  a  suitable  block,  but  in  a  few  cases,  where  the  minimum  of 
friction  and  extra  ease  is  desired  in  the  swallow,  as  with  blocks 
for  boat  davit  tackles,  three  and  one  half  times  should  be  taken, 
e.g.,  a  block  for  ordinary  purposes  to  reeve  three-inch  Manila 
would  be  9  inches,  but  if  required  for  davit  falls,  the  size  would 
be  increased  to  10  inches.  The  diameter  of  sheave  is  usually 
about  two  thirds  of  the  size  of  block,  a  12-inch  block  having  an 
8-inch  diameter  sheave. 

In  ordering  blocks  it  is  necessary  to  prepare  a  list,  giving  a 
concise  but  full  and  exact  description  of  each  individual  block, 
embracing  the  following  points  :  — 

Sheaves. — The  number  of  sheaves  to  be  indicated  by  "S," 
"  D,"  or  "  T,"  and  whether  of  lignum-vitse,  brass,  or  iron  sheaves, 
bushed  or  patent  roller  bushed. 

Name.  — The  purpose  for  which  the  block  is  intended  should  be 
given,  as,  "jib-sheets,"  "  derrick  falls, "  etc. 

Shackles  should  be  very  clearly  specified  where  they  are  for 
special  fittings.  Ordinarily  the  shackle  is  fitted  with  its  pin  at 
right  angles  to  the  axis  of  the  sheave,  this  being  the  most  natural 


592  The   Naval  Constructor 

way  to  engage  the  strap  of  block,  therefore  when  the  word 
M  shackle,"  without  further  description,  is  used,  it  is  always  fitted 
in  this  manner.  Where,  however,  it  is  essential  to  have  it  with 
the  shackle  pin  running  parallel  with  sheave  pin  (as  is  often 
necessary  to  get  the  falls  of  a  tackle  to  lead  in  line  with  hauling 
part)  the  words  "reverse  shackle  "  must  be  used.  If  the  shackle 
be  required  with  its  jaw  uppermost,  "reverse  upset  shackle" 
should  be  specified. 

It  often  happens  that  a  block  is  required  with  an  eye  to  engage 
a  shackle,  which  the  blockmaker  is  not  required  to  furnish.  In 
such  cases  it  is  well  to  state  whether  the  eye  should  be  "  worked  " 
or  a  "  shackle-eye  "  wanted.  A  "  worked  eye,"  of  course,  is  one 
having  its  edge  worked  round  like  a  ring,  the  "  shackle-eye"  being 
drilled  straight  through,  so  that  the  inserted  pin  bears  along  its 
entire  length.  For  a  given  diameter  of  pin,  that  in  a  shackle-eye 
would  be  twice  as  strong  as  the  one  bearing  on  a  worked  eye,  so 
that  where  other  considerations  do  not  count,  it  is  economy  to  fit 
a  shackle  eye. 

Beckets  are  small  eyes  fastened  at  the  breech  end  of  blocks 
to  take  the  thimble  on  the  standing  part  of  a  tackle.  They  are 
useful  to  have  on  all  spare  tackle  blocks. 

Strops.  —  When  blocks  are  intended  for  brace  or  guy  pen- 
dants, they  should  be  specified  as  having  a  score  cut  to  receive  the 
rope  strop. 

Hooks  should  not  be  used  on  blocks  where  heavy  loads  are 
dealt  with.  For  loads  under  ten  tons  they  are  equally  reliable 
with  shackles,  besides  being  handier.  They  should  be  specified  as 
"loose,"  "  stiff  front,"  "side,"  or  "  swivel  "  hook,  as  required, 
and  the  working  load  given  in  all  cases,  as  many  of  the  hooks  on 
low  grade  blocks  are  considerably  inferior  in  strength  to  the  other 
parts  of  the  fitting. 

Sister,  or  Match  Hooks  are  used  for  a  variety  of  purposes, 
and  consist  of  two  hooks  on  a  common  eye,  arranged  to  open,  and 
when  closed,  to  form  a  seemingly  solid  eye. 

Lashing  Shackles  are  especially  large  in  the  bow,  and  wider 
at  the  jaws,  than  ordinary  shackles,  being  fitted  to  the  heavier 
classes  of  double  and  treble  blocks,  to  permit  of  their  taking  a 
Manila  or  wire  rope  lashing. 

Swivel  Jaws  are  sometimes  fitted  to  the  upper  block  in  davit 
tackles. 

Appended  is  a  table  giving  actual  weights  of  blocks,  fitted  with 
shackles  and  beckets  complete,  which  will  be  of  use  in  estimating 
rigging  and  outfit  weights. 


Sheaves  for  Iron   Blocks 


593 


STRENGTH  AND  "WEIGHT  OF  RIGGING  CHAIN. 

(B  B  B  Quality.) 


*  Working  Load 

t  Breaking 

Weight 

Size. 

F.  S.  4 

Stress 

per  Foot  in 

in  Pounds. 

in  Pounds. 

Pounds. 

A 

675 

2,700 

.5 

1 

1,260 

5,040 

.75 

A 

1,876 

7,504 

1.08 

i 

2,660 

10,640 

1.50 

3,640 

14,560 

2.00 

ft 

4,620 

18,480 

2.67 

A 

5,740 

22,960 

3.33 

1 

6,860 

27,440 

4.17 

M 

8,120 

32,480 

5.17 

t 

9,800 

39,200 

6.18 

a 

11,200 

44,800 

7.00 

i 

12,460 

49,840 

8.00 

H 

14,280 

57,120 

8.85 

i 

15,960 

63,840 

10.00 

ItV 

17,640 

70,560 

12.00 

li 

19,320 

77,280 

15.00 

1'i 

23,940 

95,760 

17.50 

i| 

32,200 

128,800 

20.00 

if 

44,520 

178,080 

26.70 

2 

58,520 

234,080 

36.70 

*  B  B  quality  =  20%  less  than  table,    t  B  quality  =  30%  less  than  table. 


SIZE    OF   SHEAVES   FOR   IRON  BLOCKS. 


Sow 

A      W 
cc 

m    g 

Sow 

a    w 

cc 

oq°k 
o 

S  o  a 

ft     a 

cc 

M    O    0 

«  g 

n 

// 

a 

II 

a 

a 

II 

II 

II 

2* 

1 

7 

n 

I 

13 

2A 

H 

H 

h 

.   .   . 

8 

H 

A 

14 

2| 

I 

4 

( 

9 

if 

* 

15 

3 

tt 

4* 

I 

t\ 

10 

2 

A 

16 

81 

I 

5 

I 

i 

11 

*i 

1 

17 

»i 

H 

6 

l 

5 

12 

H 

T6 

18 

8| 

l 

594 


The  Naval  Constructor 


WEIGHT 


Kind  of 
Blocks. 

a 

§8 

02 

o3 

M 

S 
9Q 

s 

00 

2 
A 
ft 

H 

H 

H 

g 

s 

X 

09 

hi 

H' 

H 

2 

w 

30 

CO 

I 

ft 
H 

w 
2 

H 
7. 

00 

« 
g 

H 

W 

2 

M 

02 

00 

2 

H 

W 

2 

W 

Wood   .... 
Wood   .... 
Wood  .... 
Wood  .... 
Wood   .... 
Wood   .... 
Wood    .... 
Wood  .... 
Wood   .... 
Cargo  block 
Gin 

Gin 

Iron  block    } 
Wire  rope    J 
Iron  block   j 
Wire  rope    | 
Iron  block   i 
Wire  rope    ) 

Wood  snatch 
Iron  snatch . 
Rope  w.  iron 
Rope  w.  iron 
Rope  w.  iron 

8 
D 
T 

S 
D 
T 
S 
D 
T 

S 
D 
T 

S 
D 
T 

'/ 
4 

4 

4 

4 

4 
4 

i 

H 

H 
if 

2i 
31 

5 
5 
5 

5 
6 
5 

i] 

2J 
3| 
5| 

8 

6 

i; 

(3 

8 
8 

6 

6 
6 

21 
4 
4* 
41 
6 
92 

7 

ia 

14 

7 
7 
7 
7 
7 
7 
7 
7 
7 

7 
7 
7 

3 
B| 

6! 

61 

91 
12f 

71 
10 
14 

9 
13 
19 

8 
8 
8 

8 
8 

8 
8 

8 
8 

8 

8 
8 
8 

41 

71 
10 

81 
13 
18 

91 
141 
201 

12 

10 

181 
28 

B 

D 
B 
9 
9 

i) 
9 
9 
9 

51 

9 

HI 
10§ 
16 
231 
HI 
19 
27 

10 
10 
10 
10 
10 
10 
10 
10 
10 

10 

10 

sheave 

10 
sheave 

10 
sheave 

10 

10 
10 
10 
10 
10 

6 

HI 

15 

14 

251 

35 

161 

29 

39 

19 
21 
40 
60 
100 
22 
261 
22 
38 
51 

Weight  of  Blocks 


595 


OF  BLOCKS. 


s 

CO 

i 

- 

H            S 

* 

as 

s 

O 

M 

N 
5 

"Weight  ik  Lbs. 
Size. 

a 

a 

w 

M 
I* 

■■1 
BO 

GO 

P5 

H 

X 

o 

H 

s 

00 

a 

* 

00 

to 

n 

w 

0 

jjj 

EB 

CO 
HI 

W 
0 

II 

11    21 
11    3 
11    4 
11    2. 
11    3. 
11    4' 

12 

12 

12 

3J         12 

L           12 

J           12 

J          12 

)           12 

r         12 

12 

12 

12 

slieave 
12 

sheave 
12 

sheave 
12 

12 
12 
r2 
12 
12 

111    .. 
20^     .. 
28|    .. 

22  13 
33      13 
45      13 

25  13 
38      13 
50      13 

26  .  . 

23  .  . 
25i    .. 
67      .'. 

109      .  . 
145     .  . 
33      .. 
41      .  . 
31       .  . 
58     .  . 
81       .  . 

a 
14 

14 

14 

30        14 

44         14 

62        14 

33        14 

47        14 

65        14 

14 

14 

slieave 
14 

sheave 
14 

sheave 
14 

14 
14 
14 
14 
14 

20J 
35 
49 
39 
64 
89 
49 
73 
105 
35 
28 

89 
150 
210 

46 

56 

54 
100 
134 

16 

ir> 

15 

15 
15 
15 

15 

15 
15 
15 

44 
69 
100 
51 

77 
112 

35 

60 
96 
150 

18 
16 

it; 
16 
16 

16 
16 
16 

16 
10 
16 
16 
16 

71 
120 
168 

70 
62 

68 
68 

80 
166 

.'10 

18 
18 

18 

18 
18 
18 
18 
18 

188 
83 
100 

90 
105 
150 
201 

20 

20 
20 

130 

140 
147 

596 


The  Naval  Constructor 


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Cargo   Blocks 


597 


CARGO   BLOCKS. 


h#H 


>>*J  Vug  U-2-H   ?°«K>,'S 


W-^^3*.    ^ffh  iff?  I 


rfHWf 


Hfk'f--^ 


Figs.  ,345,  346. 


598 


The   Naval   Constructor 


CHAPTER  III. 


TACKLES. 


00  LBS. 
PLUS  POWER 


50  LBS. 
J      TO  BALANCE 


SINGLEWHIP 


When  ropes  are  reeved  through  blocks  to  multiply  the  power  it 
is  proposed  to  apply,  the  combined  gear  constitutes  what  is  known 
as  a  tackle.  The  principle  of  the  block  and  tackle  is  the  distribu- 
tion of  weight  in  various  points  of  support, 
the  mechanical  advantage  derived  depend- 
ing entirely  upon  flexibility  and  tension  of 
the  rope,  and  the  number  of  sheaves  in  the 
moving  block,  hence  by  tackles  the  power 
applied  to  raise  is  to  the  weight  as  the  number  of  parts 
attached  to  the  moving  block,  therefore 
(1)  divide  the  weight  to  be  raised  by  the 
number  of  parts  leading  "to,"  "from," 
or  "made  fast"  to  the 
moving  block,  and  the 
quotient  is  the  power  re- 
quired to  produce  equi- 
librium —  omitting 
friction. 

(2)  Divide  the  weight 
to  be  raised  by  the  power 
proposed,  and  the  quo- 
tient is  the  number  of 
sheaves  in,  or  parts  at- 
tached to,  the  moving 
block. 

It  should  be  noted  that 
the  upper  block  of  a  tackle  has  to  bear  the 
weight  to  be  raised,  and  the  power  applied  to 
lift  it.  No  power  is  gained  by  increasing  the 
diameter  of  the  sheaves,  but  by  doing  so  you 
decrease  friction. 

In  arranging  the  blocks  for  a  purchase,  note 
that  the  hauling  part,  -where  possible,  should 
lead  from  the  moving  block,  as  by  so  arrang- 
ing, the  power  is  increased. 

Tackles  are  named  variously,  sometimes  as  threefold,  fourfold, 
etc.,  referring  to  the  number  of  ropes  rove ;  and  as  guy-tackles, 
sheet-tackles,  etc.,  or  by  a  distinctive  name,  whose  derivation  in 
most  cases  is  obscure,  like  Spanish  burton,  etc. 

A  single  "whip  and  whip-upon-whip  are  shown  by  Figs.  272 
and  273  and  their  mechanical  advantage  indicated. 


WHIP 
UPON 
WHIP 


Fig.  347. 


Fig.  348. 


Tackles 


599 


Strictly  the  single  whip  is  not  really  a  tackle,  as  no  mechanical 
advantage  is  gained.  If  we  reverse  the  arrangement,  and  instead 
of  fixing  the  block,  we  make  one  end  of  the  rope  fast  and  haul 
on  the  other  after  it  is  rove  through  the 
block,  which  is  now  movable,  we  have  a 
tackle  with  the  power  applied  doubled. 

The  next  simplest  form  to  the  foregoing  is 
the  gun-tackle  purchase,  shown  by  Fig. 
274,  which  consists  of  two  single  blocks,  one 
movable  and  the  other  fixed.     In  the  dia- 
gram, the  power  is  shown  as  being  applied 
to  the  fixed  pulley,  which  results  in  doubling 
the  power  only.     If,  however,  the  order  be 
reversed,  and  the  rope  becketed  to  the  lower 
lbs         block,  from  which  the  hauling  end  would 
now  lead,   we   should   increase  the  power 
gained  so  that  150  lbs.  could  be  sustained 
in  equilibrium  by  the  application  of  50  lbs. 
In  all  tackles  the  hauled- 
on  block  has  not  only  to 
tackle         support  the  load  pendant 
purchase  on  it,  but  also  the  power^^g 
required  to  lift  the  load. 
The  luff-tackle  pur- 
chase shown  in  Fig.  275, 
Fig.  349.  js  ajso  known  as  a  watch- 

tackle,  and  has  exactly  the  same  mechanical 
advantages,  although  consisting  of  a  double  and 
single  block,  as  the  gun-tackle  with  the  hauling 
part  taken  from  the  movable  block,  that  is  to 
say,  the  power  applied  equals  one  third  of  the 
weight  to  be  raised.  The  case,  however,  is 
different  if  the  hauling  rope  of  the  luff-tackle  8INGLE 
be  taken  from  the  movable  block,  when  the 
ratio  of  power  to  weight  is  increased  to  one 
quarter. 

A  twof old  purchase  consists  of  two  double 
blocks,  and  has  a  ratio  of  power  to  weight  of 
one  quarter,  when  hauled  on  from  the  fixed 
block,  and  of  one  fifth  when  from  the  moving 
block. 

A  threefold  purchase  comprises  a  pair  of  treble  blocks  with 
a  mechanical  advantage  of  one  sixth  leading  from  the  fixed  block, 
and  one  seventh  when  hauled  on  from  the  moving  block. 

Fig.  276  shows  a  single  Spanish  burton,  which  is  composed 
of   two  single  blocks  with  the  tackle  reeved  as  shown.     This 


LUFF 
TACKLE 
PURCHAS 


000 


The   Naval   Constructor 


purchase  has  the  same  power  as  the  luff  tackle,  but  less  friction. 
It  is  a  handy  and  powerful  purchase,  used  for  doing  odd  jobs. 

The  double  Spanish  burton  is  made  up  of  a  luff-tackle  and  a 
whip,  with  the  standing  parts  toggled  on  together  to  the  becket  of 
the  lower  single  block.  It  has  the  same  power, 
but  with  much  less  friction,  as  a  threefold  pur- 
chase hauled  on  from  the  moving  block. 

Relieving    tackles    are    usually   two    or 

three-fold  purchases,   having   the   fixed   block 

shackled  on  end  of  spare  tiller,  and  the  hauling 

block  made  fast  on  the  quarter.     These  tackles 

are  used  for  steering,  in  case  of  break-down, 

and  need  only  to  be  figured   for  the  steamer 

going  at  slightly  over  half  speed. 

A  tackle  may  be  attached  to  the  hauling  part 

of  another  tackle,  and  so  multiply  the  powers 

of  which  they  are  comprised. 
In  arranging  purchases  the  minimum  number 
of  sheaves  for  the  power 
required  should  be  used, 
and  all  superfluous  fair- 
leads  dispensed  with,  as 
each  additional  sheave 
fitted  for  that  purpose 
absorbs  power. 

As  an  example  of  the 
application  of  the  fore- 
going notes  on  purchases 
to  the  finding  of  a  suitable  tackle  for  a  given 
load,  let  us  take  the  case  of  relieving  tackles 
on  tiller.  The  twisting  moment  on  the  rud- 
der head  is  first  calculated  by  the  rule  given 
on  page  106,  which  we  shall  assume  to  be 
150,000  inch-lbs.  With  a  spare  tiller  50 
inches  long  from  centre  of  stock  to  shackle 
burton  pin,  we  should  have  a  net  load  of  3,000  lbs. 
to  move,  and  it  is  proposed  to  use  a  four- 
fold purchase  (i.e.,  2  double  blocks)  for  the 
purpose,  which  will  increase  the  load  by  four 
tenths  (4  sheaves  by  one  tenth  of  the  load 
Pig.  352.  each  for  friction),  making  the  actual  load  to 

be  operated  3,000  +  1,200  =  4,200  lbs.     The  moving  block  being 

on  the  tiller  head,  it  is  not  practicable  to  haul  from  it,  therefore 

we  have  only  4  parts  at  this  block.     Dividing  the  total  load  by 

four  ropes,  we  get  1,050  lbs.  (.47  ton)  tension  on  each  fall.     With 


SINGLE 
SPANISH 
BURTON 


Fig.  351. 


Tackles  601 

a  factor  of  safety  of  4|,  using  the  best  Manila  rope,  we  get  the 
equivalent  circumference  from  the  formula 

Vtension  X  10  =   V^7xTo  =  2|", 

say  2\",  as  the  manufactured  sizes  grade  by  quarters. 

The  size  of  the  double  blocks  to  take  the  rope  would  be  7  inches, 
obtained  by  the  rule  on  p.  394,  and  it  would  require  four  men  to 
handle  the  hauling  part. 

It  is  desired  to  lift  a  weight  of  12  tons  with  a  ship's  derrick,  and 
the  maximum  load  on  the  winch  must  not  exceed  5  tons;  required 
the  purchase,  size  of  steel  wire  rope  falls  and  blocks  ?  Owing  to 
the  heavy  load  dealt  with  in  this  case,  the  factor  of  safety  need 
not  exceed  5.  The  hauling  part  of  falls  to  be  led  through  a  lead- 
ing block  at  heel  of  derrick. 

Load  to  be  raised 12      tons 

Friction  of  5  sheaves 6         " 

Derrick  gear A     " 

Total  load  to  overcome 18.4 

As  the  load  on  the  winch  may  not  exceed  5  tons,  the  purchase 

should  be  -^  =  four  parts  in  the  falls  —  a  twofold  purchase. 
4.o 

A  factor  of  safety  of  5  having  previously  been  decided  upon,  we 
get  for  the  breaking  stress  4.6  X  5=  23  tons,  and  the  equivalent  cir- 
cumference of  special  flexible  steel  wire  rope,  per  table  =  3  inches 
circ,  which  will  require  two  double  blocks  with  sheaves  13$ 
inches  in  diameter.  It  should  be  noted  that  the  maximum 
tension  comes  on  the  hauling  part  in  hoisting,  but  on  the  standing 
part  in  lowering. 

The  stress  on  topping  lift,  allowing  for  friction  of  one  sheave, 
and  power  applied  is  equal  to  9  4  tons,  requiring  special  flexible 
steel  wire  rope  of  3^"  circumference. 

A  fourfold  purchase  rove  with  Manila  4"  circ.  having  two  12" 
double  blocks,  with  wide  mortise  and  the  hauling  part  taken  from 
the  moving  block,  will  be  suitable  for  the  load  of  9.4  tons  minus 
the  power  applied,  i.e.,  8\  tons. 

The  following  tables  give  the  strength  of  tackles  and  the  break- 
ing stress  from  actual  test  of  hooks  and  shackles,  fitted  by  the 
makers  to  the  various  sizes  of  blocks. 

The  proper  workingload  for  new  Manila  ropes  is  $  of  the  breaking 
stress.  Of  course,  first  grade  Manila  will  develop  a  greater  strength 
than  what  is  shown  by  the  accompanying  tables  of  tackles,  which 
are  based  on  the  strength  of  new  rope  adopted  by  the  manufac- 
turers, and  consequently  should  be  worked  to  when  figuring  the 
safe  working  load. 


The   Naval  Constructor 


Rule  to  iind  the  equivalent  circumference  of  Manila  rope  tor  a 
given  working  load  or  tension  (in  tons)  on  one  part  of  a  fall,  based 
on  a  factor  of  safety  of  8  ;  — 

Circumference  =  V^O  *  tension  which  is  very  easily  memorized. 

Inversely,  the  safe  working  load  for  a  given  circumference  of 
Manila  will  be 


Circ. 
10 


=  safe  load. 


STRENGTH    OF   TACKLES 
Ordinary  Blocks. 


- 

o 
M 

s 

5 

83 

Two  Single 
Blocks. 

Two  Double 
Blocks. 

Two  Treble 
Blocks. 

Breaking 

Stress  of 

Hooks   in 

Lbs. 

Breaking 

Stress  of 

Rope  in 

Lbs. 

Breaking 

Stress  ot 

Hooks  in 

Lbs. 

Breaking 

Stress  of 

Hope  in 

Lbs. 

Breaking 

Stress  of 

Hooks  in 

Lbs. 

Breaking 

Stress  ot 

Kope  in 

Lbs. 

3 

1 

1,143 

1,400 

1,492 

2,800 

2,219 

4,200 

3* 

H 

1,492 

1,800 

2,218 

3,600 

2,985 

5,400 

4 

n 

2,218 

3,600 

2,985 

7,200 

3,987 

10,800 

5 

2 

2,985 

6,400 

3,987 

12,800 

5,410 

18,200 

6 

2i 

3,987 

8,100 

5,410 

16,200 

6,360 

24,300 

7 

2f 

6,410 

12,100 

6,360 

24,200 

9,356 

36,300 

8 

3 

6,360 

14,400 

9,356 

28,800 

13,720 

43,200 

9 

3 

9,356 

14,400 

13,720 

28,800 

16,030 

43,200 

10 

3J 

13,720 

19,600 

16,030 

39,200 

18,722 

58,800 

12 

4 

16,030 

22,500 

18,722 

45,000 

20,375 

67,500 

14 

4J 

18,722 

28,900 

20,375 

57,800 

28,300 

86,700 

16 

5 

20,375 

40,000 
Twofold 

28,300 

80,000 
Fourfold 

35,680 

120,000 
Sixfold 

Strength  of  Tackles 


603 


STRENGTH   OF    TACKLES. 
Wide  Mortise  and  Heavy  Tackle. 


Size 
of 

Two  Single 
Blocks. 

Two  Double 
Blocks. 

Two  Treble 
Blocks. 

Break- 

Break- 

Break- 

Break- 

Break- 
ing 
Stress 

of 
Hooks 
in  Lbs. 

Break- 

Block. 

S        r 

O      O 

ing 

Stress  of 

Hooks 

in  Lbs. 

ing 
Stress  of 

Kope 
in  Lbs. 

ing 

Stress  of 

Hooks 

in  Lbs. 

ing 

Stress 

of  Kope 

in  Lbs. 

ing 

Stress  of 
Kope 
in  Lbs. 

7 

3 

6,360 

14,400 

9,350 

28,800 

13,720 

43,200 

8 

H 

9,356 

19,600 

13,720 

39,200 

16,030 

58,800 

9 

3J 

13,720 

19,600 

16,030 

39,200 

18,722 

58,800 

10 

4 

16,080 

22,500 

19,050 

45,000 

19,050 

67,500 

12 

4f 

19,050 

32,400 

20,375 

64,800 

28,300 

97,200 

14 

6J 

28,300 

43,300 

35,680 

86,600 

35,680 

129,900 

16 

6i 

35,680 

48,400 

Twofold. 

72,100 

96,800 

Fourfold. 

72,100 

145,200 

Sixfold. 

Wrecking  Blocks  and  Lashing  Shackles. 


Size 

of 

Block. 

*  w  fc 

8  u  3 

m        En 
O      O 

Two  Single 
Blocks. 

Two  Double 
Blocks. 

Two  Treble 
Blocks. 

Break- 
ing 

Stress  of 
Shackles 
in  Lbs. 

Break- 
ing 
Stress  of 
Rope 
in  Lbs. 

Break- 
ing 

Stress  of 
Shackles 
in  Lbs. 

Break- 
ing 

Stress  of 

Kope 
in  Lbs. 

Break- 
ing 

Stress  of 
Shackles 
in  Lbs. 

Break- 
ing 
Stress  of 
Rope 
in  Lbs. 

18 
20 
22 
24 

7 
8 

ii 

116,300 
132,532 
155,542 
172,400 

67,600 

78,400 

115,600 

192,000 

Twofold. 

132,532 
155,542 
172,400 
235,620 

135,200 
156,800 
231,200 
384,000 

Fourfold. 

155,542 
172,400 
235,620 
265,995 

202,800 
235,200 
346,800 
576,000 

Sixfold. 

604 


The  Naval  Constructor 


DERRICK 

CAPACITY 


Item. 

2£  Tons. 

5  TOXS. 

Falls J 

130'  of  2f"  G.S.W.R., 
single  whip,  170  lbs. 

65'  of  3"  G.S.W.R., 
single  whip,  110  lbs. 

60'  of  2J"  G.I.W.R., 
60  lbs. 

8'   0"  of   fp"  crane 
chain,  25  lbs. 

30  fathoms  of  4"  Ma- 
nila, 90  lbs. 

60  fathoms  of  3"  Ma- 
nila, 96  lbs. 

2  @  50  lbs.  =  100  lbs. 

1  @  60  lbs.  =  60  lbs. 

6  @  40  lbs.  =  240  lbs. 
100  lbs. 

l^  of  3"  G.S.W.R., 
single  whip,  220  lbs. 

65'  of  3£"  G.S.W.R., 
single  whip,  135  lbs. 

60'  of  21"  G.I.W.R., 
60  lbs. 

8'   0"  of   W'  crane 
chain,  55  lbs. 

40  fathoms  of  4"  Ma- 
nila, 120  lbs. 

60  fathoms  of  3"  Ma- 
nila, 96  lbs. 

2  @  60  lbs.  =  120  lbs-. 

1  @  70  lbs.  =  70  lbs. 

6  @  40  lbs.  =  240  lbs. 
150  lbs. 

Topping  Lift | 

Guys { 

Chain { 

Topping  Lift  Purchase  .    .    j 
Guy  Purchase j 

Fall  Blocks 

Topping  Lift  Blocks  .    .    . 

Shackles,  etc 

Total  weight  of  gear  for  one 
boom,  excluding  wire  rope- 
reels,  forgings  to  mast  or 
boom,  gooseneck,  etc. 

1,051  lbs. 

1,266  lbs. 

Derrick  Rigging 


605 


RIGGING. 

OF  DERRICK. 


10  Tons. 

20  Tons. 

50  Tons. 

260'  of  3"  G.S.W.R., 
gun  tackle,  435  lbs. 

120'of3£"G.S.W.R., 
gun  tackle,  250  lbs. 

&y  of  2|"  G.I.W.R., 
80  lbs. 

300'  of  4"  G.S.W.R., 
luff  tackle,  765  lbs. 

300' of  3^"  G.S.W.R., 
tackle  rove,  630  lbs. 

60'  of  3"    G.I.W.R., 
100  lbs. 

710'  of  3"  G.P.S.W.R.  (plough 
steel),  Mech.  adv.  of  tackle 
7=  1,200  lbs. 

540'  of  3"  G.P.S.W.R.,  Mech. 
adv.  6  =  910  lbs. 

100'  @  3£"  G.I.W.R.,  210  lbs. 

Shackles  used. 

40  fathoms  of  4"  Ma- 
nila, 120  lbs. 

60  fathoms  of  3"  Ma- 
nila, 96  lbs. 

3  @  60  lbs.  =  180  lbs. 

2  @  60  lbs.  =  120  lbs. 

6  @  40  lbs.  =  240  lbs. 
200  lbs. 

40  fathoms  of  4"  Ma- 
nila, 120  lbs. 

60  fathoms  of  3£"  Ma- 
nila, 130  lbs. 

l@1001bs.  t_2o0lb 

2@  eoibs.j-^20108- 

2@  100lbs.  =  2001bs. 

6  @  40  lbs.  =  240  lbs. 
300  lbs. 

Direct  to  winch. 

100  fathoms  of  3£"  Manila, 
220  lbs. 

1  @  150  lbs. ) 

1  @  100  lbs.  \  —  370  lbs. 

2@60   lbs.) 

1  @    50  lbs. ) 

2  @  100  lbs.  [  =  310  lbs. 
1@60   lbs.) 

4  @  40  lbs.  =  160  lbs. 

800  lbs. 

1,721  lbs. 

2,705  lbs. 

4,180  lbs. 

Section  V. 


CHAPTER   I. 

EQUIPMENT. 

In  a  modern  steamship  the  Equipment,  as  understood  by  the 
classification  societies,  comprises  that  part  of  a  vessel's  outfit 
which  relates  to  the  handling  of  the  ship  and  the  safety  of  her 
complement,  and  in  Lloyd's  Register  is  represented  by  the  nu- 
meral "  1 "  after  the  character.  Under  this  heading  are  included, 
anchors,  chains,  hawsers,  boats,  steering  gear,  windlass,  and  the 
requirements  of  the  Board  of  Trade  Regulations  or  the  United 
States  Inspection  Laws. 

Lloyd's  Equipment. 

The  equipment  as  regards  anchors,  chains,  hawsers,  warps,  etc. 
is  regulated  by  the  number  produced  by  the  sum  of  the  measure- 
ments in  feet  arising  from  the  addition  of  the  half-moulded  breadth 
of  the  vessel  at  the  middle  of  the  length,  the  depth  from  the  upper 
part  of  the  keel  to  the  top  of  the  upper  deck  beams  (with  the 
normal  camber),  and  the  girth  of  the  half  midship  frame  section 
of  the  vessel,  measured  from  the  centre  line  at  the  top  of  the  keel 
to  the  upper  deck  stringer  plate,  multiplied  by  the  length  of  the 
vessel  for  a  one,  two,  and  three  decked  vessel  and  for  a  spar 
decked  vessel.  For  a  vessel  having  a  complete  awning  deck,  or 
a  continuous  shade  deck,  the  equipment  number  is  to  be  increased 
one-eighth  beyond  that  given  by  the  measurements  defined  above 
to  the  main  deck. 

For  a  steam  vessel  with  a  partial  awning  deck,  poop,  top  gal- 
lant forecastle,  bridge  house  or  a  raised  quarter  deck  the  equip- 
ment number  is  to  be  increased  beyond  that  for  a  flush  or 
spar-decked  vessel  by  that  proportion  of  the  addition  made  for  a 
complete  awning  deck  (i.e.,  one-eighth)  which  the  combined  length 
of  the  erection  bears  to  the  length  of  the  vessel.  Where  erections 
are  fitted  upon  erections,  the  equipment  number  is  to  be  corre- 
spondingly increased  in  the  same  proportion.  (Sect.  39  of  Lloyd's 
Rules. ) 

607 


The   Naval  Constructor 


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610  The  Naval  Constructor 


As  an  example  of  the  method  of  applying  the  foregoing  rule,  let 
ns  take  the  case  of  a  3-deck  vessel,  having  a  complete  shelter- 
deck,  and  a  bridge  superstructure  with  houses  erected  on  it. 
This  type  will  clearly  exemplify  all  of  the  requirements  of  the 
rule,  as  we  shall  calculate  the  numeral  firstly  for  a  3-deck  vessel, 
to  which  we  will  then  add  one  eighth  for  the  complete  shelter- 
deck,  afterwards  increasing  it  by  the  proportion  that  the  length 
of  bridge  superstructure  bears  to  the  length  of  ship  (or  how 
much  of  another  eighth  we  shall  take),  and  finally  resolving  the 
area  of  the  deck  erections  or  superstructure  into  an  equivalent 
length  of  vessel  enclosing  the  same  area,  and  adding  its  propor- 
tionate value. 

Example :  —  Required  the  equipment  numeral  for  a  three- 
decked  vessel  having  a  complete  shelter-deck  on  which  is  built  a 
superstructure  having  deck  houses  on  top  :  — 

Dimensions  :  550'  X  65'  X  41'     to  shelter  deck 

33.5' to  upper  deck 
Length  of  superstructure     .     .  250' 
Size  of  deck  houses    .     .     .     .  100'  x  40' 

=  4,000  sq.  ft.  =  4oo&=  61.5'  equivalent  length 

Half-breadth 32.50' 

Depth  (to  U.DK+16i"  camber),  34.85' 

Half  girth 63.00' 

130.35' 

Length X  550' 

71,692.5 
Add  £  for  complete  shelter 

deck 8,961.5 

Add  proportion  of  £  repre- 
sented by  250'  of  super- 
structure         4,073.1 

Add  proportion  of  •£  repre- 
sented by  61.5'  equiva- 
lent length  of  houses  .     1,001.8 
Equipment  number    .     .     .  85,728.9 


The  preceding  "Table  22  "  of  Lloyd's  Rules  shows  the  require- 
ments of  that  Society  for  steam  vessels  based  on  the  above  rule. 


American  Ship  Windlasses 


611 


AMERICAN    SHIP    WINDLASSES. 


Steam 

Steam  Pump 

Lloyd's 

Size 

Capstan 

Brake 

Equipment 

of  Chain 

Engines. 

Windlasses 

Windlasses 

Numbers. 

Cable. 

Weight  in 
Lbs. 

Weight 
in  Lbs. 

"              // 

//        // 

Lbs. 

Lbs. 

6,150-  7,490 

i|  and  1 

4X6 

7,000 

5,000 

7,490-  9,770 

Mr    ' 

'    1* 

4x    6 

8,500 

6,800 

9,770-11,740 

Mr    ' 

'  H 

5x    7 

9,000 

7,300 

11,740-13,450 

Mr    * 

'   if 

6x    8 

12,000 

9,000 

13,450-16,720 

ItV    ' 

4   l* 

7x    8 

13,000 

12,250 

16,720-19,780 

M    ' 

1   H 

8x    8 

17,000 

16,250 

19,780-24,220 

Iff    ' 

'   if 

9x    8 

17,850 

17,100 

24,220-30,020 

Iff    ' 

•  n 

9X9 

19,500 

18,750 

30,020-35,450 

4*  ' 

'    2 

10x10 

27,000 

24,000 

35,450-43,600 

Mr    ' 

'    2* 

10  x  10 

23,000 

31,000 

43,600-51,000 

Mr    ' 

1   2* 

12  x  12 

31,000 

33,000 

51,000-59,000 

2f     ' 

12  x  12 

33,000 

35,000 

THE   SHAW  AND    SPIEGLE   PATENT   AUTOMATIC 
STEAM   TOWING   MACHINE. 


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21,500 

2* 

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3 

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28,000 

3 

3 

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3 

15,000 

612 


The   Naval   Constructor 


MOORING   SWIVEL. 


r<-/-/9.54 H 

1.54 

Fig.  353. 
N.B.    In  all  chain  cable  details  the  unit  for  determining  the  dimensions  is 
the  size  of  cable  iron. 


Blake  Stopper 


613 


J 


ce/U  >]<-w>4< 
J<— -«r — 


*cy 


614 


The  Naval   Constructor 


rflhW 


u) 


Admiralty  Cable  Requirements  615 

ADMIRALTY   CABLE  REQUIREMENTS. 

Samples  shall  be  taken  by  the  Overseer  indiscriminately  for 
testing  from  every  description  of  iron  included  in  any  one  in- 
voice, provided  the  number  of  bars,  etc.,  so  included  does  not 
exceed  50,  and  if  above  that  number,  one  for  every  50  or  portion 
of  50  of  each  description.  The  samples  may  be  tested  to  show 
the  fibre,  strength,  ductility,  and  other  qualities  of  the  iron,  and 
if  not  found  satisfactory,  the  lot  from  which  they  are  taken 
may  be  rejected. 

In  cases  where  the  quantity  of  each  size  is  small,  and  the  total 
quantity  of  bars  of  all  sizes  does  not  exceed  50  No.,  one  sample 
only  need  be  tested,  provided  that  all  the  bars  represented  thereby 
are  supplied  by  one  maker,  and  that  the  Overseer  is  satisfied 
as  to  the  quality  of  the  iron;  the  sample  for  testing  shall  be 
selected  by  him,  and  the  acceptance  or  rejection  of  the  batch 
shall  depend  upon  the  result  of  the  tests. 

The  samples  of  every  description  of  iron  shall  have  an  ulti- 
mate tensile  strength  respectively:  — 

Of  not  less  than  23  tons  to  the  square  inch  of  section,  for 

sizes  under  2\  inches; 
Of  not  less  than  22^  tons  to  the  square  inch  of  section, 
for  sizes  from  2\  to  2^  inches,  both  sizes  inclusive;  and 
Of  not  less  than  22  tons  to  the  square  inch  of  section,  for 
sizes  above  2^  inches; 
with  an  elongation  of  20  per  cent,  in  a  length  of  8  inches,  for  all 
sizes  of  iron. 

Tensile  tests,  if  not  made  on  the  premises  of  the  Iron  Manu- 
facturer, shall  be  applied  at  a  public  testing  house  at  the  Con- 
tractors' expense,  and  in  the  presence  of  the  Overseer. 

Forge  Test,  Cold. 

Every  bar  of  1-inch  diameter  and  above  shall  admit  of  bending 
cold  to  the  same  radius  as      ^ — , 
the  end  of  the  link  for  which     \C~ 
it  is  to  be  used,  thus:  Z""3 

Bars  under  1  inch  to  admit  of 
bending  cold,  thus: 

A  sample  shall  be  notched  and  bent,  thus: 
to  show  the  fibre  and  quality  of  the  iron,  which  is  to  be  entirely 
satisfactory  to  the  Overseer. 

Forge  Test,  Hot. 

Bars  shall  be  punched  with  a  punch  one-third  the  diameter 
of  the  bar,  at  a  distance  of  one  and  one-half  diameters  from  the 


616  The  Naval  Constructor 


end  of  the  bar.  The  hole  may  then  be  drifted  out  to  one  and 
one-quarter  times  the  diameter  of  the  bar.  The  side  of  the 
hole  may  then  be  split;  and  the  ends  must  ad- 
mit of   turning  back  without  fracture,  thus: 

-The  whole  of  the  articles,  including  the  annealed 
crucible  cast  steel  or  forged  steel  stud  pins  of  the 
cables,  and  the  tinned  steel  pins,  etc.,  shall  be  made 
only  of  material  approved  by  the  Overseer.  The  iron 
for  the  articles  enumerated  in  Schedules  II  and  III  shall  be  also  well 
hammered  and  rolled,  and  of  quality  approved  by  the  Overseer. 

Anchor  shackle  bolts  shall  be  made  of  blooms  at  least  twice 
worked,  and  not  of  bar  iron.  The  square  links  and  shackles,  to- 
gether with  the  swivels  and  bolts,  shall  be  worked  or  drawn  out 
under  hammers  oT  sufficient  weight,  and  the  welds  or  shuts  shall  be 
made  in  the  most  perfect  and  solid  manner.  No  iron  shall  be  used 
in  which  the  brand-mark  is  so  deeply  cut  as  to  unduly  weaken  the 
section,  or  is  so  situated  as  to  make  unsatisfactory  work  in  form- 
ing the  link,  and  the  Contractors  shall  make  arrangements  for  stor- 
ing the  Admiralty  cable  iron  separately  from  all  other  cable  iron. 

All  the  stud  pins  of  the  chain  cable  shall  be  marked  on  one 
side  with  the  name  or  initials  of  the  Contractors,  and  on  the 
other  side  with  the  date  of  the  year  of  delivery  into  store.  The 
several  lengths  of  each  chain  cable,  and  mooring,  pendant  or 
bridle  chain,  and  the  joining  shackles  and  large  shackles  to  be 
connected  therewith,  shall  be  marked  as  follows,  viz. :  —  The 
end  links  of  the  lengths  of  the  cable  with  a  distinguishing  num- 
ber, and  the  broad  arrow;  the  joining  shackles  and  anchor 
shackles  with  the  same  distinguishing  number,  the  broad  arrow, 
and  the  initials  of  the  Contractors*  the  mooring  and  other 
swivels  and  splicing  shackles,  on  their  largest  part,  with  a  dis- 
tinguishing number,  the  broad  arrow,  and  the  initials  of  the 
Contractors;  and  the  splicing  shackles  and  swivels  with  the 
date  of  the  year  of  delivery  into  store,  in  addition.  Cables  and 
all  cable  gear  will  be  received  for  the  first  four  months  of  each 
year  with  the  last  year's  date  on  the  stud  pins. 

Tests.  —  The  whole  of  the  articles  enumerated  in  Schedules  I, 
II  and  III,  shall  be  subjected,  before  delivery,  to  the  proof  strains 
prescribed  in  the  Specification  and  Tables  herewith,  and  to  the 
following  breaking  test,  which  shall  be  first  applied. 

Chain  Cables,  Bridle  and  Pendant.  —  A  sample  of  three  links 
taken  from  each  length  of  chain  cable,  or  each  bridle  and  pendant 
chain,  shall  be  subject  to  tensile  strain  until  it  breaks.  The 
links  shall  be  cut  out  at  the  public  testing  machine  in  the  presence 
of  the  Overseer,  when  practicable.  Should  it  break  under  a  less 
strain  than  50  per  cent  in  excess  of  the  proof  strain,  the  entire 
length  of  which  that  portion  is  a  sample  shall  be  rejected. 


Dimensions  for  Chain  Cables 


617 


Cables  and  gear  which  pass  the  proving  and  breaking  tests 
shall  be  minutely  examined  by  the  Overseer,  and  any  flaws  or 
defects  which  he  may  point  out  shall  be  remedied  to  his  satis- 
faction before  the  cables  and  gear  are  forwarded  to  the  yards. 

The  cables,  etc.,  shall  be  cleaned  sufficiently  to  permit  of  the 
Overseer  guaranteeing  the  absence  of  flaws  or  defects. 

TABLES   OF  DIMENSIONS,   TESTS,  ETC.,  FOR 
ADMIRALTY  CHAIN   CABLES. 


41  a 

"  «  B 

«     z 
Og  s 

&<  a  3 

si! 

n  St 
£Q3 

Dimensions  of  Com- 
mon Links  Subject 

to  the  Latitude 
Stated  in  Clause  4 
of  the  Specification. 

9 

h 

IBs 

S  <  « 

w  oH 
*2 

Weight  of  100  Fathoms 
of  Cable,  with  the  Nec- 
essary Joining  Shack- 
les, ETC.,  SUBJECT  TO  THE 

Latitude  Stated  in 

6 

■ 
E 
m 

w   • 
w  5 

« 
i 

O 

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g 

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83 

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1 

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o 
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a 
o 

1 

I 

18 

III 

Mi 

T3  o3  » 
£33 

1 

£ 

£ 

Ins. 

Ins. 

Ins. 

Ozs. 

Cwts.  Qrs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Tons. 

3* 

21 

12.6 

150.0 

588      0 

0 

359 

182.25 

171.5 

134 

176.4 

3i 

19* 

11.7 

119.8 

507      0 

0 

287.5 

145.9 

137 

107.25 

161.6 

3 

18 

10.8 

94.5 

432      0 

0 

226.1 

114.75 

108 

84.38 

145.8 

2J 

16i 

9.9 

72.8 

363      0 

0 

174 

88.38 

83 

65 

129.3 

i 

15| 

9.2 

58.9 

315      0 

21 

140 

71.5 

66.3 

52.6 

118.2 

15 

9.0 

54.7 

300      0 

0 

130 

66.4 

62.5 

48.8 

112* 

14i 

8.5 

47.5 

270      3 

0 

112 

56.9 

53.5 

41.9 

101* 
91* 

2i 

13* 

8.1 

40 

243      0 

0 

95 

48.4 

45.5 

35.6 

2* 

12* 

7.6 

33.6 

216      3 

0 

80 

40.75 

38.3 

30 

8U 

2 

12 

7.2 

28. 

192      0 

0 

67 

34 

32 

25 

72 

11 

nj 

6.7 

23 

168      3 

0 

55.25 

28 

26.33 

20.6 

63i 
55i 

n 

10* 

6.3 

18.8 

147      0 

0 

44.9 

22.78 

21.5 

16.75 

i 

9| 

5.8 

15 

126      3 

0 

36 

18.25 

17.2 

13.4 

47i 

9 

5.4 

11.8 

108      0 

0 

28 

14.34 

13.5 

10.5 

40* 

it 

8* 

4.9 

9 

90      3 

0 

21.75 

11 

10.37 

8.2 

34 

» 

7* 

4.5 

6.9 

75      0 

0 

16.31 

8.32 

7.75 

6.1 

28* 
22J 

i| 

6i 

4.0 

5.0 

63      3 

4 

11.87 

6.10 

5.7 

4.5 

6 

3.6 

3.5 

52      3 

6 

8.37 

4.25 

4 

3.2 

18 

j 

3 

3.1 

2.4 

40      1 

20 

5.61 

2.84 

2.66 

2.2 

13* 

i 

2.7 

1.5 

29      2 

2 

3.53 

1.79 

1.68 

1.4 

10* 

i 

4* 

2.5 

1.14 

24      3 

23 

2.72 

1.37 

1.29 

1.1 

8* 

3f 

2.2 

0.86 

20      2 

14 

2.04 

1.03 

1.03 

0.8 

7 

i 

3f 

2.0 

0.62 

16      2 

23 

1.49 

0.75 

0.702 

0.58 

i 

3 

1.8 

0.44 

13      0 

22 

1.04 

0.53 

0.47 

0.41 

i 

21 

1.6 

0.30 

10      0 

12 

0.7 

0.34 

0.33 

0.28 

3* 

21 

1.35 

0.184 

7      1 

20 

0.44 

0.22 

0.21 

0.18 

m 

The  breaking  strain  of  the  several  sizes  of  cables  shall  not  fall  short  of  the 
above  proof  strains,  with  50  per  cent  added. 

Note.  —  The  above  proof  strains  are  equivalent  to  the  following  strains  per 
circular  *  inch  of  iron,  viz.,  3*  inch,  504  lbs.;  3*  inch,  536.5  lbs.;  3  inch,  567  lbs.; 
2f  inch,  598.5  lbs.;  2T98  inch  and  under,  630  lbs.  The  table  can  be  used  for  calcu- 
lating the  weight  of  cable  in  lengths  less  than  12*  fathoms. 


618 


The  Naval   Constructor 


ADMIRALTY    CHAIN   CABLES. 


Common  Links,  A. 

Second  End  Links,  Ii. 

Extreme  End  Links,  C. 

Size  of 
Iron, 

Length 

Ex- 
treme, 

Width 

Ex- 
treme, 

Size  of 
Iron, 

Length 

Ex- 
treme, 

Width 

Ex- 
treme, 

Size  of 
Iron, 

Length 

Ex- 
treme, 

Width 

Ex- 
treme, 

F. 

0. 

//. 

J. 

/. 

K. 

L. 

M. 

N. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

3} 

19| 

Hi 

31 

21 

13 

31 

22 

13 

3ft 

191 

ill 

3ft 

20| 

12i 

318 

211 

12} 

31 

18} 

lit 

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201 

121 

3} 

21 

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3ft 

184 

in 

3ft 

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Details  of  Links  and  Shackles 


619 


CHAIN    CABLE   LINKS. 


Fig.  356. 

PROPORTIONS    AND    DETAILS    OF   LINKS 
SHACKLES. 

h 


AND 


Q85' 


* 


^ 


Fig.  357. 


620 


The  Naval  Constructor 


ADMIRALTY   CHAIN 

'   CABLES.— 

[Continued.) 

Shackles,  D. 

Shackle  Pins,  E. 

Size  of 

Length 

Width 

Iron, 

Extreme, 

Extreme, 

R 

S 

T 

U 

V 

w 

0. 

P. 

Q. 

Ins. 

Ins. 

Ins. 

Ins. 

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Club  Shackle 


621 


CLUB    SHACKLE. 


Fig. 358. 


622 


The   Naval   Constructor 


CHAIN   SWIVEL. 

p  — 7069 - >j 

K--2 .---*|    Yi^^ms-MAo^ 


Section  A.B 


:    f<--2./59->| 

•    -Al4Ss\*- 
Section  G.H.1 


Fig.  359. 


Kenter  Shackle 


623 


KENTER    SHACKLE. 


laij 


Dimensions  of  Kenter  Shackles. 


M/M 

Approx.  ins... 

Inches 

Inches 

Inches 

Inches 

Weight  in  lbs 

M/M 

Approx.  ins.  . 

Inches 

Inches 

Inches 

Inches 

Weight  in  lbs 

M/M 

Approx.  ins.  . 

Inches 

Inches 

Inches 

Inches 

Weight  in  lbs 


D 

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1 

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13.3 


Z>     39     42     45     48     51     54     57     60     63 


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624 


The  Naval  Constructor 


MUSHROOM  MOORING  ANCHORS. 


Weight 
in  Lbs. 

A. 

B. 

a 

i>. 

£7. 

P. 

G. 

IT. 

J. 

a:. 

6,000 

5    6 

/    // 
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31 

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21 

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3    3 

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81 

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in  Lbs. 

L. 

M. 

jr. 

O. 

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<?• 

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5,000 

it 

7 

4 

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3 

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Weight 
in  Lbs. 

V. 

JF. 

X. 

r. 

z. 

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7?j5. 

cc. 

Cotter. 

5,000 

k 

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3,600 

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If 

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3 

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51 

11  x,l 

Mushroom   Mooring  Anchor  625 


Fig.  361. 


626  The  Naval   Constructor 


CHAPTER  II. 

BOATS. 

The  American  and  the  British  requirements  for  boats  carried 
by  foreign-going  steamships  are  practically  identical,  but  for 
vessels  employed  in  the  home  trade  there  is  much  dissimilarity. 
The  following  notes,  therefore,  where  they  refer  to  the  number  of 
boats  to  be  carried,  apply  only  to  ocean-going  steamships. 

Many  of  the  boats  carried  on  steamships  are  good  examples  of 
what  a  boat  should  not  be.  The  contractor  should  not  only 
supply  the  boat-builder  with  the  dimensions  of  the  boats  required, 
but  also  with  an  outline  of  the  mid  section,  more  particularly  in 
the  "case  of  life -boats  and  dinghies.  In  many  cases  these  boats 
have  much  too  quick  a  rise  of  floor  line,  making  them  dangerous 
to  step  into  in  the  light  condition.  In  addition,  their  scantlings 
are  often  inadequate  for  working  boats  exposed  at  all  times  to 
the  extremes  of  weather.  With  a  view  to  supplying  a  good 
guide  as  to  what  are  wholesome  proportions  for  the  various 
classes  of  boats  hung  under  davits,  the  subjoined  diagram  has 
been  prepared  by  the  writer.  It  is  based  on  a  long  experience 
in  designing  and  building  these  craft. 

When  outline  plans  of  boats  are  prepared,  the  following  points 
should  be  noted :  — 

Minimum  clear  distance  between  thwarts,  2'  2".  Centre  of  row 
crutches  =  10"  abaft  aft  edge  of  thwarts.  Top  of  thwarts  or 
benches  =  9"  below  bottom  of  row  crutch.  In  single-banked 
boats  stroke  is  always  starboard.  Breadth  of  transom  =  §  rds. 
midship  top  breadth  (except  in  gigs).  Rabbet  of  transom  = 
half  the  stern  depth  above  base.  Siding  of  hog  =  twice  the 
siding  of  keel.  Moulding  of  hog  =  .4  of  the  siding.  Scarphs  of 
keel,  etc.  =  4£  times  the  siding. 

Spars.  —  Diameter  of  Mast,  \"     .     .     per  foot  of  length. 
"        "  Gaff,  tV'     .     . 
"        '«  Topsail  Yard,  \n 
"        "  Boom,  Ty  .     . 
"         "  Spread  Yard,  \" 
"         "  Bowsprit,  §"    . 

Sheer.  —  Gigs  sheer  forward  .5"  per  foot ;  aft  .25"  per  foot. 
Cutters     "        "        .43"    "      "    ;    "    .2"   "      " 
Dinghies  "         "        .53"   "      "    ;    "    .22"  k'      " 

Sheers  taken  with  L.W.L.  parallel  with  keel. 


Proportions  of  Row  Boats 


627 


628 


The  Naval  Constructor 


Sails.  —  The  sail  area  may  with  advantage  be  based  on  the 
midship  section  area  measured  to  underside  of  thwarts  multiplied 
by  12.     A  x  12  =  sail  area. 

Scantlings.  —  The  scantlings  may  be  as  given  in  the  table 
which  shows  the  requirements  for  boats  of  the  Royal  Navy,  or 
these  may  be  modified  by  the  designer  in  accordance  with  his 
own  experience. 

Slings. —  Inspectors  should   insist  that    all  sling  plates  and 

lifting  rings  be  tested.  The  following  table  shows  the  tests  to 

which  these  fittings  are  usually  subjected  for  the  various  classes 
of  boats. 


TABLE   SHOWING   DIAMETER   OP   RING  BOLTS 

With  Proof  Test  to  be  Applied  and  the  Descrip- 
tions of  Boats  to  which  the  Various 
Sizes  are  to  be  fitted. 


Type  of  Boat. 

Length  of 
Boat. 

Diameter 

OF 

Bolt. 

Proof  Test. 

Feet. 

Inches. 

Tons. 

Dinghies     .... 

12 

£ 

1 

Dinghies     . 

14 

A 

H 

Cutter  gigs 

] 

Galleys  .     . 
Gigs  .     .     . 

[     32  to  18 

J 

t 

1A 

Whalers 

Cutters  .     . 

20,  18,  and  16 

H 

2 

Cutters  .     . 
Cutters  .     . 

23 

25  and  26 

u 

2I 

Cutters  .     . 

27  and  28 

f 

3TV 

Cutters  .     . 

30  and  32 

l 

4 

Cutters  .     . 

34 

if 

&A 

Position  of  Masts,  Tack  Blocks  and  Hooks  629 


02 

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5 

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630 


The  Naval   Constructor 


DIMENSIONS    AND 


Length  Extreme .    . 

Breadth 

Depth 

R. .,  ( Sided     .    .    . 

Keel)  Moulded    .    . 

Stem  and  stern  post, 

sided 

Transom,  thick    .     . 

f  Sided    .    . 

Floors  J  Moulded    . 
floors <  Grownto 

t  shape  . 
«  f  Sided  .... 
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§      MouMed  !,-£ 

fc   I  I     end 

Gunwales)  TM& 
Breasthooks  .  . 
m   ( Fixed    .    .    . 


j*  <  Portable  .  . 
H  (^  Gun  platform 
Mast  thwarts  { J™*; 

Other  thwarts  {  ™S*f 
Knees  to  thwarts,         i 

sided ) 

Thickness  of  plank      » 

when  finished  .    .    J 

Strakes,  No.,  about,     j 

No.  of  oars,  provision j 
to  be  made  for  .    .     j 


34     0 
8   10 

2  1U 
31" 

r," 


No. 
4 


li' 


No. 
2 


If' 
94" 

7" 
H" 

\" 
No. 
16 

14 


32  0 
8  6 
2  10 
3" 

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% 

3" 

No. 
4 


30   0 
8    1 

28* 

3" 

4|" 


1 
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% 

7" 

H" 

i" 
No. 

15 

IS 


28   0 

7 
2  6* 


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I 

7" 

H" 

i" 

Nu. 
15 
10 


27   0 
7 

264. 
3" 
4) 


No. 

4 

1*" 

1" 


2" 

24" 

No. 
2 
5 


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7" 

U" 

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No. 
15 

Id 


26   0 

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2  5* 


1 

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No. 

10 

10 


25  0 
7  3 
2  5* 


23   0 
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2  4* 
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I" 


n- 

2" 
No. 

2 

4 


23  0 
5  6 
2  2 

2|" 

4" 

2* 


•No. 
2 

1" 


Dimensions  and  Scantlings  of  Row   Boats    631 


SCANTLINGS   OF  ROW   BOATS. 


SO 

CO 

M 
M 
H 
H 

O 

s 

M 
h 

H 

O 

W 
0 

w 
jjjj 

ft 

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li 

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6 

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6 

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6 

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2 

0 

20    0 
5    6 
2    2 

18    0 
6    0 
2    2 
2J" 
4" 

16  0 

5  7 
2  1 

21- 
4" 

14  0 
5  2 
2  2 
21" 
3*" 

12  0 
5  0 
2   1 

32  0 
5   6 
2  2 

24" 
3§" 

30  0 
5  6 
2  2 
24" 
3f" 

28  0 
5  6 
2  2 

2J" 
3f" 

27  0 
5  6 
2  2 

24" 

3g" 

26  0 
5  6 
2  2 

24" 
3§" 

25  0 
5  6 

2  2 
24" 
3f" 

24  0 
5  6 
2  2 

24" 
3|" 

23  0 
5  6 

2  2 
24" 
3|" 

22  0 
5  6 
2  2 
24" 
3|" 

200 
5  6 
2  2 

24" 
3f" 

/  // 

18  0 
5  0 
2  2 
24" 
3§" 

2&" 

21" 

2|" 

24" 

2J" 

li" 

li" 

H" 

li" 

li" 

li" 

li" 

1|" 

l" 
f" 

No. 
4 
1" 

1" 

1" 

I" 
No. 

4 
1" 

li" 

No. 
2 
1" 

If" 
1" 

No. 
2 
1" 

11" 
1" 

No. 

2 

ir 
i" 

No. 
2 
1" 

ii" 

i" 

No. 
2 

r 

1" 

1" 
No. 
4 
1" 

1" 
1" 

1" 
No. 

4 
1" 

1" 
1" 

No. 
4 
1" 

1" 

1" 
No. 

4 
1" 

1" 

I" 
No. 

4 
1" 

1" 

J" 
Jso. 

4 

1" 

1" 
1" 

1" 
No. 

4 
1" 

1" 
No. 

4 
1" 

r 

i" 
1" 

No. 
4 
1" 

|" 

t" 

I" 

t" 

t" 

1" 

1" 

|" 

1" 

1" 

1" 

1" 

1" 

t" 

1" 

1" 

No. 

1 
7 

if" 

No. 

1 
7 

No. 
1 
7 

H" 

No. 

2 

6 

H" 

14" 

No. 
1 
6 

i" 

1|» 

No. 
2 
5 

No. 
1 
5 

No. 
2 
5 

No. 
1 
5 

14" 

No. 

1 

4 

h" 

$> 

No. 
1 
4 

No. 
4 

No. 
2 
3 

I" 

No. 
3 

11" 

No. 
1 
2 

If- 

No. 
1 
2 

1 

1 

1 

1 

14" 

7" 

W 
8" 

ii" 

7" 

4" 

8" 
4" 

7" 

H" 

7" 

H" 

7" 

1" 

7" 

1" 

7" 

1" 

7" 

1" 

7" 

7" 

1" 

7" 

1" 
7" 

1" 

7" 

1" 

7" 

1" 
7" 

1" 

7" 

i" 

14" 

1" 

r 

i" 

r 

i" 

3" 

i" 

r 

i" 

i" 

'*" 

i" 

i" 

1" 

h" 

tV 

iV 

i" 

f" 

i" 

1" 

1" 

¥' 

i" 

I" 

I" 

1" 

1" 

1" 

I" 

No. 
14 

No. 
13 

No. 
13 

No. 
13 

No. 
13 

No. 
13 

No. 
13 

No. 
13 

No. 
13 

No. 
13 

No. 
13 

No. 
13 

No. 
13 

No. 
13 

No. 
13 

No. 
13 

4 

6 

6 

6 

6 

6 

6 

6 

5 

5 

5 

4 

4 

4 

4 

4 

632 


The   Naval   Constructor 


YACHTS'    LAUNCHES. 


Length. 

Beam. 

Depth. 

Draft 
Aft. 

Weight 
Com- 
plete. 

Speed  in 
Knots. 

Class  of 
Machin- 
ery.* 

16  0 

4  3 

1  10 

1     4 

Cwts. 
8* 

5 

H.P. 
5 

18  0 

4  6 

2     0 

1     6 

10 

6 

5 

20  0 

5  0 

2     2 

1     6 

12 

6 

5 

22  0 

5  3 

2     6 

1     8 

16 

7 

10 

23  6 

5  4 

2     8 

2     0 

18 

7* 

15 

25  0 

5  6 

2  10 

2     0 

19 

8 

15 

27  0 

6  0 

2  10 

2     4 

25 

10 

25 

30  0 

6  3 

3    0 

2     4 

30 

10 

25 

35  0 

6  6 

3    2 

2  10 

45 

12 

35 

45  0 

7  6 

4     0 

3     0 

90 

12 

50 

55  0 

8  6 

5     3 

3  10 

140 

12 

80 

*  Compound  engines  with  water  tube  boilers. 


Standard  Ship's   Life-Boat 


63; 


634  The  Naval  Constructor 


CHAPTER  III. 

BRITISH   RULES   FOR   STEAMSHIPS    CARRYING 

PASSENGERS,    BOATS    AND   LIFE-SAVING 

APPLIANCES. 

(a)  Ships  of  Division  A,  Class  1,  shall  carry  boats  placed  under 
davits,  lit  and  ready  for  use,  and  having  proper  appliances  for 
getting  them  into  the  water,  in  number  and  capacity  as  pre- 
scribed by  the  table  in  the  appendix  to  these  Rules  (see  page 
433)  ;  such  boats  shall  be  equipped  in  the  manner  required  by,  and. 
shall  be  of  the  description  defined  in,  the  General  Rules  appended 
hereto. 

(6)  Masters  or  owners  of  ships  of  this  class  claiming  to  carry 
fewer  boats  under  davits  than  are  given  in  the  table  must  declare 
before  the  collector  or  other  officers  of  customs,  at  the  time  of 
clearance,  that  the  boats  actually  placed  under  davits  are  suf- 
ficient to  accommodate  all  persons  on  board,  allowing  10  (ten) 
cubic  feet  of  boat  capacity  for  each  adult  person,  or  "statute 
adult." 

(c)  Not  less  than  half  the  number  of  boats  placed  under  davits, 
having  at  least  half  the  cubic  capacity  required  by  the  tables, 
shall  be  boats  of  Section  A  or  Section  B.  The  remaining  boats 
may  also  be  of  such  description,  or  may,  in  the  option  of  the  ship- 
owner, conform  to  Section  C,  or  Section  D,  provided  that  not 
more  than  two  boats  shall  be  of  Section  D. 

(d)  If  the  boats  placed  under  davits  in  accordance  with  the 
table  do  not  furnish  sufficient  accommodation  for  all  persons  on 
board,  then  additional  wood,  metal,  collapsible  or  other  boats  of 
approved  description  (whether  placed  under  davits  or  otherwise), 
or  approved  life-rafts,  shall  be  carried.  One  of  these  boats  may 
be  a  steam  launch;  but  in  that  case  the  space  occupied  by  the 
engines  and  boilers  is  not  to  be  included  in  the  estimated  cubic 
capacity  of  the  boat. 

Subject  to  the  provisions  contained  in  paragraph  (/)  of  these 
rules,  such  additional  boats  or  rafts  shall  be  of  at  least  such 
carrying  capacity  that  they  and  the  boats  required  to  be  placed 
under  davits  by  the  table  provide  together  in  the  aggregate,  in 
vessels  of  5,000  tons  gross  and  upwards,  three  fourths,  and  in 
vessels  of  less  than  5,000  tons  gross,  one  half,  more  than  the 
minimum  cubic  contents  required  by  column  3  of  the  table.  For 
this  purpose  3  cubic  feet  of  air-case  in  the  life-raft  is  to  be  esti- 
mated as  10  cubic  feet  of  internal  capacity.  Provided  always  that 
the  rafts  will  accommodate  all  the  persons  for  which  they  are  to 


British  Rules  for  Steamships  635 

be  certified  under  the  Eules,  and  also  have  3  cubic  feet  of  air-case 
for  each  person. 

All  such  additional  boats  or  rafts  shall  be  placed  as  conveniently 
for  being  available  as  the  ship's  arrangements  admit  of,  having 
regard  to  the  avoidance  of  undue  encumbrance  of  the  ship's  deck, 
and  to  the  safety  of  the  ship  fov  her  voyage. 

(e)  In  addition  to  the  life-saving  appliances  before  mentioned, 
ships  of  this  class  shall  carry  not  less  than  one  approved  life-buoy 
for  every  boat  placed  under  davits.  They  shall  also  carry  ap- 
proved life-belts,  or  other  similar  approved  articles  of  equal  buoy- 
ancy suitable  for  being  worn  on  the  person,  so  that  there  may  be 
at  least  one  for  each  person  on  board  the  ship. 

(/)  Provided,  nevertheless,  that  no  ship  of  this  class  shall  be  re- 
quired to  carry  more  boats  or  rafts  than  will  furnish  sufficient 
accommodation  for  all  persons  on  board.  ' 

General  Rules. 

Boats.  —  All  boats  shall  be  constructed  and  properly  equipped 
as  provided  by  these  Rules,  and  all  boats  and  other  life-saving 
appliances  are  to  be  kept  ready  for  use  to  the  satisfaction  of  the 
Board  of  Trade.  Internal  buoyancy  apparatus  may  be  con- 
structed of  wood,  or  of  copper  or  yellow  metal,  of  not  less  than 
18  ounces  to  the  superficial  foot  or  of  other  durable  material. 

Section  A.  A  boat  of  this  section  shall  be  a  life-boat,  of  whale- 
boat  form,  properly  constructed  of  wood  or  metal,  having  for 
every  10  cubic  feet  of  her  capacity,  computed  as  in  Rule  2,  at 
least  one  cubic  foot  of  strong  and  serviceable  enclosed  air-tight 
compartments,  so  constructed  that  water  cannot  find  its  way  into 
them.  In  the  case  of  metal  boats,  an  addition  will  have  to  be 
made  to  the  cubic  capacity  of  the  air-tight  compartments,  so  as  to 
give  them  buoyancy  equal  to  that  of  the  wooden  boat. 

Section  B.  A  boat  of  this  section  shall  be  a  life-boat,  of  whale- 
boat  form,  properly  constructed  of  wood  or  metal,  having  inside 
and  outside  buoyancy  apparatus  together  equal  in  efficiency  to 
the  buoyancy  apparatus  provided  for  a  boat  of  Section  A.  At 
least  one-half  of  the  buoyancy  apparatus  must  be  attached  to  the 
outside  of  the  boat. 

Section  C.  A  boat  of  this  section  shall  be  a  life-boat,  properly 
constructed  of  wood  or  metal,  having  some  buoyancy  apparatus 
attached  to  the  inside  and  (or)  outside  of  the  boat  equal  in  ef- 
ficiency to  one-half  of  the  buoyancy  apparatus  provided  for  a 
boat  of  Section  A  or  Section  B.  At  least  one-half  of  the  buoy- 
ancy apparatus  must  be  attached  to  the  outside  of  the  boat. 

Section  D.  A  boat  of  this  section  shall  be  a  properly  con- 
structed boat  of  wood  or  metal. 


636  The  Naval  Constructor 

Section  E.  A  boat  of  this  section  shall  be  a  boat  of  approved 
construction,  form  and  material,  and  may  be  collapsible. 

Cubic  Capacity.  —  The  cubic  capacity  of  a  boat  shall  be 
deemed  to  be  her  cubic  capacity,  ascertained  (as  in  measuring 
ships  for  tonnage  capacity)  by  Simpson's  rule  ;  but  as  the  appli- 
cation of  that  rule  entails  much  labor,  the  following  simple  plan, 
which  is  approximately  accurate,  may  be  adopted  for  general 
purposes,  and  when  no  question  requiring  absolute  correct  ad- 
justment is  raised  :  — 

Measure  the  length  and  breadth  outside  and  the  depth  inside. 
Multiply  them  together  and  by  .6  ;  the  product  is  the  capacity  of 
the  boat  in  cubic  feet.  Thus,  a  boat  28  feet  long,  8  feet  6  inches 
broad,  and  3  feet  6  inches  deep,  will  be  regarded  as  having  a  ca- 
pacity of  28  x  8.5  x  8.5  =  499.8,  or  500  cubic  feet.  If  the  oars 
are  pulled  in  rowlocks,  the  bottom  of  the  gunwale  of  the  row- 
lock is  to  be  considered  the  gunwale  of  the  boat  for  ascertaining 
her  depth. 

Number  of  Persons  for  Boats.  —  The  number  of  persons  a 
boat  of  Section  A  shall  be  deemed  fit  to  carry  shall  be  the  num- 
ber of  cubic  feet,  ascertained  as  above,  divided  by  10. 

The  number  of  persons  a  boat  of  Section  B,  Section  C,  Sec- 
tion D,  or  Section  E  shall  be  deemed  fit  to  carry,  shall  be  the 
number  of  cubic  feet,  ascertained  as  per  rule,  divided  by  8.  The 
space  in  the  boat  shall  be  sufficient  for  the  seating  of  the  persons 
carried  in  it,  and  for  proper  use  of  the  oars. 

Appliances  for  Lowering  Boats.  —  Appliances  for  getting  a 
boat  into  the  water  must  fulfil  the  following  conditions  :  —  Means 
are  to  be  provided  for  speedily,  but  not  necessarily  simultaneously 
or  automatically,  detaching  the  boats  from  the  lower  blocks  of  the 
davit  tackles ;  the  boats  placed  under  davits  are  to  be  attached  to 
the  davit  tackles  and  kept  ready  for  service  ;  the  davits  are  to  be 
strong  enough  and  so  spaced  that  the  boats  can  be  swung  out  with 
facility  ;  the  points  of  attachment  of  the  boats  to  the  davits  are  to 
be  sufficiently  away  from  the  ends  of  the  boats  to  insure  their 
being  easily  swung  clear  of  the  davits  ;  the  boat's  chocks  are  to  be 
such  as  can  be  expeditiously  removed  ;  the  davits,  falls,  blocks, 
eyebolts,  rings,  and  the  whole  of  the  tackling  are  to  be  of  sufficient 
strength  ;  the  boat's  falls  are  to  be  long  enough  to  lower  the  boat 
into  the  water  with  safety  when  the  vessel  is  light.  The  life-lines 
shall  be  fitted  to  the  davits,  and  be  long  enough  to  reach  the  water 
when  the  vessel  is  light ;  and  hooks  are  not  to  be  attached  to  the 
lower  tackle  blocks. 

Equipments  for  Collapsible  or  other  Boats,  and  for 
Life-Rafts.  —  In  order  to  be  properly  equipped,  each  boat  shall 
be  provided  as  follows  :  — 


Number  of  Persons  for  Life-Rafts       637 


(a)  With  the  full  single-banked  complement  of  oars,  and  two 
spare  oars. 

(b)  With  two  plugs  for  each  plug-hole,  attached  with  lanyards 
or  chains,  and  one  set  and  a  half  of  thole  pins  or  crutches,  attached 
to  the  boat  by  sound  lanyards. 

(c)  With  a  sea-anchor,  a  baler,  a  rudder  and  a  tiller,  or  yoke 
lines,  a  painter  of  sufficient  length,  and  a  boat-hook.  The  rudder 
and  the  baler  to  be  attached  to  the  boat  by  sufficiently  long  lan- 
yards, and  kept  ready  for  use.  In  boats  where  there  may  be  a 
difficulty  in  fitting  a  rudder,  a  steering  oar  may  be  provided 
instead. 

(d)  A  vessel  to  be  kept  filled  with  fresh  water  shall  be  provided 
for  each  boat. 

(e)  Life-rafts  shall  be  fully  provided  with  a  suitable  approved 
equipment. 

Additional  Equipments  for  Boats  of  Section  A  and 
Section  B. — In  order  to  be  properly  equipped,  each  boat  of 
Sections  A  and  B,  in  addition  to  being  provided  with  all  the 
requisites  laid  down  in  Kule,  shall  be  equipped  as  follows,  but 
not  more  than  four  boats  in  any  one  ship  require  to  have  this 
outfit,  and  where  boats  of  Sections  A  or  B  are  carried  in  lieu 
of  boats  of  Sections  C  or  D,  this  additional  outfit  need  not  be 
insisted  on :  — 

(a)  With  two  hatchets  or  tomahawks,  one  to  be  kept  in  each 
end  of  the  boat,  and  to  be  attached  to  the  boat  by  a  lanyard. 

(6)  With  mast  or  masts,  and  with  at  least  one  good  sail,  and 
proper  gear  for  each. 

(c)  With  a  line  becketted  round  the  outside  of  the  boat  and 
securely  made  fast. 

{d)  With  an  efficient  compass. 

(e)  With  one  gallon  of  vegetable  or  animal  oil,  and  a  vessel  of 
an  approved  pattern,  for  distributing  it  in  the  water  in  rough 
weather. 

(/)  With  a  lantern  trimmed,  with  oil  in  its  receiver  sufficient 
to  burn  eight  hours. 

Number  of  Persons  for  Life-Rafts.  —  The  number  of  persons 
that  any  approved  life-raft  for  use  at  sea  shall  be  deemed  to  be 
capable  of  carrying,  shall  be  determined  with  reference  to  each 
separate  pattern  approved  by  the  Board  of  Trade  ;  provided 
always,  that  for  every  person  so  carried  there  shall  be  at  least 
three  cubic  feet  of  strong  and  serviceable  enclosed  air-tight  com- 
partments, constructed  so  that  water  cannot  find  its  way  into 
them.  Any  approved  life-raft  of  other  construction  may  be  used, 
provided  that  it  has  equivalent  buoyancy  to  that  hereinbefore 


638  The  Naval  Constructor 

described.  Every  such  approved  life-raft  shall  be  marked  in  such 
a  way  as  to  plainly  indicate  the  number  of  adult  persons  it  can 
carry. 

Buoyant  Apparatus.  —  Approved  buoyant  apparatus  shall  be 
deemed  sufficient,  so  far  as  buoyancy  is  concerned,  for  a  number 
of  persons,  to  be  ascertained  by  dividing  the  number  of  pounds  of 
iron  which  it  is  capable  of  supporting  in  fresh  water  by  32. 
Such  buoyant  apparatus  shall  not  require  to  be  inflated  before 
use,  shall  be  of  approved  construction,  and  marked  in  such  a 
way  as  plainly  to  indicate  the  number  of  persons  for  whom  it  is 
sufficient. 

Life-Belts.  —  An  approved  life-belt  shall  mean  a  belt  which 
does  not  require  to  be  inflated  before  use,  and  which  is  capable  at 
least  of  floating  in  the  water  for  24  hours  with  15  pounds  of  iron 
suspended  from  it.  Life-belts  are  to  be  cut  out  2  inches  under 
the  arm-pits,  and  fitted  so  as  to  remain  securely  in  their  place 
when  put  on. 

Lif e-Buoys.  —  An  approved  life-buoy  shall  mean  either :  (a) 
A  life-buoy  built  of  solid  cork,  capable  of  floating  in  water  for 
at  least  24  hours  with  32  pounds  of  iron  suspended  from  it ;  or 
(6)  A  strong  life-buoy  of  any  other  approved  pattern  or  material, 
provided  that  it  is  capable  of  floating  in  water  for  at  least  24 
hours  with  32  pounds  of  iron  suspended  from  it,  and  provided 
also  that  it  is  not  stuffed  with  rushes,  cork  shavings,  or  other 
shavings,  or  loose  granulated  cork  or  other  loose  material,  and 
does  not  require  inflation  before  use. 

All  life-buoys  shall  be  fitted  with  beckets  securely  seized,  and 
not  less  than  two  of  them  shall  be  fitted  with  life-lines  15  fathoms 
in  length. 

Position  of  Life-Buoys  and  Life-Belts.  Water-tight 
Compartments.  — All  life-buoys  and  lif e-belts  shall  be  so  placed 
as  to  be  readily  accessible  to  all  persons  on  board,  and  so  that 
their  position  may  be  known  to  those  for  whom  they  are  intended. 

When  ships  of  any  class  are  divided  into  efficient  water-tight 
compartments  to  the  satisfaction  of  the  Board  of  Trade,  they 
shall  only  be  required  to  carry  additional  boats,  rafts  and  buoy- 
ant apparatus  of  one-half  the  capacity  required  by  these  Kules, 
but  the  exemption  shall  not  extend  to  life-jackets  or  similar 
approved  articles  of  equal  buoyancy  suitable  to  be  worn  on  the 
person. 

The  table  referred  to  in  the  foregoing  Rules,  showing  the  mini- 
mum number  of  boats  to  be  placed  under  davits  and  their  mini- 
mum cubic  contents,  follows  :  — 


Number  and  Capacity  of  Boats 


639 


BOAT   CAPACITY  FOR   STEAMERS. 

(British  Law.) 


Gross  Tonnage. 


10,000 
9,000 
8,500 
8,000 
7,750 
7,500 
7,250 
7,000 
6,750 
6,500 
6,250 
6,000 
5,750 
5,500 
5,250 
5,000 
4,750 
4,500 
4,250 
4,000 
3,750 
3,500 
3,250 
3,000 
2,750 
2,500 
2,250 
2,000 
1,750 
1,500 
1,250 
1,000 
900 
800 
700 


500 
400 
300 
200 
100 


and  upwards     . 

and  upwards     . 

and  under  9,000 
8,500 
8,000 
7,750 
7,500 
7,250 
7,000 
6,750 
6,500 
6,250 
6,000 
5,750 
5,500 
5,250 
5,000 
4,750 
4,500 
4,250 
4,000 
3,750 
3,500 
3,250 
3,000 
2,750 
2,500 
2,250 
2,000 
1,750 
1,500 
1,250 
1,000 
900 
800 
700 


500 
400 
300 
200 


Minimum  Num 

BEB  OF 

Boats  to  be 

Placed  under 

Davits. 


Total 
Minimum  Cubic 

Contents 
of  Boats  to  be 

Placed 
under  Davits 
LxfixDx.6 


5,500 
5,250 
5,100 
5,000 
4,700 
4,600 
4,500 
4,400 
4,300 
4,200 
4,100 
4,000 
3,700 
3,600 
3,500 
3,400 
3,300 
2,900 
2,900 
2,800 
2,700 
2,600 
2,500 
2,400 
2,100 
2,050 
2,000 
1,900 
1,800 
1,700 
1,500 
1,200 
1,000 
900 
800 
700 
600 
400 
350 


640  The  Naval  Constructor 

Note.  —  Where  in  ships  already  fitted  the  required  cubic  con- 
tents of  boats  placed  under  davits  is  provided,  although  by  a 
smaller  number  of  boats  than  the  minimum  required  by  this  table, 
such  ships  shall  be  regarded  as  complying  with  the  rules  as  to 
boats  to  be  carried  under  davits. 

In  case  of  vessels  under  200  tons  gross  tonnage,  the  capacity  of 
any  boat  to  be  supplied  should  not  be  less  than  125  feet.  If,  how- 
ever, in  any  case  this  rule  be  found  impracticable,  a  discretion  may 
then  be  exercised  by  the  Board  of  Trade. 

In  cases  where  a  small  vessel  is  unable  to  cany  more  than  one 
boat,  a  discretion  may  be  exercised  by  the  Board  of  Trade ;  but 
whenever  one  boat  only  is  carried,  there  must  be  proper  provision 
to  enable  it  to  be  placed  readily  in  the  water  on  either  side  of  the 
ship. 

Capacity  and  Form  of  Life-Boats.  —  As  regards  the  boats  of 
Sections  A,  B,  C,  and  D,  Rule  1,  the  surveyors  will  see  that  the 
requirements  of  the  Rules  are  observed,  and  that  the  capacity  of 
the  boats,  and  the  number  of  persons  they  are  fit  to  carry,  are 
ascertained  by  Rules  2  and  3  (page  430).  In  measuring  boats 
the  length  and  breadth  are  to  be  regarded  as  the  extreme  dimen- 
sions measured  to  the  outside  of  the  plank.  The  number  of  per- 
sons for  which  a  boat  is  to  be  passed  is,  however,  subject  to  the 
further  condition  that  the  space  in  the  boat  shall  be  sufficient  for 
the  seating  of  them  all,  and  the  proper  use  of  the  oars.  That  this 
requirement  is  fulfilled  must  be  ascertained  by'  practical  experi- 
ment in  all  cases  before  a  declaration  is  granted,  unless  one  or 
more  boats  in  a  ship  are  of  the  same  pattern,  when  only  one  of 
such  boats  need  be  tested.  Life-boats  (except  those  of  Section  C) 
should  be  built  whale-boat  fashion,  both  ends  alike.  In  ships 
which  have  been  fitted  with  boats  previous  to  the  Rules  coming  into 
force,  square-sterned  boats  need  not  be  condemned  if  fitted  with 
the  required  amount  of  buoyancy,  but  all  life-boats  of  Sections  A 
and  B  subsequently  supplied,  or  supplied  to  new  ships,  must  be 
built  whale-boat  fashion.  All  collapsible  boats,  and  all  boats 
whether  collapsible  or  not,  if  constructed  of  any  material  other 
than  wood  or  metal,  must  be  in  accordance  with  a  pattern  approved 
by  the  Board  of  Trade  before  they  are  passed  as  a  portion  of  the 
life-saving  appliances  required  by  the  Rules. 

Stowage  of  Boats.  —  All  boats  required  by  the  Rules  to  be 
placed  under  davits  are  to  be  kept  fit  and  ready  for  use  ;  and  when 
they  are  swung  inboard  and  resting  on  the  chocks,  the  chocks  are 
to  be  so  constructed  that  the  boat  can  be  at  once  swung  outboard 
without  requiring  to  be  lifted  by  the  tackles  —  i.e.,  it  shall  not  be 
necessary  to  take  more  than  the  weight  of  the  boat. 

The  manner  in  which  the  additional  boats,  not  requiring  to  be 


Lifeboat  Buoyancy  641 

placed  under  davits,  are  to  be  stowed,  will  vary  in  different  ships, 
but  they  must  be  stowed  to  the  satisfaction  of  the  surveyors,  so  as 
to  be  as  readily  available  for  use  as  is  practicable,  having  due  con- 
sideration to  the  circumstances  mentioned  in  the  Rules. 

In  all  cases  where  boats  are  stowed  on  skids,  a  batten  and  space 
platform  of  about  2J"  planks  should  be  fitted  from  skid  to  skid, 
under  and  alongside  the  boat,  when  being  launched  forward  or  aft, 
and  as  a  platform  for  the  men. 

Equipments.  —  The  equipments  for  all  boats  are  provided  for 
in  the  Rules,  and  surveyors  are  to  see  that  the  requirements  are 
carefully  complied  with.  The  painters  for  boats  are  not  to  be  less 
than  20  fathoms  in  length. 

When  the  Rules  require  a  life-boat  of  Section  C  to  be  carried, 
and  owners  choose  to  provide  a  boat  of  Section  A  or  J5,  the  addi- 
tional equipments  required  by  General  Rule  6  for  boats  of  Section 
A  and  Section  B  need  not  be  insisted  on. 

Rudder.  —  In  some  of  the  collapsible  boats  it  is  difficult  to  fit 
a  rudder  ;  in  this  case  a  steering  oar  properly  fitted  may  be  passed 
instead. 

Buoyancy.  —  The  buoyancy  of  life-boats  of  Section  B  must  be 
partly  inside  and  partly  outside  the  boat,  and  a  boat  in  which  it  is 
wholly  inside  or  wholly  outside  shall  not  be  passed  as  a  boat  of 
Section  B. 

In  the  case  of  life-boats  of  Section  C,  one-half  the  buoyancy 
must  be  outside  the  boat ;  the  remainder  may  be  either  inside  or 
outside,  or  partly  inside  and  partly  outside. 

The  inside  buoyancy  for  boats  of  Sections  A,  B,  and  C,  must 
consist  of  strong  and  serviceable  enclosed  air-tight  compartments, 
such  that  water  cannot  find  its  way  into  them. 

The  outside  buoyancy  for  boats  of  Section  B  must  consist  of 
solid  cork  covered  with  canvas,  and  painted  and  attached  to  the 
outer  skin  of  the  boat  to  the  satisfaction  of  the  surveyors,  both  as 
regards  its  position  and  also  as  regards  its  attachment.  No  other 
material  is  to  be  used  unless  expressly  sanctioned  by  the  Board  of 
Trade.  The  outside  buoyancy  must  be  equal  to  at  least  half  the 
buoyancy  required  for  boats  of  Section  A,  and  the  inside  and  out- 
side buoyancy  together  must  equal  in  efficiency  the  buoyancy  re- 
quired for  a  boat  of  Section  A. 

To  effect  this  1.25  cubic  feet  of  cork  is  to  be  considered  as 
equivalent  to  1  cubic  foot  of  air-case. 

The  foregoing  remarks  apply  to  outside  buoyancy  for  boats  of 
Section  C,  excepting  that  the  total  buoyancy  is  only  required  to 
be  half  that  of  boats  of  Section  A  or  Section  B.  When  the  solid 
cork  is  not  permanently  attached  to  the  side  of  the  boat  in  such  a 


642  The  Naval  Constructor 


manner  that  moisture  cannot  collect  between  the  two  surfaces,  it 
wiil  require  to  be  removed  every  time  a  declaration  is  granted  to 
ascertain  (1)  whether  the  cork  is  becoming  sodden ;  (2)  whether 
moisture  is  collecting  between  the  cork  and  the  skin  of  the  boat, 
and  in  that  way  rotting  the  wood.  The  consideration  (2)  will  not 
apply  to  metal  boats. 

Air-Cases,  Material  and  Construction. —  Air-cases  are  re 
quired  by  the  Rules  to  be  constructed  of  wood,  or  of  copper  or 
yellow  metal  of  not  less  than  18  ounces  to  the  superficial  foot,  or 
of  other  durable  material. 

The  average  weight  of  18  ounce  copper  air-cases  is  about  5 
pounds  per  cubic  foot,  and  if  air-cases  of  other  material  exceed  this 
weight,  the  cubic  capacity  of  the  air-cases  must  be  correspondingly 
increased. 

As  yellow  metal  in  time  becomes  extremely  brittle,  copper  is  far 
preferable.  Zinc  is  not  durable  material,  and  should  not  be 
passed  ;  neither  should  galvanized  iron  or  steel  cases  be  passed 
for  new  boats. 

A  note  should  be  made  in  each  district  of  all  ships  whose  boats 
are  already  tilled  with  galvanized  iron  or  steel  air-cases,  with  a 
view  to  their  being  frequently  inspected.  Steel  or  iron  air-cases 
previously  passed  of  less  thickness  than  21  ounces  are  not  to  be 
rejected  so  long  as  they  continue  in  good  condition. 

Copper  and  yellow  metal  air-cases  are  to  be  made  with  proper 
hook  joints  not  less  than  three-eighths  of  an  inch  in  width,  ham- 
mered well  down  and  soldered,  and  no  other  joint  is  to  be  passed 
unless  specially  approved  by  the  Board  of  Trade. 

The  cases  are  not  to  exceed  four  feet  in  length  ;  they  are  to  he 
substantially  enclosed  with  wood,  which  is  to  be  close-jointed  so 
as  to  cover  any  exposed  part  of  the  air-case,  and  the  wood  form- 
ing the  top  is  not  to  be  less  than  one  inch  in  thickness. 

The  coverings  in  the  boats  over  the  air-cases  should  be  secured 
with  brass  screws,  so  as  to  enable  the  cases  to  be  removed  with- 
out difficulty  for  examination,  and  no  air-case  which  is  not  en- 
closed from  the  outer  shell  of  the  boat  should  be  passed. 

Spaces  filled  with  or  containing  any  material  are  not  to  be  deemed 
air-spaces  unless  specially  approved  by  the  Board  of  Trade. 

Copper  or  yellow  metal  air-cases  must  not  be  carried  in  con- 
tact with  the  skin  of  the  metal  boats. 

Where  boats  not  required  by  the  Rules  to  be  fitted  with  air- 
cases  are  so  fitted,  as,  for  instance,  in  some  of  the  collapsible  or 
semi-collapsible  boats,  these  provisions  as  to  air-cases  need  not  be 
insisted  upon. 

Steam  Launches,  etc.,  Carried  by  Steamships.  —  In  the 
cases  of  launches  er  other  boats  propelled  by  steam  power,  which 


Life-Rafts,  Buoyant  Apparatus         643 


31  e  carried  as  part  of  the  additional  boat  equipment  required  by 
the  Rules  made  under  the  provisions  of  the  Merchant  Shipping- 
Act,  an  inspection  of  the  boat,  machinery,  and  boilers,  and  of  the 
mounting  and  fitting  thereof,  should  be  made.  Steam  launches 
must  not  be  passed  as  a  part  of  the  boat  equipment  required  to  be 
under  davits. 

In  case  of  any  vessel  provided  with  a  steam  launch  or  boat  in 
addition  to  the  boat  capacity  required  under  the  Rules,  the  sur- 
veyors need  not  interfere  unless  they  have  reason  to  believe  that 
there  is  some  defect  in  the  boat,  machinery,  or  boiler,  or  in  the 
fittings  or  arrangement  thereof,  which  might  be  dangerous  to 
life. 

Boats  Already  Supplied.  —  In  carrying  these  instructions 
into  effect,  surveyors  are  to  be  careful  not  to  interfere  unnecessa- 
rily with  boats  supplied  before  November,  1890,  but  in  the  case  of 
new  boats  coming  under  survey  for  the  first  time,  as  well  as  in 
all  cases  in  which  the  fittings  of  the  boats  require  renewal,  the 
Rules  contained  in  these  instructions  are  to  be  strictly  adhered  to. 

Appliances  for  Lowering  Boats.  —  These  appliances  must 
be  in  accordance  with  Rule  4,  of  the  General  Rules,  and  must,  in 
the  surveyor's  opinion,  be  such  as  not  to  endanger  human  life. 
They  should  be  tested  at  each  survey  for  renewal  of  a  passenger 
certificate. 

The  question  of  determining  whether  the  requirements  of  the 
Rules  respecting  appliances  for  lowering  boats  are  complied  with 
in  the  case  of  any  particular  kind  of  gear  coming  under  the  sur- 
veyor's notice,  shall  be  left  to  the  principal  officers  of  the  districts. 

In  order  to  insure  uniformity  of  practice,  each  principal  officer, 
who  may  pass  any  particular  disengaging  gear,  should  request  the 
maker  to  supply  50  copies  of  the  plans  and  specifications  for 
distribution  among  the  surveyors  in  the  several  districts.  These 
copies  should  be  sent  to  the  Board  of  Trade  by  the  Principal 
Officer,  together  with  his  report  upon  the  gear.  No  certificates 
of  approval  for  disengaging  gear  will  be  issued. 

The  Principal  Officer  should  also  report  to  the  Board  of  Trade 
when  any  particular  disengaging  gear  has  been  inspected  and 
deemed  unsatisfactory  or  unsafe,  and  should  explain  fully  in  such 
report  the  details  which,  in  his  opinion,  render  it  undesirable. 
No  formal  certificate  of  approval  will,  however,  be  granted  by 
the  Board  of  Trade  or  their  officers  for  any  special  kind  of  gear. 

Life-Rafts,  Buoyant  Apparatus.  —  No  part  of  the  gear  which 
is  intended  to  bear  the  weight  of  the  boat  must  be  made  of  cast 
iron,  and  life-rafts  are  to  be  approved  by  the  Board  of  Trade  ; 
they  are  to  be  supplied  with  a  suitable  equipment  to  the  satisfac- 


644  The  Naval  Constructor 

tion  of  the  surveyors,  and  this  must  include  a  sea-anchor,  not  less 
than  20  fathoms  of  hawser,  and  oars  in  proportion  to  the  size  of 
the  raft. 

The  number  of  persons  that  any  approved  life-raft  for  use  at 
sea  is  to  be  deemed  capable  of  carrying  is  the  number  that  the 
raft  is  able  to  seat  safely,  provided  always  that  for  every  person 
so  carried  there  are  at  least  three  cubic  feet  of  strong  and  service- 
able enclosed  air-tight  compartments. 

Approved  buoyant  apparatus  is  to  be  deemed  sufficient  for  a 
number  of  persons  to  be  ascertained  by  dividing  the  number  of 
pounds  of  iron  which  it  is  capable  of  supporting  in  fresh  water  by 
32,  provided  also  that  the  sides  and  ends  of  the  apparatus  shall 
afford  a  space  of  one  horizontal  foot  for  each  person  for  whom  it 
is  certified,  and  that  a  line  for  the  people  to  cling  to  is  properly 
becketted  all  round  it.  Such  buoyant  apparatus  shall  not  re- 
quire to  be  inflated  before  use,  and  shall  be  of  approved  con- 
struction. 

Marking.  —  Surveyors  will  note  that  rafts  and  buoyant  ap- 
paratus shall  be  marked  in  such  a  way  as  to  plainly  indicate  the 
number  of  adult  persons  for  which  they  are  deemed  sufficient. 
Plates  will  be  supplied  by  the  Board  of  Trade  to  be  screwed  on  to 
the  woodwork  of  both  rafts  and  buoyant  apparatus,  indicating 
this  number  ;  and  forms  of  demand  (surveys  116  for  rafts  and  116a 
for  buoyant  apparatus)  for  plates,  to  be  filled  up  and  returned  to 
the  Board  of  Trade,  will  be  issued  for  the  use  of  the  Principal 
Officer.  No  raft  or  buoyant  apparatus  is  to  be  regarded  as  finally 
approved  until  the  marking-plate  has  been  affixed. 

Air-Cases  of  Rafts,  etc.  — The  instructions  in  the  case  of  life- 
boats apply  equally  to  life-rafts  and  buoyant  apparatus,  so  far  as 
the  length,  weight  and  enclosure  of  the  air-cases  are  concerned, 
excepting  that  as  life-rafts  and  buoyant  apparatus  are  only  in- 
tended to  be  used  in  cases  of  extreme  need,  and  are  consequently 
not  exposed  to  the  same  wear  and  tear  as  the  life-boats,  a  mini- 
mum weight  of  16  ounces,  copper  or  yellow  metal,  may  be  passed. 

Life-Belts.  —  No  life-belt  is  to  be  passed  that  is  not  capable  of 
floating  in  fresh  water  for  24  hours  with  15  pounds  of  iron  sus- 
pended from  it.  It  should  be  cut  out  2  inches  under  the  arm- 
pits, and  fitted  so  as  to  remain  securely  in  its  place  when  put  on. 
When  any  other  material  than  solid  cork  is  used  for  buoyancy,  it 
must  be  specially  approved  by  the  Board  of  Trade.  All  new  life- 
belts should  be  fitted  with  adjustable  shoulder-straps. 

It  is  desirable  that  notices  should  be  posted  indicating  the  place 
of  stowage  of  any  belts  which  are  not  plainly  visible  to  pas- 
sengers. 


Life- Buoys  645 

Life-Buoys.  —  No  life-buoy  stuffed  with  rushes  or  with  cork 
shavings  or  other  shavings,  or  granulated  cork,  or  any  loose 
material,  is  to  be  passed.  All  cork  life-buoys  are  to  be  built  of 
solid  cork,  and  fitted  with  lines  becketted  and  securely  seized  to 
the  life-buoy,  and  none  are  to  be  passed  that  will  not  float  for  24 
hours  in  fresh  water  with  32  pounds  of  iron  suspended  from  them. 
If  life-buoys  are  not  made  of  solid  cork,  the  pattern  and  material 
must  be  approved  by  the  Board  of  Trade.  No  contrivance  is  to 
be  passed  as  a  life-buoy  that  requires  inflation  before  use.  Life- 
buoys are  to  be  secured  by  a  toggle  and  becket,  or  any  other 
similar  method,  so  that  they  can  be  quickly  released  ;  they  must 
not  be  lashed  or  seized  to  the  rail  or  any  part  of  the  vessel,  but 
must  be  kept  so  as  to  be  ready  for  use  at  a  moment's  notice  in 
case  of  an  emergency. 

Not  less  than  two  of  the  life-buoys,  one  on  each  side  of  the 
ship,  are  to  be  fitted  with  life-lines  15  fathoms  in  length. 

Oil-distributing  Apparatus.  —  Vessels  for  distributing  oil 
are  to  be  to  the  satisfaction  of  the  surveyors,  and  are  to  be  so  con- 
structed as  to  distribute  the  oil  evenly  and  gradually  on  the  sur- 
face of  the  water. 


646  The  Naval  Constructor 


CHAPTER   IV. 

UNITED   STATES   NAVIGATION   LAWS    RELAT- 
ING TO   BOATS   AND   LIFE-SAVING 
APPLIANCES. 

The  British  requirements  as  to  the  build  of  boats,  number  of 
oars,  life-lines,  and  the  rule  for  calculating  the  capacities  of  life- 
boats, are  similar  to  the  American  regulations,  excepting  that  for 
river  steamers  the  capacity  is  divided  by  7  to  give  the  number  of 
persons  carried. 

Boat  Ladders.  —  Where  ladders  or  steps  are  necessary  to  en- 
able passengers  on  board  to  escape  conveniently  to  the  life-boats, 
such  steps  shall  be  provided  and  placed  on  each  side  of  the 
steamer,  with  manropes  of  suitable  size  and  of  sufficient  length 
to  reach  the  water ;  and  one  of  the  means  of  escape  from  one  deck 
to  another  shall  be  near  the  stern  of  the  vessel. 

Relieving  Tackle.  —  Extra  steering  apparatus  for  all  steamers 
carrying  passengers,  consisting  of  relieving  tackles  or  tiller,  must 
be  provided. 

Metal  Life-Boats  must  be  constructed  of  good  iron  or  other 
suitable  metal  not  less  in  thickness  than  18  B.W.G. 

Davits.  —  All  life-boats  must,  if  possible,  be  carried  on  cranes 
or  davits  ;  but  if  impossible  so  to  carry  all  the  life^boats  required, 
the  remainder  must  be  stowed  near  at  hand,  so  as  to  be  easily  and 
readily  launched  when  required. 

River  Steamers.  —  Steamers  navigating  rivers  only  (except 
ferry-boats,  canal-boats,  and  towing-boats,  of  less  than  50  tons) 
must  have  one  good  substantial  boat.  The  cubic  capacity  of  such 
boat  as  found  by  the  rule  given  on  p.  444  divided  by  7  will  deter- 
mine the  number  of  persons  to  be  carried. 

Freight,  Canal,  and  Towing  Steamers.  —  Freight,  canal, 
and  towing  steamers  of  less  than  50  tons  must  be  equipped  with 
boats  or  rafts,  as,  in  the  opinion  of  the  inspectors,  may  be  neces- 
sary, in  case  of  disaster,  to  secure  the  safety  of  all  persons  on 
board. 

Excursions  by  Permit.  —  Steamers  making  an  excursion 
under  a  permit  must  have  at  least  one  life-boat,  and  shall  be 
equipped  with  other  life-boats,  or  their  equivalents,  as,  in  the 


Life-Boats  for  Ocean  Steamers  647 


judgment  of  the  inspectors,  will  best  secure  the  safety  of  all  per- 
sons on  board  in  case  of  disaster. 

Automatic  Plug.  —  All  metal  life-boats  hereafter  built  shall 
be  furnished  with  an  automatic  plug. 

River  Passenger  Steamers.  —  Passenger  steamers  navigat- 
ing rivers  (excepting  steamers  of  100  gross  tons  and  under,  here- 
inafter provided  for)  must  be  supplied,  in  addition  to  the  boat 
required  in  the  paragraph  "River  Steamers,"  with  life-boats  in 
proportion  to  their  tonnage,  as  follows : 

Steamers  over     100  and  not  over     300  gross  tons    .   1  boat. 
Steamers  over     300  and  not  over     600  gross  tons     .  2  boats. 
Steamers  over     600  and  not  over     900  gross  tons     .  3  boats. 
Steamers  over     900  and  not  over  1,200  gross  tons     .  4  boats. 
Steamers  over  1,200  gross  tons 5  boats. 


Aggregate  Capacity.  —  The  aggregate  capacity  of  life-boats 
on  steamers  navigating  the  Red  River  of  the  North  and  rivers 
whose  waters  flow  into  the  Gulf  of  Mexico  and  their  tributaries, 
shall  not  be  less  than  120  cubic  feet  to  each  boat  for  the  number 
of  boats  as  given  in  the  table  ;  and  for  life-boats  on  steamers  navi- 
gating other  rivers  than  those  named,  the  aggregate  capacity  shall 
not  be  less  than  180  cubic  feet  to  each  boat  as  given  in  the  table  ; 
and  where  smaller  life-boats  are  employed  for  either  class  of 
river  steamers,  their  aggregate  capacity  shall  not  be  less  than  the 
aggregate  capacity  of  the  larger  boats ;  provided,  however,  that 
river  steamers  required,  under  the  table,  to  carry  more  than  two 
boats,  may,  where  the  owners  prefer  to  do  so,  supply  the  boat 
capacity  above  that  number  with  a  good,  substantial  life-raft  or 
rafts,  such  raft  or  rafts  to  be  of  an  aggregate  carrying  capacity  not 
less  than  that  of  the  boats  so  omitted. 

Capacity  may  Equal  Complement.  —  No  steamer  embraced 
in  the  foregoing  section  shall  be  required  to  have  more  life-boats, 
or  of  a  greater  capacity,  than  sufficient  to  carry  the  passengers 
allowed  by  the  certificate  of  inspection  (including  the  crew).  One 
of  the  life-boats,  unless  exempted  by  the  supervising  inspector, 
must  be  made  of  metal. 

Life-Boats  for  Ocean  Steamers.  — The  total  capacity  of  life- 
boats, or  of  life-boats  and  life-rafts,  on  steamers  navigating  the 
ocean  (except  steamers  of  100  gross  tons  and  under,  hereinafter 
provided  for),  shall  not  be  less  than  the  capacity  given,  according 
to  tonnage,  in  the  following  table  : 


648 


The  Naval  Constructor 


BOAT    CAPACITY   FOR    OCEAN    STEAMERS. 

(American  Law.) 


Gross  Tonnage. 


Total  Capacity 

of  Boats 
in  Cubic  Feet. 


Steamers 

over : 

100  and  not  over   200 

200  ■ 

300 

300  ' 

"      400 

400  ' 

500 

500  « 

1,000 

1,000  « 

1,500 

1,500  ' 

"    2,000 

2,000  ' 

2,500 

2,500  ' 

■    «    3,000 

3,000  ' 

3,500 

3,500  « 

4,000 

4,000  « 

5,000 

5,000  ■ 

5,500 

5,500  ' 

6,000 

6,000  ' 

"    6,500 

6,500  ' 

'    »•    7,000 

7,000  • 

7,500 

7,500  • 

8,000 

8,000  « 

8,500 

8,500  ' 

9,000 

9,000  « 

9,500 

9,500  ' 

10,000 

10,000  « 

10,500 

10,500  « 

11,000 

11,000  ' 

'    "    11,500 

11,500  « 

12,000 

12,000  ' 

i    m    12,500 

12,500  « 

13,000 

13,000  « 

13,500 

13,500  « 

"    14,000 

14,000  ' 

14,500 

14,500  ■ 

15,000 

15,000  . 

540 
720 
1,080 
1,260 
1,620 
1,800 
2,160 
2,340 
2,700 
2,880 
3,240 
3,420 
3,870 
4,320 
4,770 
5,220 
5,670 
6,120 
6,570 
7,020 
7,470 
7,920 
8,145 
8,370 
8,595 
8,820 
9,045 
9,270 
9,495 
9,720 
9,945 
10,170 
10,395 


Note.  —  Not  more  than  one-third  of  the  boat  capacity  required  on  ocean 
steamers  may  be  substituted  by  its  equivalent  in  approved  life  rafts  or 
approved  collapsible  (folding)  life-boats. 

These  boats  must  be  of  suitable  dimensions,  and  each  not  less  than  180 
cubic  feet  capacity.    (For  good  proportions  of  boats,  see  diagram  on  p.  421.) 


Life-boats  of  Lake,  Bay,  and  Sound  Steamers  649 


LIFE-BOATS    FOR    STEAMERS    NAVIGATING 

NORTHWESTERN   LAKES,    BAYS,    AND 

SOUNDS. 


Gross  Tonnage. 

No.  OF 
Boats. 

Capacity 
of  Boats. 

Steamers  over : 

100  and  not  over     200 .     .     . 

200     "         "            300 

300     "         "            400 

400     "         "            500 

500     "         "         1,000 

1,000     "         "         1,500 

1,500     "         "        2,000 

2,000     "         "         2,500 

2,500     "         "         3,000 

3,000     "         "        3,500 

3,500     "         "        4,000.     .... 

4,000     "         "        4,500 

4,500     "         "         5,000 

5,000     m         "         5,500 ..... 

2 
3 
4 
5 
6 
7 
8 
9 

10 
11 
12 
13 
14 
15 

Cu.  Ft. 

360 

540 

720 

900 

1,080 

1,260 

1,440 

1,620 

1,800 

1,980 

2,160 

2,340 

2,835 

3,330 

Note  on  Table.  —  Steamers  above  5,500  gross  tons  shall  be 
furnished  with  an  additional  boat  of  hot  less  than  495  cubic  feet 
capacity  for  each  additional  500  tons  burden,  or  fraction  thereof  ; 
or  if  the  owners  or  agents  prefer,  two  boats  may  be  used ;  pro- 
vided, the  aggregate  capacity  shall  be  the  same  as  the  one  boat 
described. 

These  boats  shall  be  substantially  built  with  reference  to  the 
trade  in  which  the  steamer  is  engaged,  and  shall  not  be  of  less 
dimensions  than  20  ft.  x  5  ft.  x  3  ft.,*  unless,  where  smaller  life- 
boats are  employed,  their  aggregate  capacity  shall  equal  the  aggre- 
gate capacity  of  the  larger  boats ;  provided,  however,  that  no 
steamer  shall  be  required  to  have  more  life-boats  than  sufficient  to 
carry  the  passengers  she  is  allowed  by  the  certificate  of  inspection, 
together  with  her  officers  and  crew. 

Not  more  than  one  third  of  the  boat  capacity  required  on  lake, 
bay,  and  sound  steamers  may  be  substituted  by  its  equivalent  in 
approved  life-rafts  or  approved  collapsible  (folding)  life-boats. 


*  For  good  proportions,  see  diagram  on  page  421. 


650  The  Naval  Constructor 


Marking  of  Boats. — All  wood  boats  required  on  steam-ves- 
sels shall  have  branded  or  cut  on  the  stem  thereof  the  net  cubic 
feet  contents  of  such  boats,  figured  as  follows  : 

Multiply  the  outside  length,  outside  width,  and  inside  depth 
together  and  the  product  by  .6,  and  divide  the  product  by  10  for 
ocean,  lake,  bay,  or  sound  steamers  ;  and  for  river  steamers,  di- 
vide the  product  by  7  ;  the  quotient  will  be  the  number  of  persons 
such  a  boat  is  allowed  to  carry. 

Example.  — The  carrying  capacity  of  a  boat  20  feet  in  length, 
6  feet  6  inches  in  breadth,  and  2  feet  3  inches  deep,  will  be  deter- 
mined as  under : 

For  ocean,  lake,  bay,  or  sound  steamers, 

20  x  5.5  x  2.25  X  .6      148.5      „_ 

-10-       -  =  -^0-=  15  persons. 

For  river  steamers,  same  boat,    — ^—  =  21  persons. 

Metal  boats  shall  have  net  cubic  feet  measurement  painted  on 
stem  in  black  letters  and  figures  not  less  than  £  inch  high  on  a 
white  ground. 

Every  life-raft  shall  have  stencilled  on  it  in  a  conspicuous  place 
(the  number  of  persons  it  can  carry,  as  determined  by)  the  net 
cubic  feet  contents  as  per  ratio  in  the  following  paragraph  : 

Life-Raft  Capacity. — All  life-rafts  and  floats  shall  have  an 
actual  buoyancy  of  187£  lbs.  upon  oceans  for  every  person  al- 
lowed, and  150  lbs.  upon  lakes,  bays,  sounds,  and  rivers  for 
every  person  allowed.  Such  life-rafts  and  floats  must  be  suitably 
equipped  with  life-lines  and  oars. 

All  rubber  and  canvas  rafts  shall  be  kept  inflated  at  all  times. 

Life-Floats.  —  When  wooden  life-floats  are  required  on  steam- 
vessels,  in  compliance  with  law  they  shall  be  at  least  of  the  follow- 
ing dimensions,  or  other  proper  dimensions  of  equal  cubical  capac- 
ity, viz.,  4  feet  in  length,  14  inches  in  breadth,  and  2  inches  in 
thickness.  These  floats  shall  be  made  of  white  pine  wood,  or  any 
other  wood  not  exceeding  white  pine  *  in  weight  per  cubic  foot. 

Drags,  or  Floating  Anchors.  —  Drags,  or  floating  anchors, 
shall  be  constructed  so  as  to  be  capable  of  being  compactly  stowed 
near  the  head  of  the  ship.  (For  a  detail  of  these  anchors,  see  p. 
363.) 

Steamers  navigating  the  ocean  must  be  provided  with  at  least 
one  drag,  of  area  as  follows  :  —  For  steamers  of  400  gross  tons  and 

*  What  is  known  as  white  pine  in  the  States  is  called  yellow  pine  in  the 
British  Isles. 


Drags  or  Floating  Anchors  651 

under,  not  less  than  25  superficial  feet ;  for  steamers  of  over  400 
gross  tons,  the  area  of  drag  shall  not  be  less  than  that  deter- 
mined by  adding  to  25  square  feet  one  square  foot  for  each  addi- 
tional 25  gross  tons  above  400  tons. 

Example.  —  The  area  of  a  drag  on  a  vessel  of  1,000  tons  will 
equal :  — 

or  ,  1,000-400      .n  .    4 

2 ^  H ^"H —  49  square  feet. 

25 

Steamers  of  over  5,000  tons  gross  may  be  equipped  with  two  or 
more  drags,  provided  the  total  area  is  not  less  than  that  required 
by  this  rule.  Steamers  whose  routes  do  not  extend  off  anchor- 
age are  not  required  to  have  drags,  or  floating  anchors,  on  board. 
(A  table  giving  areas  for  sea-anchors  based  on  the  above  rule  is 
given  on  p.  362.) 

Every  life-preserver  adjustable  to  the  body  of  a  person  shall 
be  made  of  good,  sound  cork  blocks  or  other  suitable  material, 
with  belts  and  shoulder  straps  properly  attached,  and  shall  be  con- 
structed so  as  to  place  the  cork  underneath  the  shoulders  and 
around  the  body  of  the  person  wearing  it,  the  shoulder  straps  to 
be  sewed  on  at  least  eight  inches  apart  on  the  back  of  the  preserver, 
and  sewed  together  at  an  angle  where  they  cross  the  body,  and 
must  also  have  a  strap  across  the  breast  from  one  shoulder  strap 
to  the  other,  sewed  fast  at  one  end  and  with  a  buttonhole  at  the 
other,  with  a  button  on  shoulder  strap  to  which  the  cross  piece 
can  be  buttoned,  and  all  belt  life-preservers  shall  be  not  less 
than  54  inches  in  length,  measurement  from  end  to  end  around 
the  body.  And  it  shall  be  the  duty  of  the  inspectors  to  see  by 
actual  examination  that  every  such  life-preserver  contains  at  least 
six  pounds  of  good  cork,  which  shall  have  a  buoyancy  of  at  least 
four  pounds  to  each  pound  of  cork.  Inspectors  are  further  re- 
quired to  see  such  life-preservers  are  distributed  throughout  the 
cabins,  staterooms,  berths,  and  other  places  convenient  for 
passengers  on  such  steamer  ;  and  there  shall  be  a  printed  notice 
posted  in  every  cabin  and  stateroom,  and  in  conspicuous  places 
about  the  decks,  informing  passengers  of  the  location  of  life- 
preservers  and  other  life-saving  appliances,  and  of  the  mode  of 
applying  or  adjusting  the  same.  Cork  cushions,  when  constructed 
of  good,  sound  cork  blocks  or  other  suitable  material,  with  belts 
and  shoulder  straps  properly  attached,  said  cushions  to  contain 
not  less  than  six  pounds  of  cork,  when  passed  by  local  inspectors, 
may  be  used  in  lieu  of  life-preservers  on  small  pleasure  steamers. 

Barges  towed  by  steamers  and  carrying  passengers  on  regular 
"night  routes"  shall  have  a  life-preserver  for  each  passenger; 
and,  in  addition  thereto,  shall  be  supplied  with  a  yawl  boat,  ten 
buckets  and  three  axes. 


652 


The  Naval  Constructor 


Every  sea-going  steamer  and  every  steamer  navigating  the  great 
Northern  and  Northwestern  lakes  carrying  passengers  shall  have 
not  less  than  three  water-tight  cross  bulkheads.  Such  bulkheads 
shall  reach  to  the  main  deck  in  single -decked  vessels,  otherwise  to 
the  deck  next  below  the  main  deck.  For  wooden  hulls  they  shall 
be  fastened  to  suitable  framework,  which  framework  must  be 
securely  attached  to  the  hull  and  caulked.  For  iron  hulls  they 
shall  be  well  secured  to  the  framework  of  the  hulls  and  strengthened 
by  stanchions  of  angle  iron  placed  not  more  than  two  feet  from 
centre  to  centre.  One  of  the  bulkheads  must  be  placed  forward 
and  one  abaft  of  the  engines  and  boilers. 

The  third  or  collision  bulkhead  must  be  placed  not  nearer  than 
five  feet  from  the  stem  of  the  vessel.  Iron  bulkheads  must  be 
made  not  less  than  one-quarter  of  an  inch  in  thickness,  and  wooden 
bulkheads  must  be  of  equal  strength  and  covered  with  iron  plates 
not  less  than  one-sixteenth  of  an  inch  in  thickness. 

Steam  ferry-boats  of  50  tons  burden  and  over  must  be  supplied 
with  life-boats  as  in  the  judgment  of  the  inspector  will  best  pro- 
mote the  security  of  life  on  board  of  such  vessels  in  case  of  disas- 
ter, according  to  the  average  number  of  passengers  carried  per 
trip. 

Table  of  dimensions  of  boats  for  passenger  steamers  of  100  gross 
tons  and  under,  navigating  lakes,  bays,  sounds,  and  rivers,  other 
than  the  Red  River  of  the  North  and  rivers  whose  waters  flow  into 
the  Gulf  of  Mexico.  Boats  of  other  dimensions  of  equivalent 
cubical  capacity  may  be  used  i  — 


Number  of  Tons 
(Gross). 

as  < 
<p  o 

*8 

Dimensions. 

M 
O 
H 
U 

A 

H 
K 

W 
H 

g 
o 
Q 

Length. 

Breadth. 

Depth. 

Steamers  over : 

Ft. 

Ft.     In. 

Ft.  In. 

Cu.  Ft. 

50  and  not  over 

100 

1 

18 

5       6 

2     3 

.7 

155.9 

30     m 

50 

1 

10 

5      0 

2     3. 

-.7 

138.6 

10     " 

30 

1 

14 

5      0 

2     2 

.7 

106.1 

0     " 

10 

1 

14 

4      6 

2     0 

.7 

88.2 

The  cubical  capacity  of  life-boats  on  steamers  of  100  gross  tons 
and  under,  navigating  the  Red  River  of  the  North  and  rivers  whose 


Buoyancy  Apparatus  653 

waters  flow  into  the  Gulf  of  Mexico,  shall  be  as  follows,  measured 
as  per  example  in  Section  2,  Kule  III :  — 

Cubic  Feet. 
Steamers  over  50  and  not  over  100  gross  tons      .     .     105 
Steamers  over  30  and  not  over    50  gross  tons      .     .       92 
Steamers  over  10  and  not  over    30  gross  tons      .     .       71 
Steamers  of  10  gross  tons  and  under 60 

The  life-boat  on  steamers  between  50  and  100  tons  must  be  in 
addition  to  the  working  boat  required  by  Section  6  of  this  rule. 

The  boat  for  passenger  steamers  of  10  tons  and  less  may  be 
dispensed  with  if  such  steamer  is  provided  with  metallic  air 
chambers,  placed  under  the  seats  and  in  the  ends  of  said  vessel,  of 
sufficient  capacity  to  float  the  inert  weight  of  said  vessel  including 
her  boilers  and  machinery  ;  otherwise  the  life-boat  referred  to  in 
the  above  table  must  be  either  carried  or  towed  at  all  times  when 
being  navigated  with  passengers  on  board  ;  and  all  such  vessels 
referred  to  in  this  section  shall  also  be  provided  with  one  life- 
preserver  for  every  person  which  the  inspection  certificate  shall 
allow  them  to  carry,  including  officers  and  crew. 

All  open  steam  launches  or  other  steam-vessels  of  five  tons  burden 
or  less,  used  for  pleasure  purposes  only,  will  not  be  required  to  carry 
a  life-boat.  Such  steamers  when  licensed  to  carry  passengers  may 
dispense  with  the  life-boat  when  such  vessels  are  provided  with 
metallic  air  chambers  placed  under  the  seats  and  in  the  ends  of  said 
vessels,  of  sufficient  capacity  to  float  the  inert  weight  of  said 
vessel,  including  her  boilers  and  machinery  ;  and  such  vessels 
shall  also  be  provided  with  one  life-preserver  for  every  person 
which  the  inspection  certificate  shall  allow  them  to  carry,  including 
the  officers  and  crew  ;  and  every  such  steam-vessel  carrying  fifteen 
passengers  or  less  shall  carry  at  least  two  fire  buckets  and  one  axe. 

All  steam-vessels  certificated  as  ocean,  lake,  bay,  or  sound  at  their 
annual  inspection  after  the  adoption  of  this  rule  (except  vessels  of 
100  tons  and  under,  inspected  under  the  provisions  of  Section  4426, 
Revised  Statutes,  and  freight  and  towing  steamers,  inspected 
under  the  provisions  of  Section  4427,  Revised  Statutes)  shall  be 
provided  with  a  line-carrying  projectile  and  the  means  of  propel- 
ling it,  such  as  may  have  received  the  formal  approval  of  the  Board 
of  Supervising  Inspectors. 

All  inland  passenger  steamers  are  required  to  be  provided  with 
fire  buckets,  barrels,  axes,  as  follows : 


654 


The  Naval   Constructor 


Gross  Toxs. 

Barrels. 

Buckets. 

Axes. 

All  steamers  not  over  10  tons  .     . 

All  steamers  over  10  tons  and  not 

over  25  tons 

2 

4 

6 

8 

18 

24 

35 
50 

1 

1 

2 

2 

4 

6 

8 
10 

All  steamers  over  25  tous  and  not 

over  50  tons 

All  steamers  over  50  tons  and  not 

over  100  tons 

All  steamers  over  100  .tons  and 

not  over  200  tons     .... 
All  steamers  over  200  tons  and 

not  over  500  tons     .... 
All  steamers  over   500  tons  and 

not  over  1000  tons   .... 
All  steamers  over  1000  tons     .     . 

1 

1 
2 
4 

6 

8 

For  tug,  tow,  freight,  and  small  ferry  steamers : 


Gross  Tons. 

Barrels. 

Buckets. 

Axks. 

All  steamers  not  over  10  tons  .     . 

All  steamers  over  10  tons  and  not 

over  25  tons 

.      .      . 

2 

4 

6 

8 

12 

15 

20 

25 

1 

1 

2 

2 
2 
3 
4 
5 

All  steamers  over  25  tons  and  not 

over  50  tons 

All  steamers  over  50  tons  and  not 

over  100  tons 

All  steamers  over  100  tons  and 

not  over  200  tons    .... 
All   steamers  over  200  tons  and 

not  over  500  tons     .... 
All   steamers  over   500  tons  and 

not  over  1000  tons  .... 
All  steamers  over  1000  tons,  not 

less  than 

1 

1 
1 

2 
3 
4 

Provided,  however,    That  tanks  of  suitable  dimensions  and  arrange- 
ments, or  buckets  in  sufficient  number  may  be  substituted  for  barrels  on 
all  vessels.    Five  buckets  shall  be  considered  as  equivalent  to  one  barrel. 

Boilers  655 


Fire  buckets,  barrels,  or  tanks,  must  be  constantly  filled  with 
water,  and  in  such  positions  on  board  as  shall  be  most  convenient 
for  extinguishment  of  fire. 

All  axes  must  be  so  located  as  to  be  readily  found  in  time  of 
need,  must  not  be  used  for  general  purposes,  and  must  be  kept  in 
good  condition. 

All  hay,  straw,  or  baled  shavings  carried  on  deck  of  passenger 
steamers  shall  be  covered  with  a  tarpaulin  while  on  board. 

Boilers.  —  All  boilers  shall  have  a  clear  space  of  at  least  8 
inches  between  the  underside  of  the  cylindrical  shell  and  the  floor 
or  keelson. 

All  boilers  shall  have  a  clear  space  at  the  back  and  ends  thereof 
of  2  feet  opposite  the  back  connection  door ;  provided,  that  on 
vessels  constructed  of  iron  or  steel  with  metal  bulkheads  the  dis- 
tance between  back  connection  doors  and  such  metal  bulkheads 
shall  not  be  less  than  16  inches. 

Donkey  Boiler.  —  Every  sea-going  steamer  carrying  passen- 
gers shall  be  supplied  with  an  auxiliary  or  donkey  boiler  of  suffi- 
cient capacity  to  work  the  fire  pumps,  and  such  boiler  shall  not 
be  placed  below  the  lower  decks  except  on  single-deck  vessels. 


656  The  Naval  Constructor 

CHAPTER  V. 

INTERNATIONAL   RULES   OF   1897* 

Preliminary  Definitions.  —  In  the  following  rules  every 
steam-vessel  which  is  under  sail  and  not  under  steam  is  to  be  con- 
sidered a  sailing-vessel,  and  every  vessel  under  steam,  whether 
under  sail  or  not,  is  to  be  considered  a  steam-vessel. 

The  word  "steam-vessel  "  shall  include  any  vessel  propelled  by 
machinery. 

A  vessel  is  "under  way"  within  the  meaning  of  these  rules 
when  she  is  not  at  anchor,  or  made  fast  to  the  shore,  or  aground. 

Lights,  etc.  —  The  word  "  visible  "  in  these  rules  when  applied 
to  lights  shall  mean  visible  on  a  dark  night  with  a  clear  atmos- 
phere. 

The  rules  concerning  lights  shall  be  complied  with  in  all 
weathers  from  sunset  to  sunrise,  and  during  such  time  no  other 
lights  which  may  be  mistaken  for  the  prescribed  lights  shall  be 
exhibited. 

Steam- Vessel's  Masthead  Light.  —  A  steam-vessel,  when 
under  way,  shall  carry:  (a)  On  or  in  front  of  the  foremast,  or  if  a 
vessel  without  a  foremast,  then  in  the  fore  part  of  the  vessel,  at  a 
height  above  the  hull  of  not  less  than  twenty  feet,  and  if  the 
breadth  of  the  vessel  exceeds  twenty  feet,  at  a  height  above  the 
hull  not  less  than  such  breadth,  so,  however,  that  the  light  need 
not  be  carried  at  a  greater  height  above  the  hull  than  forty  feet, 
a  bright,  white  light,  so  constructed  as  to  show  an  unbroken  light 
over  an  arc  of  the  horizon  of  twenty  points  of  the  compass,  so 
fixed  as  to  throw  the  light  ten  points  on  each  side  of  the  vessel, 
namely,  from  right  ahead  to  two  points  abaft  the  beam  on  either 
side,  and  of  such  a  character  as  to  be  visible  at  a  distance  of  at 
least  five  miles. 

Steam-Vessel's  Side-Lights.  —  (6)  On  the  starboard  side  a 
green  light  so  constructed  as  to  show  an  unbroken  light  over  an 
arc  of  the  horizon  of  ten  points  of  the  compass,  so  fixed  as  to 
throw  the  light  from  right  ahead  to  two  points  abaft  the  beam 
on  the  starboard  side,  and  of  such  a  character  as  to  be  visible  at  a 
distance  of  at  least  two  miles. 

(c)  On  the  port  side  a  red  light  so  constructed  as  to  show  an 
unbroken  light  over  an  arc  of  the  horizon  of  ten  points  of  the 
compass,  so  fixed  as  to  throw  the  light  from  right  ahead  to  two 
*  Subscribed  to  by  tbe  Maritime  Nations. 


Side  and  Range  Lights 


657 


points  abaft  the  beam  on  the  port  side,  and  of  such  a  character  as 
to  be  visible  at  a  distance  of  at  least  two  miles. 

(d)  The  said  green  and  red  side-lights  will  be  fitted  with  in- 
board screens  projecting  at  least  three  feet  forward  from  the  light, 
so  as  to  prevent  these  lights  from  being  seen  across  the  bow. 
(Fig.  286.' 


Fig.  364. 

Steam-Vessels'  Range  Lights.  —  (e)  A  steam-vessel  when 
under  way  may  carry  an  additional  white  light  similar  in  con- 
struction to  the  light  mentioned  in  subdivision  (a).  These  lights 
shall  be  so  placed  in  line  with  the  keel  that  one  shall  be  at  least 
fifteen  feet  higher,  than  the  other,  and  in  such  a  position  with 
reference  to  each  other  that  the  lower  light  shall  be  forward  of 
the  upper  one.  The  vertical  distance  between  these  lights  shall 
be  less  than  the  horizontal  distance. 

Steam-Vessels  -when  Towing.  —  A  steam-vessel  when  tow- 
ing another  vessel  shall,  in  addition  to  her  side-lights,  carry  two 
bright  white  lights  in  a  vertical  line  one  over  the  other,  and  not 
less  than  six  feet  apart ;  and  when  towing  more  than  one  vessel 
shall  carry  an  additional  bright  white  light  six  feet  above  or  below 
such  light,  if  the  length  of  the  tow  measuring  from  the  stern  of 
the  towing  vessel  to  the  stern  of  the  last  vessel  towed  exceeds  six 
hundred  feet.  Each  of  these  lights  shall  be  of  the  same  construc- 
tion and  character,  and  shall  be  carried  in  the  same  position  as  the 
white  light  mentioned  in  Article  2  (a),  excepting  the  additional 
light,  which  may  be  carried  at  a  height  of  not  less  than  fourteen 
feet  above  the  hull. 

Such  steam-vessels  may  carry  a  small  white  light  abaft  the  fun- 
nel or  aftermast  for  the  vessel  towed  to  steer  by,  but  such  light 
shall  not  be  visible  forward  of  the  beam. 


658  The  Naval  Constructor 


Special  Lights.  —  (a)  A  vessel  which  from  any  accident  is  not 
under  command  shall  carry  at  the  same  height  as  the  white  light 
mentioned  in  Article  2  (a),  where  they  can  be  best  seen,  and  if 
a  steam-vessel  in  lieu  of  that  light,  two  red  lights,  in  a  vertical 
line  one  over  the  other,  not  less  than  six  feet  apart,  and  of  such  a 
character  as  to  be  visible  all  around  the  horizon  at  a  distance  of  at 
least  two  miles  ;  and  shall  by  day  carry  in  a  vertical  line  one  over 
the  other,  not  less  than  six  feet  apart,  where  they  can  be  best  seen, 
two  black  balls  or  shapes,  each  two  feet  in  diameter. 

(6)  A  vessel  employed  in  laying  or  in  picking  up  a  telegraph 
cable  shall  carry  in  the  same  position  as  the  white  light  mentioned 
in  Article  2  (a),  and  if  a  steam-vessel  in  lieu  of  that  light,  three 
lights  in  a  vertical  line  one  over  the  other,  not  less  than  six  feet 
apart.  The  highest  and  lowest  of  these  lights  shall  be  red,  and 
the  middle  light  shall  be  white,  and  they  shall  be  of  such  a  char- 
acter as  to  be  visible  all  around  the  horizon  at  a  distance  of  at 
least  two  miles.  By  day  she  shall  carry  in  a  vertical  line  one  over 
the  other,  not  less  than  six  feet  apart,  where  they  can  be  best  seen, 
three  shapes  not  less  than  two  feet  in  diameter,  of  which  the  high- 
est and  the  lowest  shall  be  globular  in  shape  and  red  in  color,  and 
the  middle  one  diamond  in  shape  and  white. 

(c)  The  vessels  referred  to  in  this  article,  when  not  making  way 
through  the  water,  shall  not  carry  the  side-lights,  but  when  mak- 
ing way  shall  carry  them. 

(d)  The  lights  and  shapes  required  to  be  shown  by  this  article 
are  to  be  taken  by  other  vessels  as  signals  that  the  vessel  showing 
them  is  not  under  command  and  cannot  therefore  get  out  of  the 
way. 

These  signals  are  not  signals  of  vessels  in  distress  and  requiring 
assistance.     Such  signals  are  contained  in  Article  31. 

Lights  for  Sailing-Vessels  and  Vessels  in  Tow.  —  A  sail- 
ing-vessel under  way  and  any  vessel  being  towed  shall  carry  the 
same  lights  as  are  prescribed  by  Article  2  for  a  steam-vessel 
under  way,  with  the  exception  of  the  white  lights  mentioned 
therein,  which  they  shall  never  carry. 

Lights  for  Small  Vessels.  —  Whenever,  as  in  the  case  of 
small  vessels  under  way  during  bad  weather,  the  green  and  red 
lights  cannot  be  fixed,  these  lights  shall  be  kept  at  hand,  lighted 
and  ready  for  use ;  and  shall  on  the  approach  of  or  to  other 
vessels,  be  exhibited  on  their  respective  sides  in  sufficient  time  to 
prevent  collision,  in  such  manner  as  to  make  them  most  visible, 
and  so  that  the  green  light  shall  not  be  seen  on  the  port  side,  nor 
the  red  light  on  the  starboard  side,  nor,  if  practicable,  more  than 
two  points  abaft  the  beam  on  their  respective  sides.  To  make 
the  use  of  these  portable  lights  more  certain  and  easy,  the  lanterns 


Lights  for  Pilot  Vessels  659 

containing  them  shall  each  be  painted  outside  with  the  color  of 
the  light  they  respectively  contain,  and  shall  be  provided  with 
proper  screens. 

Lights  for  Small  Steam  and  Sail  Vessels  and  Open 
Boats.  —  Steam-vessels  of  less  than  forty,  and  vessels  under  oars 
or  sails  of  less  than  twenty  tons  gross  tonnage,  respectively,  and 
rowing  boats,  when  under  way,  shall  not  be  required  to  carry  the 
lights  mentioned  in  Article  2  (a),  (6),  and  (c),  but  if  they  do  not 
carry  them  they  shall  be  provided  with  the  following  lights  :  — 

First :  Steam-vessels  of  less  than  forty  tons  shall  carry  :  — 

(a)  In  the  fore  part  of  the  vessel  or  on  or  in  front  of  the  funnel, 
where  it  can  be  best  seen,  and  at  a  height  above  the  gunwale  of 
not  less  than  nine  feet,  a  bright  white  light  constructed  and  fixed 
as  prescribed  in  Article  2  (a),  and  of  such  a  character  as  to  be 
visible  at  a  distance  of  at  least  two  miles. 

(&)  Green  and  red  side-lights  constructed  and  fixed  as  pre- 
scribed in  Article  2  (6)  and  (c),  and  of  such  a  character  as  to  be 
visible  at  a  distance  of  at  least  one  mile,  or  a  combined  lantern 
showing  green  and  red  light  from  right  ahead  to  two  points  abaft 
the  beam  on  their  respective  sides.  Such  lanterns  shall  be  car- 
ried not  less  than  three  feet  below  the  white  light. 

Second:  Small  steamboats,  such  as  are  carried  by  sea-going 
vessels,  may  carry  the  white  light  at  a  less  height  than  nine  feet 
above  the  gunwale,  but  it  shall  be  carried  above  the  combined 
light  mentioned  in  subdivision  one  (b). 

Third:  Vessels  under  oars  or  sails  of  less  than  twenty  tons 
shall  have  ready  at  hand  a  lantern  with  a  green  glass  on  one  side 
and  a  red  glass  on  the  other  side,  which,  on  the  approach  of  or  to 
other  vessels,  shall  be  exhibited  in  sufficient  time  to  prevent  col- 
lision, so  that  the  green  light  shall  not  be  seen  on  the  port  side, 
nor  the  red  light  on  the  starboard  side. 

Fourth :  Rowing  boats,  whether  under  oars  or  sail,  shall  have 
ready  at  hand  a  lantern  showing  a  white  light  which  shall  be 
temporarily  exhibited  in  sufficient  time  to  prevent  collision. 

The  vessels  referred  to  in  this  article  shall  not  be  required  to 
carry  the  lights  prescribed  by  Article  4  (a)  and  Article  11,  last 
paragraph. 

Lights  for  Pilot -Vessels.  —  Pilot  vessels,  when  engaged  on 
their  station  on  pilotage  duty,  shall  not  show  the  lights  required 
for  other  vessels,  but  shall  carry  a  white  light  at  the  masthead, 
visible  all  around  the  horizon,  and  shall  also  exhibit  a  flare-up 
light  or  flare-up  lights  at  short  intervals,  which  shall  never  exceed 
fifteen  minutes. 

On  the  near  approach  of  or  to  other  vessels  they  shall  have  their 
side-lights  lighted,  ready  for  use,  and  shall  flash  or  show  them  at 


660  The  Naval  Constructor 

short  intervals,  to  indicate  the  direction  in  which  they  are  head- 
ing ;  but  the  green  light  shall  not  be  shown  on  the  port  side,  nor 
the  red  light  on  the  starboard  side. 

A  pilot  vessel  of  such  a  class  as  to  be  obliged  to  go  alongside  of 
a  vessel  to  put  a  pilot  on  board,  may  show  the  white  light  instead 
of  carrying  it  at  the  masthead,  and  may  instead  of  the  colored 
lights  above  mentioned,  have  at  hand,  ready  for  use,  a  lantern 
with  green  glass  on  one  side  and  red  glass  on  the  other,  to  be  used 
as  prescribed  above. 

Pilot  vessels,  when  not  engaged  on  their  station  on  pilotage 
duty,  shall  carry  lights  similar  to  those  of  other  vessels  of  their 
tonnage. 

A  steam  pilot  vessel  when  engaged  on  her  station  on  pilotage 
duty  and  in  the  waters  of  the  United  States,  and  not  at  anchor, 
shall,  in  addition  to  the  lights  required  for  all  pilot  boats,  carry  at 
a  distance  of  eight  feet  below  her  white  masthead  light  a  red 
light,  visible  all  around  the  horizon,  and  of  such  character  as  to  be 
visible  on  a  dark  night  with  a  clear  atmosphere  at  a  distance  of 
at  least  two  miles,  and  also  the  colored  side-lights  required  to  be 
carried  by  vessels  when  under  way . 

When  engaged  on  her  station  on  pilotage  duty  and  in  waters  of 
the  United  States,  and  at  anchor,  she  shall  carry,  in  addition  to  the 
lights  required  for  all  pilot  boats,  the  red  light  above  mentioned, 
but  not  the  colored  side-lights. 

When  not  engaged  on  her  station  on  pilotage  duty,  she  shall 
carry  the  same  lights  as  other  steam-vessels. 

Lights,  etc.,  of  Fishing  Vessels. —  (Article  9,  act  of  August 
19,  1890,  was  repealed  by  act  of  May  28,  1894,  and  Article  10,  act 
of  March  3,  1885,  was  re-enacted  in  part  by  act  of  August  13, 
1894,  and  is  reproduced  here  in  part  as  Article  9.  It  will  be  the 
object  of  further  consideration  by  the  maritime  powers.) 

Fishing  vessels  of  less  than  twenty  tons  net  registered  tonnage, 
when  under  way  and  not  having  their  nets,  trawls,  dredges,  or 
lines  in  the  water,  shall  not  be  obliged  to  carry  the  colored  side- 
lights ;  but  every  such  vessel  shall  in  lieu  thereof  have  ready  at 
hand  a  lantern  with  a  green  glass  on  the  one  side  and  red  glass  oil 
the  other  side,  and  on  approaching  to  or  being  approached  by  an- 
other vessel,  such  lanterns  shall  be  exhibited  in  sufficient  time  to 
prevent  collision,  so  that  the  green  light  shall  not  be  seen  on  the 
port  side,  nor  the  red  light  on  the  starboard  side. 

Lights  for  Fishing  Vessels  on  European   Coasts. — The 

following  portion  of  this  article  applies  only  to  fishing  vessels  and 
boats  when  in  the  sea  off  the  coast  of  Europe  lying  north  of  Cape 
Finisterre  :  — 

(a)  All  fishing  vessels  and  fishing  boats  of  twenty  tons  net  regis- 


Lights  for  Fishing  Vessels  661 

tered  tonnage  or  upward,  when  under  way  and  when  not  having 
their  nets,  trawls,  dredges,  or  lines  in  the  water,  shall  carry  and 
show  the  same  lights  as  other  vessels  under  way. 

(b)  All  vessels  when  engaged  in  fishing  with  drift-nets  shall 
exhibit  two  white  lights  from  any  part  of  the  vessel  where  they 
can  be  best  seen.  Such  lights  shall  be  placed  so  that  the  vertical 
distance  between  them  shall  not  be  less  than  six  feet  and  more 
than  ten  feet,  and  so  that  the  horizontal  distance  between  them, 
measured  in  a  line  with  the  keel  of  the  vessel,  shall  not  be  less 
than  five  feet  and  not  more  than  ten  feet.  The  lower  of  these 
two  lights  shall  be  the  more  forward,  and  both  of  them  shall  be  of 
such  a  character  and  contained  in  lanterns  of  such  construction  as 
to  show  all  around  the  horizon,  on  a  dark  night  with  a  clear  at- 
mosphere, for  a  distance  of  not  less  than  three  miles. 

(c)  All  vessels  when  trawling,  dredging,  or  fishing  with  any  kind 
of  drag-nets,  shall  exhibit,  from  some  part  of  the  vessel  where  they 
can  be  best  seen,  two  lights.  One  of  these  lights  shall  be  red,  and 
the  other  shall  be  white.  The  red  light  shall  be  above  the  white 
light,  and  shall  be  at  a  vertical  distance  from  it  of  not  less  than 
six  feet  and  not  more  than  twelve  feet ;  and  the  horizontal  dis- 
tance between  them,  if  any,  shall  not  be  more  than  ten  feet. 
These  two  lights  shall  be  of  such  a  character  and  contained  in 
lanterns  of  such  construction  as  to  be  visible  all  around  the  hori- 
zon, on  a  dark  night  with  a  clear  atmosphere,  the  white  light  to  a 
distance  of  not  less  than  three  miles,  and  the  red  light  of  not  less 
than  two  miles. 

(d)  A  vessel  employed  in  line  fishing,  with  her  lines  out,  shall 
carry  the  same  lights  as  a  vessel  engaged  in  fishing  with  drift- 
nets. 

(e)  If  a  vessel,  when  fishing  with  a  trawl,  dredge,  or  any  kind 
of  drag-net,  becomes  stationary  in  consequence  of  her  gear  getting 
fast  to  a  rock  or  other  obstruction,  she  shall  show  the  light  and 
make  the  fog  signal  for  a  vessel  at  anchor. 

(/)  Fishing  vessels  may  at  any  time  use  a  flare-up  in  addition 
to  the  lights  which  they  are  by  this  article  required  to  carry  and 
show.  All  flare-up  lights  exhibited  by  a  vessel  when  trawling, 
dredging,  or  fishing  with  any  kind  of  drag-net,  shall  be  shown  at 
the  after-part  of  the  vessel,  excepting,  if  that  vessel  is  hanging  by 
the  stern  to  her  trawl,  dredge,  or  drag-net,  they  shall  be  exhib- 
ited from  the  bow. 

(g)  Every  fishing  vessel,  when  at  anchor  between  sunset  and 
sunrise,  shall  exhibit  a  white  light,  visible  all  around  the  horizon 
at  a  distance  of  at  least  one  mile. 

(h)  In  a  fog  a  drift-net  vessel  attached  to  her  nets,  and  a  vessel 
when  trawling,  dredging,  or  fishing  with  any  kind  of  drag-net, 
and  a  vessel  employed  in  line  fishing  with  her  lines  out,  shall,  at 


662  The  Naval   Constructor 


intervals  of  not  more  than  two  minutes,  make  a  blast  with  her  fog- 
horn and  ring  her  bell  alternately. 

Lights  for  an  Overtaken  Vessel.  —  A  vessel  which  is  being 
overtaken  by  another  shall  show  from  her  stern  to  such  last-men- 
tioned vessel  a  white  light  or  flare-up  light. 

The  white  light  required  to  be  shown  by  this  article  may  be 
fixed  and  carried  in  a  lantern,  but  in  such  case  the  lantern  shall 
be  so  constructed,  fitted,  and  screened  that  it  shall  throw  an  un- 
broken light  over  an  arc  of  the  horizon  of  twenty  points  of  the 
compass ;  namely,  for  six  points  from  right  aft  on  each  side  of  the 
vessel,  so  as  to  be  visible  at  a  distance  of  at  least  one  mile.  Such 
light  shall  be  carried  as  nearly  as  practicable  on  the  same  level  as 
the  side-lights. 

Anchor  Lights.  — A  vessel  under  150  feet  in  length,  when  at 
anchor,  shall  carry  forward,  where  it  can  best  be  seen,  but  at  a 
height  not  exceeding  twenty  feet  above  the  hull,  a  white  light,  in 
a  lantern  so  constructed  as  to  show  a  clear,  uniform,  and  unbroken 
light  visible  all  around  the  horizon  at  a  distance  of  at  least  one 
mile. 

A  vessel  of  150  feet  or  upwards  in  length,  when  at  anchor,  shall 
carry  in  the  forward  part  of  the  vessel,  at  a  height  of  not  less  than 
twenty  feet  and  not  exceeding  forty  feet  above  the  hull,  one  such 
light,  and  at  or  near  the  stern  of  the  vessel,  and  at  such  a  height 
that  it  shall  be  not  less  than  fifteen  feet  lower  than  the  forward 
light,  another  such  light. 

The  length  of  a  vessel  shall  be  deemed  to  be  the  length  appear- 
ing in  her  certificate  of  registry. 

A  vessel  aground  in  or  near  a  fairway  shall  carry  the  above 
light  or  lights  and  the  two  red  lights  prescribed  by  Article  4  (a). 


UNITED    STATES   INLAND   RULES* 

Steam-Vessels'  Masthead  Lights. — A  steam-vessel  when 
under  way  shall  carry  (a)  on  or  in  front  of  the  foremast,  or,  if  a  j 
vessel  without  a  foremast,  then  in  the  fore  part  of  the  vessel,  a 
bright  white  light  so  constructed  as  to  show  an  unbroken  light 
over  an  arc  of  the  horizon  of  twenty  points  of  the  compass,  so 
fixed  as  to  throw  the  light  ten  points  on  each  side  of  the  vessel,  — 
namely,  from  right  ahead  to  two  points  abaft  the  beam  on  either 
side,  and  of  such  a  character  as  to  be  visible  at  a  distance  of  at 
least  five  miles.  , 

*  For  all  vessels  navigating  harbors,  rivers  and  inland  waters  of  the 
United  States,  except  the  Great  Lakes. 


Towing  Lights  663 

Steam-Vessels'  Side-Lights.  —  (b)  On  the  starboard  side  a 
green  light  so  constructed  as  to  show  an  unbroken  light  over  an 
arc  of  the  horizon  of  ten  points  of  the  compass,  so  fixed  as  to 
throw  the  light  from  right  ahead  to  two  points  abaft  the  beam  on 
the  starboard  side,  and  of  such  character  as  to  be  visible  at  a  dis- 
tance of  at  least  two  miles. 

(c)  On  the  port  side  a  red  light  so  constructed  as  to  show  an  un- 
broken light  over  an  arc  of  the  horizon  of  ten  points  of  the  com- 
pass, so  fixed  as  to  throw  the  light  from  right  ahead  to  two  points 
abaft  the  beam  on  the  port  side,  and  of  such  a  character  as  to  be 
visible  at  a  distance  of  at  least  two  miles.     (See  Fig.  286.) 

(d)  The  said  green  and  red  side-lights  shall  be  fitted  with  in- 
board screens  projecting  at  least  three  feet  forward  from  the  light, 
so  as  to  prevent  these  lights  from  being  seen  across  the  bow. 

Steam-Vessels'  Range-Lights.  —  (e)  A  sea-going  steam-ves- 
sel when  under  way  may  carry  an  additional  white  light  similar  in 
construction  to  the  light  mentioned  in  subdivision  (a).  These  two 
lights  shall  be  so  placed  in  line  with  the  keel  that  one  shall  be  at 
least  fifteen  feet  higher  than  the  other,  and  in  such  a  position 
with  reference  to  each  other  that  the  lower  light  shall  be  forward 
of  the  upper  one.  The  vertical  distance  between  these  lights  shall 
be  less  than  the  horizontal  distance. 

(/)  All  steam-vessels  (excepting  sea-going  vessels  and  ferry- 
boats) shall  carry  in  addition  to  green  and  red  lights  required  by 
Article  2  (b)  (c),  and  screens  as  required  by  Article  2  (d),  a  central 
range  of  two  "white  lights,  the  after  light  being  carried  at  an  eleva- 
tion at  least  fifteen  feet  above  the  light  at  the  head  of  the  vessel. 
The  head-light  shall  be  so  constructed  as  to  show  an  unbroken 
light  through  twenty  points  of  the  compass, — namely,  from  right 
ahead  to  two  points  abaft  the  beam  on  either  side  of  the  vessel, 
and  the  after  light  so  as  to  show  all  around  the  horizon. 

Steam-Vessels  -when  Towing.  —  A  steam-vessel  when  tow- 
ing another  vessel  shall,  in  addition  to  her  side-lights,  carry  two 
bright  white  lights  in  a  vertical  line  one  over  the  other,  not  less 
than  three  feet  apart ;  and  when  towing  more  than  one  vessel 
shall  carry  an  additional  bright  white  light  three  feet  above  or 
below  such  lights,  if  the  length  of  the  tow  measuring  from  the 
stern  of  the  towing  vessel  to  the  stern  of  the  last  vessel  towed  ex- 
ceeds six  hundred  feet.  Each  of  these  lights  shall  be  of  the  same 
construction  and  character,  and  shall  be  carried  in  the  same  posi- 
tion as  the  white  light  mentioned  in  Article  2  (a),  or  the  after 
range-light  mentioned  in  Article  2  (/). 

Such  steam-vessels  may  carry  a  small  white  light  abaft  the  fun- 
nel or  aftermast  for  the  vessel  towed  to  steer  by,  but  such  light 
shall  not  be  visible  forward  of  the  beam. 


664  The  Naval   Constructor 


Lights  for  Sailing-Vessels  and  Vessels  in  Tow.  —  A  sail- 
ing-vessel under  way  or  being  towed  shall  carry  the  same  lights 
as  are  prescribed  by  Article  2  for  a  steam- vessel  under  way,  with 
the  exception  of  the  white  lights  mentioned  therein,  which  they 
shall  never  carry. 

Lights  for  Ferry-Boats,  Barges,  and  Canal-Boats  in 
Tow.  —  The  supervising  inspectors  of  steam-vessels  and  the 
Supervising  Inspector-General  shall  establish  such  rules  to  be 
observed  by  steam-vessels  in  passing  each  other,  and  as  to  the 
lights  to  be  carried  by  ferry-boats  and  by  barges  and  canal-boats 
when  in  tow  of  steam-vessels,  not  inconsistent  with  the  provisions 
of  this  Act,  as  they  from  time  to  time  may  deem  necessary  for 
safety,  which  rules,  when  approved  by  the  Secretary  of  Commerce 
and  Labor,  are  hereby  declared  special  rules  duly  made  by  local 
authority,  as  provided  for  in  Article  30  of  Chapter  802  of  the  Laws 
of  1890.  Two  printed  copies  of  such  rules  shall  be  furnished  to 
such  ferry-boats  and  steam-vessels,  which  rules  shall  be  kept 
posted  up  in  conspicuous  places  in  such  vessels. 

Lights  for  Small  Vessels.  —  Whenever,  as  in  the  case  of  ves- 
sels of  less  than  ten  gross  tons  underway  during  bad  weather,  the 
green  and  red  side-lights  cannot  be  fixed,  these  lights  shall  be 
kept  at  hand,  lighted  and  ready  for  use  ;  and  shall,  on  the  ap- 
proach of  or  to  other  vessels,  be  exhibited  on  their  respective  sides 
in  sufficient  time  to  prevent  collision,  in  such  manner  as  to  make 
them  most  visible,  and  so  that  the  green  light  shall  not  be  seen  on 
the  port  side,  nor  the  red  light  on  the  starboard  side,  nor,  if  prac- 
ticable, more  than  two  points  abaft  the  beam  on  their  respective 
sides.  To  make  the  use  of  these  portable  lights  more  certain  and 
easy,  the  lanterns  containing  them  shall  each  be  painted  outside 
with  the  color  of  the  light  they  respectively  contain,  and  shall  be 
provided  with  proper  screens. 

Rowing  boats,  whether  under  oars  or  sail,  shall  have  ready  at 
hand  a  lantern  showing  a  white  light,  which  shall  be  temporarily 
exhibited  in  sufficient  time  to  prevent  collision. 

Lights  for  Pilot  Vessels.  —  Pilot  vessels,  when  engaged  on 
their  stations  on  pilotage  duty,  shall  not  show  the  lights  required 
by  other  vessels,  but  shall  carry  a  white  light  at  the  masthead, 
visible  all  around  the  horizon,  and  shall  also  exhibit  a  flare-up 
light  or  flare-up  lights  at  short  intervals,  which  shall  never  exceed 
fifteen  minutes. 

On  the  near  approach  of  or  to  other  vessels  they  shall  have 
their  side-lights  lighted,  ready  for  use,  and  shall  flash  or  show  them 
at  short  intervals,  to  indicate  the  direction  in  which  they  are  head- 


Rafts  and  Craft  not  Provided  for       665 


ing ;  but  the  green  light  shall  not  be  shown  on  the  port  side,  nor  the 
red  light  on  the  starboard  side. 

A  pilot  vessel  of  such  a  class  as  to  be  obliged  to  go  alongside  of 
a  vessel  to  put  a  pilot  on  board,  may  show  the  white  light  instead 
of  carrying  it  at  the  masthead,  and  may,  instead  of  the  colored  lights 
above  mentioned,  have  at  hand,  ready  for  use,  a  lantern  with  green 
glass  on  the  one  side  and  red  glass  on  the  other,  to  be  used  as  pre- 
scribed above. 

Pilot  vessels,  when  not  engaged  on  their  station  on  pilotage 
duty,  shall  carry  lights  similar  to  those  of  other  vessels  of  their 
tonnage. 

A  steam  pilot  vessel  when  engaged  on  her  station  on  pilotage 
duty  and  in  waters  of  the  United  States,  and  not  at  anchor,  shall, 
in  addition  to  the  lights  required  for  all  pilot  boats,  carry  at  a  dis- 
tance of  eight  feet  below  her  white  masthead  light  a  red  light,  visi- 
ble all  around  the  horizon,  and  of  such  a  character  as  to  be  visible 
on  a  dark  night  with  a  clear  atmosphere  at  a  distance  of  at  least 
two  miles,  and  also  the  colored  side-lights  required  to  be  carried 
by  vessels  when  under  way. 

When  engaged  on  her  station  on  pilotage  duty  and  in  waters  of 
the  United  States,  and  at  anchor,  she  shall  carry,  in  addition  to 
the  lights  required  for  all  pilot  boats,  the  red  light  above  men- 
tioned, but  not  the  colored  side-lights. 

When  not  engaged  on  her  station  on  pilotage  duty,  she  shall 
carry  the  same  lights  as  other  steam-vessels. 

Lights,  etc.,  of  Fishing  Vessels.  —  Fishing  vessels  of  less 
than  ten  gross  tons,  when  under  way  and  not  having  their  nets, 
trawls,  dredges,  or  lines  in  the  water,  shall  not  be  obliged  to  carry 
the  colored  side-lights  ;  but  every  such  vessel  shall,  in  lieu  thereof, 
have  ready  at  hand  a  lantern  with  a  green  glass  on  one  side  and  a 
red  glass  on  the  other  side,  and  on  approaching  to  or  being  ap- 
proached by  another  vessel,  such  lantern  shall  be  exhibited  in  siif- 
ficient  time  to  prevent  collision,  so  that  the  green  light  shall  not 
be  seen  on  the  port  side,  nor  the  red  light  on  the  starboard  side. 

All  fishing  vessels  and  fishing  boats  of  ten  gross  tons  or  upward, 
when  under  way  and  when  not  having  their  nets,  trawls,  dredges, 
or  lines  in  the  water,  shall  carry  and  show  the  same  lights  as 
other  vessels  under  way. 

All  vessels  when  trawling,  dredging,  or  fishing  with  any  kind  of 
drag-nets  or  lines,  shall  exhibit,  from  some  part  of  the  vessel 
where  they  can  be  best  seen,  two  lights.  One  of  these  lights  shall 
be  red,  and  the  other  shall  be  white.  The  red  light  shall  be  above 
the  white  light,  and  shall  be  at  a  vertical  distance  from  it  of  not 
less  than  six  feet  and  not  more  than  twelve  feet ;  and  the  horizon- 
tal distance  between  them,  if  any,  shall  not  be  more  than  ten  feet. 


666  The  Naval  Constructor 

These  two  lights  shall  be  of  such  a  character  and  contained  in  lan- 
terns of  such  construction  as  to  be  visible  all  around  the  horizon, 
the  white  light  at  a  distance  of  not  less  than  three  miles,  and  the 
red  light  not  less  than  two  miles. 

Lights  for  Rafts,  or  Other  Craft,  not  Provided  for. — 

Rafts,  or  other  water  craft,  not  herein  provided  for,  navigating  by 
hand  power,  horse  power,  or  by  the  current  of  the  river,  shall 
carry  one  or  more  good  lights,  which  shall  be  placed  in  such  man- 
ner as  shall  be  prescribed  by  the  Board  of  Supervising  Inspectors 
of  Steam- Vessels. 

Lights  for  an  Overtaken  Vessel.  —  A  vessel  which  is  being 
overtaken  by  another,  except  a  steam-vessel  with  an  after  range- 
light  showing  all  around  the  horizon,  shall  throw  from  her  stern 
to  such  last-mentioned  vessel  a  white  or  a  flare-up  light. 

Anchor  Lights.  —  A  vessel  under  150  feet  in  length,  when  at 
anchor,  shall  carry  forward,  where  it  can  be  best  seen,  but  at  a 
height  not  exceeding  twenty  feet  above  the  hull,  a  white  light  in  a 
lantern  so  constructed  as  to  show  a  clear,  uniform,  and  unbroken 
light  visible  all  around  the  horizon  at  a  distance  of  at  least  one 
mile. 

A  vessel  of  150  feet  or  upwards  in  length,  when  at  anchor,  shall 
carry  in  the  forward  part  of  the  vessel,  at  a  height  of  not  less  than 
twenty  feet  and  not  exceeding  forty  feet  above  the  hull,  one  such 
light,  and  at  or  near  the  stern  of  the  vessel,  and  at  such  a  height 
that  it  shall  not  be  less  than  fifteen  feet  lower  than  the  forward 
light,  another  such  light. 

The  length  of  a  vessel  shall  be  deemed  to  be  the  length  appear- 
ing in  her  certificate  of  registry. 

Special  Signals.  —  Every  vessel  may,  if  necessary,  in  order  to 
attract  attention,  in  addition  to  the  lights  which  she  is  by  these 
rules  required  to  carry,  show  a  flare-up  light,  or  use  a  detonating 
signal  that  cannot  be  mistaken  for  a  distress  signal. 

Naval  Lights  and  Recognition  Signals.  —  Nothing  in  these 
rules  shall  interfere  with  the  operation  of  any  special  rules  made 
by  the  Government  of  any  nation  with  respect  to  additional  sta- 
tion and  signal  lights  for  two  or  more  ships  of  war  or  for  vessels 
sailing  under  convoy,  or  with  the  exhibition  of  recognition  signals 
adopted  by  ship  owners,  which  has  been  authorized  by  their  re- 
spective Governments  and  duly  registered  and  published. 

Steam- Vessels  under  Sail  by  Day.  — A  steam-vessel  pro- 
ceeding under  sail  only,  but  having  her  funnel  up,  may  carry  in 
daytime,  forward,  where  it  can  be  best  seen,  one  black  ball  or 
shape  two  feet  in  diameter. 


Tonnage 


667 


CHAPTER   VI. 


TONNAGE. 

Tonnage  is  a  term  used  to  define  the  hundredth  part  of  the 
cubic  capacity  of  the  combined  space  enclosed  by  the  holds  and 
erections  of  vessels  after  making  certain  restrictions  and  deduc- 
tions. When  measured  below  the  upper  deck,  i.e.,  the  internal 
capacity  of  the  boat  from  stem  to  stern,  it  is  known  as  under 
deck  tonnage  ;  when  forecastle,  poop,  bridge  house,  deck  houses, 
hatches,  etc.,  are  added  to  the  foregoing,  it  is  called  gross  ton- 
nage, which  in  turn  becomes  the  net  register  tonnage  after 
the  legal  allowances  for  the  machinery  spaces,  crew  space,  and 
any  rooms  used  for  the  ship's  use  proper,  as  carpenter  shop, 
bo'sn's  store,  steering  gear  house,  chain  locker,  officers'  w.c's., 
etc.,  have  been  deducted. 


Tonnage  Leirgth 


Pig.  365. 

The  rules  for  computing  tonnage,  and  the  deductions  allowed, 
are  practically  the  same  in  the  legal  enactments  of  all  the  princi- 
pal maritime  nations,  although  there  is  a  slight  difference  in  the 
amount  of  the  deduction  for  propelling  power  in  some  of  them. 

All  dimensions  should  be  measured  in  feet  and  decimals  of  a 
foot,  not  to  exceed  two  places,  unless  in  the  case  of  the  one-third 
of  the  common  interval,  when  three  decimal  places  should  be 
worked  to. 

Tonnage  Deck.  —  The  tonnage  deck  is  the  upper  deck  in 
all  ships  which  have  less  than  three  decks,  and  the  second  deck 
from  below  in  all  other  ships. 


668 


The  Naval  Constructor 


SPECIMEN    SCHEDULE   FOR 


Ship's  Name. 

Length,  112.75  ft,  -=-6=  18.792  ft.,  the  Common  Interval  between  Areas. 

Depths  -J-  4,  the  Middle  Depth  being  Less  than  16  Ft. 

Area  1. 

Area  2. 

Area  3. 

Area  4. 

Area  5. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Depths. 

12.65 

12.3 

11.85 

11.4 

Common 

Interval 
between 

3.162 

3.075 

2.962 

2.85 

Breadths. 

—  — 

.     ■ 

■ 

5 

■ 

CO 

CO 

■ 

CO 

& 

co 

CO 

."9 

3.2 

•°  s 

p 

'O  « 

p 

•O  0> 

3 

2^ 

P 

1| 

P 

o  « 

*& 

2  J 

u 

1 

©fa 

■a 

o 

g3  0> 

1 

o 

1 

« 

oq 

Ph 

« 

Ph 

« 

Ph 

M 

Ph 

Ph 

Ph 

, 

1 

19.35 

19.35 

20.2 

20.2 

20.4 

20.4 

20.2 

20.2 

2 

4 

18.85 

75.4 

20.4 

81.6 

20.5 

82.0 

20.35 

81.4 

3 

2 

16.65 

33.3 

20.15 

40.3 

20.25 

40.5 

20.0 

40.0 

4 

4 

11.85 

47.4 

19.6 

78.4 

19.85 

79.4 

17.8 

71.2 

5 

1 

1.85 

1.85 

3.0 

3.0 

6.35 

6.35 

6.35 

6.35 

177.3 

223.5 

228.65 

219.15 

*i  of  Com- 
mon In- 

1.05* 
8865 

1.03 
6705 

.99 

.95 
109575 

205785 

terval 

17730 

22350 

205785 

197235 

Breadths. 

186.165 

230.205 

226.363 

208.192 

Area  1. 

Area  2. 

Area  3. 

Area  4. 

Area  5. 

Schedule  for  Tonnage  Calculations      669 


TONNAGE    CALCULATIONS. 


Cubic  Content 

and 

Register  Tonnage 


Tonnage  of  Poop  ok  Other 
Closed-in  Space. 


Break  of  Deck. 


Mean  Length,  32.15  Ft. 


Common  Interval  between 
Breadths,  16.075  Ft. 


Area  C. 


Feet. 
10.9 


-  i. 
2= 


19.10 
18.65 
14.95 
8.75 
1.0 


09 

ja 

0 

r3% 

"5 

Hi   0) 

o 

?>fc 

PM 

w 

19.1 

74.6 

29.9 

.35.0 

1.0 

159.6 
.91 


145.236 
Area  6. 


Area  7. 


Feet. 


O 


8 

.2 

3 

^  OCG 

g 

n 

l 

0 

4 

186.17 

2 

230.21 

4 

226.36 

2 

208.19 

4 

145.24 

1 

0 

^3 

- 


o 

744.68 
460.42 
905.44 
416.38 
580.96 
0 


5 

i. 

3 

a 

11 

2^ 

« 

i 

20.0 

4 

18.6 

1 

17.15 

20.0 
74.4 
17.15 


111.55 


£  of  com.  inter, 
betw.  breadths. 


ht.  of  break 
Cu.  ft.  1,195.82  -f  100  =  11.96  reg.  T 
3107.88 
6.26 


f  i  of  common  interval 
i     between  areas. 


621576 
1864728 


Area  7. 


19455.32  -f  100 
=  194.55  reg.  T.  under  deck. 
11.96  break  of  deck  as  above 
206.51  gross  tonnage. 


670  The  Naval  Constructor 


Length  for  Tonnage.  —  The  length  at  the  tonnage  deck  in 
all  cases  of  the  usual  sheer  is  to  be  taken  on  the  upper  surface  of 
the  deck  to  the  inside  of  the  stringer  angle  bar  at  stem  and  stern, 
the  length  so  obtained  being  subdivided  into  an  equal  number  of 
parts  as  under  :  — 

Subdivision  of  Tonnage  Length  per  British  Law. 

Class     I.    Length  of  50  feet  and  under,  4  equal  parts. 
Class    II.   Length  above  50  feet  to  120  feet,  into  6  equal 

parts. 
Class  III.    Length  above  120  feet  to  180  feet,  into  8  equal 

parts. 
Class  IV.   Length   above  180  feet  to  225  feet,  into  10 

equal  parts. 
Class    V.    Length  above  225  feet  and  upwards,  into  12 

equal  parts. 

Subdivision    of   Tonnage    Length   per  American 

Law. 

Class     I.    Length  of   50  feet  and  under,  into  6  equal 

parts. 
Class    II.    Length  above  50  feet  to  100  feet,  into  8  equal 

parts. 
Class  III.   Length  above  100  feet  to  150  feet,  into  10  equal 

parts. 
Class  IV.   Length  above   150  feet  to  200  feet,  into  12 

equal  parts. 
Class    V.   Length  above  200  feet  to  250  feet,  into  14  equal 

parts. 
Class  VI.    Length  above  250  feet,  into  16  equal  parts. 

The  stations  at  these  subdivisions  are  the  points  at  which  the 
areas  are  calculated,  and  are  numbered  from  forward  aft,  the 
foremost  being  numbered  one,  making  the  last  ordinate  in  each 
case  an  odd  number. 

Depths.  —  The  depths  are  taken  at  each  point  of  division  as 
above,  from  the  under  side  of  tonnage  deck  to  the  ceiling  at  inner 
edge  of  limber  strake,  deducting  therefrom  one-third  of  the  beam- 
camber  ;  the  depths  so  taken  are  to  be  divided  into  four  equal 
parts  if  the  midship  depth  does  not  exceed  16  feet,  otherwise  into 
six  equal  parts.    (See  Fig.  287.) 

Breadths.  — These  are  measured  off  at  each  point  of  the  verti- 
cal division  of  the  depth  as  described,  to  the  inner  edge  of  the 


Marking  of  Ship  671 


side  ceiling.  In  the  case  of  vessels  having  no  ceiling  or  sparring, 
the  breadths  must  be  taken  to  the  inner  edge  of  frame-bars. 

The  lower  breadth,  when  the  vessel  has  no  horizontal  flat  or 
floor,  is  limited  to  the  distance  between  the  two  limber  strakes, 
and  in  flat-floored  vessels  to  the  extent  of  the  horizontal  flatness. 

Where  the  ceiling  varies  in  thickness  on  the  sides,  as  in  crossing 
a  keelson  or  stringer,  or  at  dumping  pads,  the  average  thickness 
should  be  taken.     (See  Fig.  287.) 

Sections  for  Areas.  —  When  the  sections  have  been  prepared 
in  accordance  with  the  foregoing,  the'  half -breadths  may  be  meas- 
ured off  and  tabulated  in  the  manner  shown  in  the  accompanying 
table,  and  integrated  by  means  of  Simpson's  first  rule  to  deter- 
mine the  under-deck  tonnage. 

The  erections,  hatches,  and  shelter-deck,  'tween  decks  (if  any), 
may  now  be  calculated  in  detail,  and  added  to  the  under-deck 
tonnage  to  obtain  the  gross. 

Engine  Room  Deduction.  —  The  actual  space  enclosed  by 
the  engine  room  must  be  calculated,  and  the  percentage  it  bears  to 
the  gross  tonnage  determined  to  enable  the  allowance  conceded 
by  law  to  be  made.  Should  this  percentage  be  over  thirteen  and 
under  twenty,  an  allowance  of  thirty-two  per  cent  may  be  de- 
ducted from  the  gross  tonnage  in  computing  the  net  register,  or 
the  tonnage  on  which  a  ship's  dues  are  usually  paid. 

Should,  however,  the  actual  engine  room  not  exceed  thirteen 
per  cent  of  the  gross  tonnage,  the  allowance  would  then  be  the 
actual  space  plus  §  of  same. 

It  should  be  noted  that  the  gross  tonnage  is  the  same  whether 
the  vessel  is  a  steamer  or  a  sailing  ship. 

Tonnage  Deductions.  —  All  spaces  which  have  been  meas- 
ured and  deducted  from  the  gross  tonnage,  as  officers'  rooms, 
crew's  forecastle,  chain-locker,  chart-house,  etc.,  mustbe  properly 
marked  over  the  door  by  having  the  certification  cut  in,  and  also 
inside,  on  a  beam  or  other  conspicuous  place. 

MARKING  OP  SHIP. 

Name.  —  The  vessel's  name  must  be  marked  on  each  bow,  and 
the  name  and  port  of  registry  on  the  stern,  on  a  dark  ground,  in 
white  or  yellow  letters,  or  on  a  light  ground  in  black  letters.  The 
letters  should  preferably  be  black,  and  not  less  than  4  inches 
long. 

In  addition,  ships  of  American  registry  must  have  their  name 
cut  in  large  name  boards  fitted  on  each  side  of  top  of  pilot  .house, 
with  letters  not  less  than  6  inches  high. 


672  The  Naval  Constructor 


Official  Number  and  Tonnage.  —  The  official  number  and 
the  net  registered  tonnage  must  be  cut  in  on  the  main  beam  or  the 
'thwartship  coaming  of  main  hatch. 

Draught  Marks.  —  A  scale  of  feet  denoting  the  draught  of 
water  must  be  cut  in  on  each  side  of  the  stem  and  stern-post  from 
one  foot  below  light  line  to  about  two  feet  above  deep  load 
draught.  These  should  be  in  Roman  letters  or  figures,  6  inches 
long,  the  lower  line  of  such  letters  or  figures  to  coincide  with  the 
draught  line  indicated.  The  figures,  after  being  cut  in,  should  be 
painted  white  or  yellow  on  a  dark  ground. 

Space  for  Seamen.  —  In  arranging  crew's  quarters,  care  must 
be  taken  that  a  minimum  capacity  of  72  cubic  feet  is  allowed  for 
each  seaman,  and  a  clear  floor  space  of  not  less  than  twelve 
square  feet. 

NEW   YORK  YACHT   CLUB   RACING   RULES. 

Rating  Formula.  —  Yachts  shall  be  rated  for  classification 
and  time  allowance  according  to  the  following  formula :  — 

. f  Length  multiplied  by  square 

Rating  measurement  =  ^-^  J      «**  of  sail  area  divided  by 


5  -\/D    1 


placement. 

The  result  is  the  measurement  for  classification  and  time  allow- 
ance. 

Length.  —  The  mean  of  the  length  over  all,  exclusive  of  bul- 
warks and  rail,  and  of  the  length  on  the  load  water  plane,  both 
measurements  to  be  taken  parallel  to  the  middle  vertical  plane, 
and  at  a  distance  from  it  equal  to  one-quarter  (^)  of  the  greatest 
beam  at  the  load  water  line. 

In  case  the  width  of  the  stern  on  deck  exceeds  one-half  (£)  the 
greatest  beam  at  the  load  water  line,  the  measurement  for  the 
length  over  all  shall  be  taken  to  a  point  abaft  the  stern,  where 
the  continuation  of  the  fair  line  of  the  top  edge  of  the  plank- 
sheer  would  intersect  the  quarter  beam  line. 

Sail  Area.  —  Sail  area  to  be  obtained  as  follows,  and  the 
square  root  of  this  area  to  be  the  yJSA  in  formula  :  — 

Mainsail.  —  A.  Measured  from  the  top  of  the  boom  (under 
the  pin  for  outhaul  shackle  on  traveller,  or  clew  slide,  when 
hauled  chock  out)  to  the  gaff  under  the  pin  of  the  sheave  of  the 
topsail  sheet,  provided  the  peak  cringle  of  the  mainsail  does  not 
extend  beyond  the  pin  ;  in  the  case  of  the  yacht  having  no  top- 


Measurement  of  Sails 


673 


sail,  or  of  the  peak  cringle  extending  beyond  the  pin  of  the 
topsail-sheet  sheave,  the  measurement  to  be  taken  to  the  peak 
lacing-hole. 

B.  Perpendicular  to  A,  measured  to  underside  of  gaff  close  in 
to  the  mast. 

C.  Measured  from  top  of  boom  over  the  pin  of  the  sheave  or 
outhaul  or  end  of  clew  slide  to  underside  of  gaff  close  in  to  the 
mast. 


Fig.  366. 

D.  Perpendicular  to  C,  measured  in  to  the  mast,  in  a  line  with 
the  top  of  the  boom,  or  to  tack  cringle  of  mainsail,  if  below  top 
of  boom. 

Club  Topsail. — E.  Measured  from  upper  side  of  gaff  close 
in  to  the  mast  to  pin  of  sheave  for  topsail  sheet,  or  to  lacing-hole 
in  club. 

F.  Perpendicular  to  E,  measured  to  lower  lacing-hole  in  sprit. 

G.  From  lacing-hole  to  lacing-hole  in  sprit. 

H.  Perpendicular  to  (?,  measured  to  pin  of  sheave  for  topsail 
sheet  in  gaff ;  or  to  upper  lacing-hole  in  club. 

Jib  Header.  —  K.  Measured  from  top  of  gaff  close  in  to  mast 
to  pin  of  halyard  sheave  in  topmast. 

L.  Perpendicular  to  K,  measured  to  pin  of  topsail  sheet  sheave 
in  gaff  j  or  to  upper  lacing-hole  in  club. 


674  The  Naval  Constructor 


Lugs  ail  —  To  be  measured  as  mainsail,  except  as  follows  :  — 
A.    Upper  end  measured  to  peak  lacing-hole  in  yard. 
B  and  C.   Forward  end  measured  to  lower  lacing-hole  in  yard. 
D.   Lower  end  measured  to  tack  cringle  of  mainsail,  if  below 
top  of  boom,  or  forward  of  mast. 

Headsails.  —  I.  The  perpendicular  I  to  be  measured  from  the 
deck,  at  the  foreside  of  the  mast  to  where  the  line  of  the  luff  of 
the  foremost  headsail,  or  of  the  spinnaker  halyard,  as  the  case 
may  be,  when  extended,  cuts  such  perpendicular.  In  the  case  of 
a  schooner  the  perpendicular  I  shall  be  measured  upon  the  fore- 
mast, unless  she  has  a  main  spinnaker,  the  height  of  which  exceeds 
the  perpendicular  upon  the  foremast,  in  which  case  the  excess  shall 
be  added  to  the  perpendicular  I. 

J.  The  base  J  to  be  measured  from  the  foreside  of  the  mast  to 
where  the  line  of  the  luff  of  the  foremost  headsail,  when  extended, 
cuts  the  bowsprit,  other  spar,  hull,  etc.,  as  the  case  may  be.  In 
all  cases,  if  the  distance  from  the  centre  fore-and-aft  line  of  the 
mast  to  the  outer  end  of  the  spinnaker  boom  exceeds  the  distance 
from  the  foreside  of  the  mast  to  the  bowsprit  end  (where  cut  by 
the  line  of  the  luff  of  the  foremost  headsail)  the  excess  shall  be 
added  to  the  base  of  the  fore  triangle. 

In  the  case  of  a  schooner,  the  base  J  shall  be  measured  from 
the  foremast,  but  if  the  main  or  longest  spinnaker  boom  exceeds 
the  before-mentioned  distance,  the  excess  shall  be  added  to  the 
base  J. 

In  the  case  of  a  yacht  having  no  headsail,  but  carrying  a  spin- 
naker, the  area  for  headsail  shall  be  computed  from  the  length  of 
spinnaker  boom,  and  the  height  from  deck  to  where  the  line  of 
the  halyard  of  the  spinnaker  when  extended  cuts  the  mast. 

A  spinnaker  may  have  a  headstick,  or  board,  not  longer  than 
one-twentieth  the  length  of  the  spinnaker  boom,  but  not  a  foot- 
yard,  or  more  than  one  sheet,  or  any  other  contrivance  for  extend- 
ing the  sail  to  other  than  a  triangular  shape. 

In  the  case  of  a  yacht  carrying  a  square  sail,  or  square  topsail, 
or  raffee  (together  or  separately),  the  actual  area  of  the  same  shall 
be  computed  ;  and  if  such  area  exceed  the  area  of  the  fore  trian- 
gle, the  excess  shall  be  used  in  the  total  area  for  determining  the 
rating. 

Foresail  of  Schooners.  —  To  be  measured  as  mainsail,  except 
that  the  lower  end  of  A  is  to  be  taken  at  foreside  of  mainmast,  in 
a  line  with  main  boom  gooseneck. 

Directions  for  Measuring  Sails.  —  The  measurer  shall  take 
measurements  I  and  J  for  fore  triangle,  G  and  E  for  club  topsail, 
and  the  length  of  spinnaker  boom.     If  the  other  measurements 


Calculation  of  Sail  Areas  675 

are  supplied  by  the  sailmaker,  the  measurer  shall  check  them  by 
measuring  the  following  :  — 

Boom,  —  from  lower  end  of  A  to  lower  end  of  D. 

Gaff  or  lug  yard,  — from  upper  end  of  A  to  forward  end  of  B. 

Club  Topsail,  —  sheet  to  outer  lacing-hole. 

•In  cases  where  it  is  necessary  for  the  official  measurer  to  meas- 
ure the  sails,  he  shall  do  so  in  the  following  manner :  Take  the 
length  of  boom  from  mast  to  pin  of  sheave  for  outhaul,  and  length 
of  gaff  from  mast  to  pin  of  topsail  sheet  sheave  or  lacing-hole,  as 
the  case  may  require ;  then  hoist  the  sail  with  the  tack  fast  and 
set  the  peak  and  luff  up  taut,  and  let  go  the  topping  lifts  so  that 
the  weight  of  the  boom  coines  on  the  leach  of  the  sail.  With  a 
line  and  tape,  measure  the  leach  and  luff  and  the  diagonal  C.  For 
the  beadsail  measure  the  height  I  and  the  distance  J,  as  provided 
for  in  the  section  dealing  with  headsail.  For  topsail  the  sail 
should  be  hoisted  and  marked  in  a  line  with  the  gaff ;  then  low- 
ered and  the  other  dimensions  taken.  From  the  measurements  so 
taken  a  sail  plan  should  be  made  and  the  other  above-specified 
measurements  obtained  therefrom. 

CALCULATION   OP   SAIL   AREAS. 

Mainsail.  —  Multiply  A  by  B  and  C  by  D,  and  add  the  two 

products  together  and  divide  by  2. 

Yard  Topsail.  —  Multiply  E  by  F  and  G  by  H,  and  add  the 
two  products  together  and  divide  by  2. 

Jib  Header.  —  Multiply  K  by  L  and  divide  by  2. 

Headsails.  —  Multiply  I  by  J"  and  divide  by  2. 

Lugsails  and  Headsails. — No  deduction  is  to  be  made  from 
headsail  area  on  the  score  of  any  portion  of  the  lugsail  area  ahead 
of  the  mast. 

Sails  Bounded  by  Curved  Edges.  —  Any  increase  in  the 
area  of  sails  due  to  curved  edges,  extended  by  battens,  or  other- 
wise, beyond  the  line  between  the  points  for  measurement,  shall 
be  computed  as  follows  :  Multiply  the  base  E  by  two-thirds  of  the 
perpendicular  P. 

Displacement.  —  Z>.    Displacement  to  be  obtained  as  follows  : 

At  points  dividing  the  length  of  the  load  water  line  into  five 
equal  parts,  find  areas  of  immersed  cross  sections  in  square  feet ; 
from  the  areas  in  square  feet  obtained  and  load  water  line  length, 
find  approximate  displacement  in  cubic  feet,  which  will  be  the  L 
in  formula. 


676  The  Naval  Constructor 


Limit  of  L.W.L.  —  One  half  (£)  of  any  excess  of  L.W.L.  over 
one  hundred  and  fifteen  per  cent  (115%)  of  L  shall  be  added  to  the 
rating  measurement. 

The  L.W.L.  shall  be  the  distance  in  a  straight  line  between  the 
points  farthest  forward  and  farthest  aft,  where  the  hull,  exclusive 
of  the  rudder  post,  is  intersected  by  the  surface  of  the  water  when 
the  yacht  is  afloat,  in  racing  trim. 

Limit  of  Draught.  —  Limit  of  draught  in  feet  =.133  (rating 
measurement)  +  2.66. 

Any  excess  of  draught,  exclusive  of  centre-board,  as  per  above 
formula,  shall  be  multiplied  by  five  (5)  and  added  to  the  rating 
measurement. 

The  draught  of  any  vessel,  exclusive  of  centre-board,  shall  not 
exceed  eighteen  (18)  feet. 

Limit  of  Sail  Area.  — Any  excess  of  the  square  root  of  sail 
area  over  one  hundred  and  thirty-five  per  cent  (135%)  of  I  shall 
be  added  to  the  rating  measurement. 

All  measurements  of  hull  shall  be  taken  with  only  such  persons 
on  board  as  shall  be  required  by  the  measurer. 

All  measurements  specified  may  be  certified  to  by  the  designer, 
in  a  certificate  to  be  filed  with  the  measurer  of  the  club,  but  such 
certificate  must  be  accompanied  by  drawings,  showing  the  meas- 
urements taken,  and  the  true  line  of  flotation  of  the  vessel  when 
measured  in  racing  trim,  which  measurement  and  line  of  flotation 
must  be  verified  by  the  measurer,  before  any  certificate  of  meas- 
urement shall  be  accepted  by  the  secretary. 

If  from  any  peculiarity  in  the  build  of  a  yacht,  or  other  cause, 
the  measurer  shall  be  of  opinion  that  the  rule  will  not  rate  the 
yacht  fairly,  or  that  in  any  respect  she  does  not  comply  with  the 
requirements  of  these  rules,  he  shall  report  the  circumstances  to 
the  Regatta  Committee,  who,  with  the  measurer,  after  due 
inquiry,  shall  award  such  a  certificate  of  rating  as  they  may 
consider  equitable,  and  the  measurement  shall  be  deemed  incom- 
plete until  this  has  been  done. 

CLASSIFICATION. 

Schooners.  —  Class  A.   All  over  100  feet,  rating  measurement. 

Class  B.  Not  over  100  feet  and  over  80  feet,  rating  measure- 
ment. 

Class  C.  Not  over  80  feet  and  over  64  feet,  rating  measure- 
ment. 

Class  D.  Not  over  64  feet  and  over  51  feet,  rating  measurement. 

Class  E.  Not  over  51  feet,  rating  measurement. 


Ballast,  etc.  ^1 

Single-masted  Vessels  and  Yawls.  —  Class  F.  All  over 
100  feet,  rating  measurement. 

Class  G.  Not  over  100  feet  and  over  80  feet,  rating  measurement. 

Class  H.  Not  over  80  feet  and  over  64  feet,  rating  measure- 
ment. 

Class  I.  Not  over  64  feet  and  over  51  feet,  rating  measure- 
ment. 

Class  J.  Not  over  51  feet  and  over  40  feet,  rating  measure- 
ment. 

Class  K.   40  feet  and  under,  rating  measurement. 

Sails.  — Yachts  in  races  may  carry  the  following  sails  :  — 

Schooners.  —  Mainsail,  foresail,  fore  staysail,  jib,  flying-jib, 
jib-topsail,  fore  and  main  gaff  topsail,  maintopmast  staysail,  and 
spinnaker. 

Sloops  and  Cutters.  —  Mainsail,  fore  staysail,  jib,  flying- 
jib,  jib-topsail,  gaff  topsail,  and  spinnaker. 

Yawls.  —  Same  as  sloops  and  cutters,  with  mizen  and  mizen- 
staysail. 

Balloon  Sails. — Yachts  may  set  light  sails  over  working 
sails. 

Boats  and  Life-Buoys.  —  All  yachts  shall  carry  at  least  two 
serviceable  life-buoys  on  deck  ready  for  use. 

Classes  A  and  B  of  schooners,  and  F  and  G  of  single-masted 
vessels  and  yawls,  shall  carry  on  deck  a  serviceable  round-bottom 
boat,  not  less  than  14  feet  in  length  ;  and  classes  C  and  D  of 
schooners,  and  JET  and  I  of  single-masted  vessels  and  yawls,  a 
boat  as  above,  not  less  than  12  feet  in  length;  and  in  classes  E  of 
schooners,  and  J  and  K  of  single-masted  vessels  and  yawls,  a 
boat  as  above,  not  less  than  10  feet  in  length.  All  boats  to  have 
oars  and  rowlocks  or  tholepins  lashed  in. 

Bulkheads,  Ballast,  etc.  —  Floors  must  be  left  down  and 
bulkheads  and  doors  left  standing ;  water-tanks  kept  in  place, 
and  at  least  one  bower  anchor  and  cable  kept  on  board.  All 
yachts,  except  in  classes  A  of  schooners  and  G  of  single-masted 
vessels  and  yawls,  shall  keep  their  galley  fixtures  and  fittings  on 
board  and  in  their  proper  places.  Trimming  by  dead-weight  shall 
not  be  allowed  after  the  preparatory  signal.  Neither  ballast  nor 
water  shall  be  taken  in  or  discharged  after  9  p.m.  of  the  day 
before  a  race,  but  the  above  restriction  may  be  waived  as  to 
water,  only  by  permission. 

Crew.  —  The  number  of  men  permitted  on  a  yacht  during  a 
race  shall  not  exceed  that  given  by  the  following  table  :  — 


678  The  Naval  Constructor 


Classes  A  and  F.  One  man  for  every  250  square  feet  of  sail 
area,  or  fraction  thereof. 

Classes  B,  C,  Z),  E,  G,  H,  I,  J,  and  K.  One  man  for  every 
300  square  feet  of  sail  area,  or  fraction  thereof. 


BUILDERS'   OLD    MEASUREMENT   TONNAGE 

This  tonnage,  commonly   called   B.    O.   M.,  is  still  much  in 
vogue  with  yacht  builders,  but  obsolete  otherwise. 

B.O.M.=<L-^BX^, 
94 

where  L  is  the  length  of  vessel  measured  along  top  of  keel 
from  after  side  of  stern  post,  to  the  intersection  of  a  perpendicu- 
lar with  the'  fore  part  of  stem  under  the  bowsprit,  and  B  is  the 
extreme  breadth  to  outside  of  planking,  exclusive  of  doublings. 


THAMES   MEASUREMENT   TONNAGE. 

This  rule  was  formulated  by  the  Royal  Thames  Yacht  Club, 
and  is  much  used  for  the  measurement  of  yachts. 

TM~ 94 ' 

where  L  is  the  length  measured  in  a  straight  line  at  the  deck 
from  the  fore  part  of  stem  to  the  after  part  of  stern  post,  and  B 
is  the  extreme  breadth  to  outside  of  planking. 


Section  VI. 


WEIGHT  OF  A  CUBIC  FOOT  OF  SUBSTANCES. 

Name  of  Substances.  Pounds 

A. 

Acacia 44.4 

Alder 34.6 

Aluminum,  cast 160 

Aluminum,  sheet 168 

Aluminum,  bronze 478 

Alum 107 

Antimony ....  417 

Anthracite  coal,  broken,  cubic  foot  averages 54 

A  ton,  loose,  occupies  40-43  cubic  feet. 

Apple  wood 49.5 

Air      .     .' 0.08 

Ash  (American) 39 

Asphalte 156 

Asbestos  Board  |"  thick,  per  square  foot 65 

B. 

Barley 38 

Basalt 170 

Babbit,  white  brass 456 

Beech 43.8 

Bell,  metal 502.5 

Birch 33 

Bismuth 608 

Bitumastic  solution  per  gallon 9 

Bituminous  coal,  broken,  cubic  foot  averages      ....  49 
A  ton,  loose,  occupies  43-48  cubic  feet. 

Box  wood 62.5 

Brick,  best  pressed 150 

Brick,  common  hard 125 

Brick,  soft  inferior 100 

Brickwork,  pressed  brick 140 

Brickwork,  ordinary 112 

Brass,  common 525-530 

Brass,  wire 533 

Bronze 544 

679 


680  The  Naval  Constructor 


Name  of  Substances.  Pounds. 
C. 

Camphor 62 

Cedar,  American  red 30.8 

Cedar,  white 23 

Cement,  hydraulic,  ground,  loose,  American 56 

Cement,  hydraulic,  ground,  loose,  English,  Portland  .     .  90 

Cement  and  sand  (3  to  1) 130 

Cement,  hydraulic,  Louisville,  hushel  = 62 

Cement,  hydraulic,  Portland,    bushel  = 96 

Cement,  Roman 100 

Charcoal 183 

Cherry 42 

Chalk 183 

Chestnut 41 

Clay 119 

Clay,  in  lump,  loose 63 

Coral 168 

Cork 15.0 

Copper     . 554 

Coal,  bituminous,  solid 84 

Coal,  bituminous,  broken,  loose 49 

Coal,  bituminous,  heaped  bushel,  loose 74 

Coke,  loose,  of  good  coal 62 

Coke,  loose,  heaped  bushel 40 

Cypress 41 

D. 

Deals,  Riga 43 

E. 

Earth,  common  loam,  dry,  loose 76 

Earth,  common  loam,  dry,  moderately  rammed  ....  95 

Ebony 79.4 

Elder 43.4 

Elm,  English 35 

Emery 251 

Elm,  Canada 45 

F. 

Felspar 168 

Fir  (see  Red  Pine,  etc.) 31-41 

Flagging 168 

Flint 164 

Freestone 153 


Weight  of  a  Cubic  Foot  of  Substances  681 

Name  of  Substances.  Pounds. 
G 

Granite    .'....' 164 

Graphite 137 

Glass,  flint 192 

Glass,  crown 157 

Glass,  plate •     .     .     .  172 

Gold,  pure  cast 1,200 

Gold,  standard 1,106 

Gneiss 168 

Greenheart 62.5 

Gunmetal 534 

Gum  wood 37 

Gypsum 143 

Gypsum,  ground,  bushel  = 70 

H. 

Hay  (compact,  old) 8 

Hawthorn 56.8 

Hazel 53.7 

Hemlock 25 

Hornbeam 47.4 

I. 

Ice 58.7 

India-rubber 58 

Iron,  cast  (average) 450 

Iron,  wrought,  purest 485 

Iron,  wrought,  average  . 480 

Ironwood 71 

Ivory 114 

J. 

Jackwood 42 

L. 

Laburnum 67.4 

Larch 31.0 

Lancewood 42.1 

Lead,  cast 708.5 

Lead,  sheet 711.5 

Lignum-vitse 83.2 

Lime,  quick,  ground,  loose,  or  in  small  lumps    ....  53 

Lime,  quick,  ground,  loose,  thoroughly  shaken  ....  75 

Lime,  quick,  ground,  loose,  struck  bushel 66 

Limestones .  168 


682  The  Naval  Constructor 


Name  of  Substances.  Pounds 

Limestones,  loose,  in  irregular  fragments 96 

Lime,  loose,  bushel  = 70 

Lime,  well  shaken,  bushel  = 80 

Lime  wood  .     .          35 

Linoleum,  \"  thick  (incl.  cement)  per  sq.  ft 1.5 

M. 

Mahogany,  Spanish 53 

Mahogany,  Honduras 35 

Marble 170 

Maple 49 

Masonry,  of  granite  or  limestone,  well  dressed   ....  165 

Masonry,  of  dry  rubble,  well  scabbled 138 

Masonry,  of  sandstone,  well  dressed 144 

Mercury,  fluid       849 

Mercury,  solid 977 

Mica 183 

Mortar,  hardened 103 

Muntz  metal 511 

N. 

Nickel  (hammered) 541 

Nickel  (cast) 516 

Nitric  Acid 79.4 

O. 

Oak,  British 58 

Oak,  Riga 43 

Oak  (American,  red,  black  or  yellow) 45 

Oak  (American,  white) 50 

Oil  (linseed) 58 

Oil  (olive) 57 

Oil  (petroleum) 48-58 

Oil  (whale) 58 

Ore  (red  iron) .327 

Ore  (brown) 245 

Ore  (Clydesdale) 191 

Oregon  Pine  (Douglas  Spruce) 32 

P. 

Paper  (building)  per  roll  of  400  sq.  ft 52 

Petroleum,  standard  refined    .          ........  57.75 

Petroleum,  Texas 58. 

Phosphor  Bronze       537 

Pitch 69 


Weight  of  a  Cubic  Foot  of  Substances     683 

Name  of  Substances.  Pounds. 

Pitch  pine  (U.  S.  yellow  pine) 41 

Pine  (long  leafed  Georgia  yellow  pine) 38 

Platinum 1,414 

Plumbago 140 

Poplar 32 

Pewter 703 

Q. 

Quartz 163-169 

S. 

Salt,  coarse 45 

Sand,  of  pure  quartz,  dry,  loose   ...  ....     90-106 

Sand,  well  shaken 99-117 

Sand,  perfectly  wet 120-140 

Sandstones  (fit  for  building) 151 

Satinwood 60 

Snow,  freshly  fallen 5-12 

Snow,  moistened  and  compacted  by  rain 15-50 

Shingle .     .        88 

Silver  (standard) 644 

Slate , 178 

Spruce,  Northern 26 

Spruce,  Southern 30 

Steel    .     . 490 

Steel,  cast 493 

Sycamore 36.8 

T. 

Tallow 59 

Tar 63 

Talc     .    . .  168 

Teak  Burmese 46 

Tile,  common 113 

Tiling,  inlaid  rubber,  per  sq.  ft 2 

Tiling,  vitrified  brick,  1^  thick,  per  sq.  ft 9 

Tiling,  white,  ^  in.  thick,  per  sq.  ft 5 

Tin 462 

Type  metal 653 

Trap 170 

W. 

Walnut,  black ,        38 

Water,  pure  rain  or  distilled,  at  60°  F 62£ 


684  The  Naval  Constructor 

Name  of  Substances.  Pounds. 

Water,  salt «64 

Wheat 48 

Willow 25.3 

White  Pine  (called  yellow  pine  in  England) 24 

White  metal,  Babbitt 456 

Y. 
Yew o     .     .     .        50.3 

Z. 

Zinc,  rolled 449 

Zinc,  cast 437 


WEIGHT   OF   SAIL   CANVAS. 


Canvas,  No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

Lbs.  per  Sq.  Ft. 

.205 

.197 

.184 

.171 

.154 

.141 

.128 

.113 

.104 

Oil  Fuel  Chart 


685 


OIL   FUEL   CHART. 


Xk?a-i3d(qT0irZZ)suoi 


uox usd  (|*3-Zfr)?pjji?g 


Fiq.  367. 


686 


The   Naval   Constructor 


DATA   FOR  FUEL   OIL. 


Specific 
Gravity. 

°Bb. 

Weight 
in  Lbs. 
per  Gal. 

Weight 
in  Lbs. 
per  Bbl. 

Weight 
in  Lbs. 

per 
Cv.  Ft. 

Cu.  Ft. 
per  Ton. 

Gallons 
per  Ton. 

Barrels 
per  Ton. 

1.0000 

10 

8.33 

349.86 

62.355 

35.9 

268.9 

6.43 

0.9929 

11 

8.27 

347.34 

61.912 

36.1 

270.8 

6.46 

0.9859 

12 

8.21 

344.82 

61.475 

36.5 

272.8 

6.50 

0.9722 

13 

8.16 

342.72 

61.045 

36.7 

274.6 

6.54 

0.9790 

14 

8.10 

340.20 

60.621 

36.9 

276.6 

6.59 

0.9655 

15 

8.04 

337.68 

60.202 

37.2 

278.6 

6.65 

0.9589 

16 

7.99 

335.58 

59.792 

37.5 

280.3 

6.69 

0.9523 

17 

7.93 

333.06 

59.380 

37.7 

282.4 

6.73 

0.9459 

18 

7.88 

330.96 

58.981 

38.1 

284.2 

6.77 

0.9395 

19 

7.83 

328.86 

58.582 

38  3 

286.0 

6.82 

0.9333 

20 

7.78 

326.76 

58.195 

38.5 

287.9 

6.86 

0.9271 

21 

7.72 

324.24 

57.809 

38.8 

290.0 

6.91 

0.9210 

22 

7.67 

322.14 

57.428 

39.0 

292.0 

6.96 

0.9150 

23 

7.62 

320.04 

57.053 

39.2 

293.9 

7.01 

0.9090 

24 

7.57 

317.94 

56.680 

39.5 

295.7 

7.06 

0.9032 

25 

7.53 

316.26 

56.319 

39.8 

297.4 

7.09 

0.8974 

26 

7.48 

314.16 

55.957 

40.1 

299.4 

7.14 

0.8917 

27 

7.43 

312.06 

55.601 

40.3 

301.4 

7.18 

0.8860 

28 

7.38 

309.96 

55.149 

40.6 

303.5 

7.24 

0.8805 

29 

7.34 

308.28 

54.903 

40.8 

305.2 

7.28 

0.8750 

30 

7.29 

306.18 

54.560 

41.1 

307.2 

7.32 

0.8484 

35 

7.07 

296.94 

52.991 

42.4 

316.8 

7.55 

0.8235 

40 

6.86 

288.12 

51.349 

43.7 

326.3 

7.78 

140 

The  above  table  is  based  on  the  formula  

130  + 
For  each  10°  F.  above  60°  F.  add  0.7°  Be. 
For  each  10°  F.  below  60°  F.  subtract  0.7°  Be. 
42  gals.  =  1  bbl.    1  ton  =  2240  lbs. 


He. 


=  Sp.  Gr. 


Weight  and  Stowage  of  Oil  687 


-WEIGHT   AND    STOWAGE    OP   OIL. 

(Petroleum.) 


Weight 

ix  Pounds  per 

Gallon. 

Pounds 

per 

Cubic  Foot. 

Cubic  Feet 
per  Ton. 

Gallons  per 
Ton. 

6.50 

48.63 

46.06 

344.6 

6.55 

49.05 

45.67 

342.0 

6.60 

49.38 

45.36 

339.4 

6.65 

49.75 

45.02 

336.8 

6.70 

50.13 

44.68 

334.3 

6.75 

50.50 

44.36 

331.9 

6.80 

50.88 

44.03 

329.4 

6.85 

51.25 

43.71 

327.0 

6.90 

51.62 

43.39 

324.6 

6.95 

52.00 

43.07 

322.3 

7.00 

52.36 

42.78 

320.0 

7.05 

52.75 

42.46 

317.8 

7.10 

53.12 

42.17 

315.5 

7.15 

53.50 

41.87 

313.2 

7.20 

63.86 

41.59 

311.1 

7.25 

54.24 

41.30 

309.0 

7.30 

54.61 

41.01 

306.9 

7.35 

54.99 

40.73 

304.8 

7.40 

55.37 

40.46 

302.7 

7.45 

55.74 

40.19 

300.7 

7.50 

56.11 

39.92 

298.6 

7.55 

56.48 

39.66 

296.6 

7.60 

56.85 

39.40 

294.7 

7.65 

57.23 

39.14 

292.8 

7.70 

57.61 

38.88 

290.9 

7.75 

57.99 

38.63 

289.0 

7.80 

58.36 

38.39 

287.2 

7.85 

58.73 

38.14 

285.3 

7.90 

59.10 

37.90 

283.5 

7.95 

59.47 

37.66 

281.7 

8.00 

59.85 

37.42 

280.0 

688 


The  Naval  Constructor 


WHITWORTH   STANDARD   BOLTS    AND   NUTS. 

(Dimensions  are  Given  to  the  Nearest  ^  Inch.) 


£h 

Bolt  Head  and  Nuts. 

§« 

Size 

£3 

2  w 

of 

DlAMETEB 

w,2 
5° 

Width  across 
Flats. 

Width  across 
Corners. 

Height 

of 

Bolt  Head. 

-- 

Split- 
pins 
L.S.G. 

of  Tap- 
ping Hole. 

" 

a 

11 

a 

11 

NO. 

a 

A 

A 

\  a^  A 

f  andA 

24 

15 

J  andA 

i 

i  and  A 

A   "  A 

a  ::  a 

20 

14 

A 

A 

A    "   A 

H 

\   "  A 

18 

14 

i 

§ 

if  '«  A 

II 

A  "  A 

16 

13 

i   "  A 

A 

if  "  A 

if  "  A 

1 

14 

13 

A  "  A 

i 

J   "A 

}A 

A 

12 

12 

f  "  A 
A  "  A 

A 

1      "  A 

1 1  "  A 

A  "  A 

12 

12 

I 

;    ••  a 

J  \   "  A 

\   "  A 
A  "  A 

11 

11 

i    "  A 

ft 

1A  "  A 

H   "  A 

11 

11 

A  "  A 

i 

i*   "  A 

if 

f   "  A 

10 

10 

1 

if 

if   "  A 

iA  "  A 

if  M  A 

10 

10 

if 

1 

JA  "  A 

1 

rf   "  A 

\   "  A 

9 

9 

if  "  A 

if 

JA  "  A 

1 

!  "  A 

if 

9 

9 

*   "  A 

;  i  m  a 

1 

rf   "  A 

1 

8 

8 

if  "  A 

H 

Hf  "  A 

2i    "  A 

if  "  A 

7 

7 

if  "  A 

1} 

2     »  A 

2A  "  A 

;a  "  a 

7 

6 

iA 

if 

2*  "  * 

n  "  a 

iA  "  A 

6 

5 

H   "A 

1* 

21 ""  ^ 

2f    "  A 

iA 

6 

4 

ii   "  A 

if 

2*    * 

2if  "  A 

if   "  A 

5 

3 

if 

if 

2| 

8A 

1  *   "A 

5 

2 

I'J 

1* 

2* 

»A  "  A 

1 1   "  A 

4£ 

1 

iA  "  A 

2 

2*     * 

ff 

if 

4 

1 

iff  "  A 

21 

3|    "  A 

fA  "  A 

m  "  a 

4 

A 

4f 

2} 

?  *       A 

1ft » S 

2A 

4 

A 

2A 

2f 

» 

2  f  "  A 

81 

f 

2|    "  A 

3 

1*  "  a 

*A  "  A 

2f 

8| 

f 

2f    "  A 

3* 

fif  "  A 

*A  u  A 

m  "  a 

3i 

f 

2if   "  A 

ft 

jH    "  A 

«r*  "  A 

3A 

gi 

A 

3f 

3J 

H    "  A 

«t    "  A 

3*    "  A 

3 

A 

3A  "  A 

4 

5ff  M  A 

6 1 

84 

3 

1 

3A  "  A 

*i 

2) 

7A  "  A 

3U  "  A 

H 

i 

3f   "  A 

4£ 

6if  M  A 

n 

m 

8| 

4      "  A 

41 

l\      u    ♦ 

2* 

4*   "  A 

2| 

A 

4i   "  A 

5 

7 !   "A 

9     "  A 

M 

*f 

I 

4*    "  A 

5* 

8if    "  ^ 

10A  "  A 

*H 

2f 

if 

5       M    A 

6 

10 

11  i    "  A 

n 

2| 

| 

&A  "  A 

Weight  of  Bolts  and  Nuts 


689 


,0    00       C<1 


8    g    g    °. 

00     t~     ta     e^ 

«'     ei     fl     « 


•  <o  ©  ©  o  eo 

2  t-  t~  00  -h  e<i 

rO  uj  «  ©  ©  t- 

^  '  e4  <n  «  t* 


&         l 


8    § 


•00«O-*COtJ<MO00O© 
,_}    <N        10       IS       O       «       S       *       >*       ©. 

^    2    ?    §    n    S!    S    S 

^rH-*cocoJj©i>jeo© 

^<NrH©lflM|>TH<N© 

,o3&3Si2£38S 

^    q        rH        rH        rH        rH        ©        ©        rt        © 
•"*ei5©«Ot-^<N>Ot» 

^Aosoot-tort-^it-:© 
^©©o©©©©©© 


t-        <N        rH 

8    S    © 


W    £     o     a 

ff>        m        P.       P. 


a   ,3 


M  a  IS  a 
i2  o  a  o 
W    o    pq    « 


690 


The   Naval  Constructor 


CAPACITIES  OP  TANKS  PER  FOOT 


Width 

of 
Tank. 

Length 

2" 

2' 6" 

3' 

3' 6" 

4' 

4' 6" 

5' 

5'  6" 

6' 

6'  6" 

2ft.   .    . 

2  ft.  6  in. 

3  ft.   .    . 

Gal. 
29.9 

Gal. 
37.4 

46.75 

Gal. 
44.88 

56.1 

67.32 

Gal. 
52.36 

65.45 

78.54 

91.63 

Gal. 
59.84 

74.80 

89.76 

104.72 

119.68 

Gal. 
67.32 

84.15 

101. 

117.81 

134.64 

151.47 

Gal. 

74.8 

93.5 
112.2 
130.9 
149.6 
168.30 
187. 

Gal. 

82.28 

102.85 

123.42 

144. 

164.56 

185.13 

205.7 

226.27 

Gal. 
89.76 

112.20 

134.64 

157.08 

179.52 

202. 

224.4 

246.84 

269.28 

Gal. 
97.24 

121.55 

145.86 

170.17 

194.48 

218.79 

243.1 

267.41 

291.72 

316.03 

3  ft.  6  in. 

4  ft 

4  ft.  6  in. 

5  ft.    .     . 

5  ft.  6  in. 

6  ft.   .     . 

6  ft.  6  in. 

7  ft.    .     . 

7  ft.  6  in. 

8  ft.   . 

8  ft.  6  in. 

9  ft.   .    . 

9  ft.  6  in. 
10  ft.   .    . 

Note.  — To  convert  to  British  gallons,  multiply  by 


Capacities  of  Tanks 


691 


OP   DEPTH  (Rectangular) 


of  Tank. 

7' 

7'  6" 

8' 

8' 6" 

9' 

9' 6" 

10' 

10'  6" 

11' 

11'  6" 

13' 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

104.72 

112.20 

119.68 

127.16 

134.64 

142.12 

149.6 

157. 

164.56 

172. 

179.52 

130.9 

140.25 

149.6 

158.95 

168.3 

177.65 

187. 

196.35 

205.7 

215.05 

224.4 

157. 

168.3 

179.52 

190.74 

202. 

213.18 

224.4 

235.62 

246.84 

258.06 

269.28 

183.26 

196.35 

209.44 

222.53 

235.62 

248.71 

261.8 

274.89 

288. 

301.07 

314.16 

209.44 

224.4 

239.36 

254.32 

269.28 

299.2 

314.16 

329.12 

344.08 

359. 

374. 

235.62 

252.45 

269.28 

286.11 

303. 

319.77 

336.6 

353.43 

370.26 

387.09 

404. 

261.8 

280.5 

299.2 

317.9 

336.6 

355.3 

374. 

392.7 

411.4 

430.1 

448.8 

288. 

308.55 

329.12 

349.7 

370.26 

390.83 

411.4 

332. 

452.54 

473.11 

493.68 

314.16 

336.6 

359.04 

381.48 

403.92 

426.36 

448.80 

471.24 

493.68 

516.12 

538.56 

340.34 

364.65 

388.96 

413.27 

437.58 

461 .89 

486.2 

510.51 

534.82 

559.13 

583.44 

366.52 

392.70 

418.88 

445.06 

471.24 

497.42 

523.6 

549.78 

575.96 

602.14 

628.32 

420.75 

448.8 

476.85 

405.9 

532.95 

561. 

589.05 

G17.1 

645.15 

673.2 

478.72 

508.64 

538.56 

568.48 

598.4 

628.32 

658.24 

688.16 

718.08 

540.43 

572.22 

604.01 

635.80 

667.59 

699.38 

731.17 

762.96 

605.88 

639.54 

673.2 

706.86 

740.52 

774.18 

807.84 

675.07 

710.6 

746.13 

781.66 

817.19 

852.72 

748.          7MK  4 

822.8 

860.2 

897.6 

Weight  of  a  U.S.  gallon  =  8£  lbs.    Weight  of  a  Britifi  gallon,  F. W.  =  10  lbs. 


692 


The  Naval  Constructor 


CONTENTS    OF   TANKS    PER   FOOT   OF   DEPTH 

(Cylindrical). 


DlAM. 

U.S. 
Gallons. 

DlAM. 

U.S. 
Gallons. 

DlAM. 

U.S. 
Gallons. 

Ft.   In. 

1  Foot  in 
Depth. 

Ft.  In. 

1  Foot  in 
Depth. 

Ft.    In. 

1  Foot  in 
Depth. 

1     0 

5.87 

11    0 

710.69 

21    0 

2,590.22 

1     3 

9.17 

11    3 

743.36 

21    3 

2,652.25 

1     6 

13.21 

11    6 

776.77 

21    6 

2,715.04 

1     9 

17.98 

11    9 

810.91 

21    9 

2,778.54 

2  •  0 

23.49 

12    0 

848.18 

22    0 

2,842.79 

2     3 

29.73 

12    3 

881.39 

22    3 

2,907.76 

2     6 

36.70 

12    6 

917.73 

22    6 

2,973.48 

2     9 

44.41 

12    9 

954.81 

22    9 

3,039.92 

3     0 

52.86 

13    0 

992.62 

23    0 

3,107.10 

3     3 

62.03 

13    3 

1,031.17 

23    3 

3,175.01 

3     6 

73.15 

13    6 

1,070.45 

23    6 

3,243.65 

3     9 

82.59 

13    9 

1,108.06 

23    9 

3,313.04 

4    0 

93.97 

14    0 

1,151.21 

24    0 

3,383.15 

4     3 

103.03 

14    3 

1,192.69 

24    3 

3,454.00 

4     6 

118.93 

14    6 

1,234.91 

24    6 

3,525.59 

4    9 

132.52 

14    9 

1,277.86 

24    9 

3,597.90 

5     0 

146.83 

15    0 

1,321.54 

25    0 

3,670.95 

5     3 

161.88 

15    3 

1,365.96 

25    3 

3,744.74 

5     6 

117.67 

15    6 

1,407.51 

25    6 

3,819.26 

5     9 

194.19 

15    9 

1,457.00 

25    9 

3,894.52 

6     0 

211.44 

16    0 

1,503.62 

26    0 

3,970.50 

6     3 

229.43 

16    3 

1,550.97 

26    3 

4,047.23 

6     6 

248.15 

16    6 

1,599.06 

26    6 

4,124.68 

6    9 

267.61 

16    9 

1,647.89 

26    9 

4,202.96 

7     0 

287.80 

17    0 

1,697.45 

27    0 

4,281.80 

7     3 

308.72 

17    3 

1,747.74 

27    3 

4,361.46 

7     6 

330.38 

17    6 

1,798.76 

27    6 

4,441.86 

7     9 

352.76 

17    9 

1,850.53 

27    9 

4,522.98 

8     0 

375.90 

18    0 

1,903.02 

28    0 

4,604.85 

8     3 

399.76 

18    3 

1,956.25 

28    3 

4,686.48 

8     6 

424.36 

18    6 

2,010.21 

28    6 

4,770.77 

8    9 

449.21 

18    9 

2,064.91 

28    9 

4,854.84 

9     0 

475.75 

19    0 

2,120.34 

29    0 

4,939.64 

9     3 

502.55 

19    3 

2,176.51 

29    3 

5,025.17 

9     6 

530.08 

19    6 

2,233.29 

29    6 

5,111.44 

9     9 

558.35 

19    9 

2,291.04 

29    9 

5,198.44 

10     0 

587.35     | 
617.08    J 

647.55    f 

20    0 

2,349.41 

30    0 

5,286.18 

10     3 

20    3 

2,408.51 

30    3 

5,374.65 

10     6 

20    6 

2,468.35 

30    6 

5,463.85 

10     9 

678.27 

20    9 

2,528.92 

30    9 

5,553.79 

Note.  —  To  clnvert  to  British  gallons,  x  .8 


Pressure  of  Water  at  Various  Heads       693 


PRESSURE   OF   WATER   AT   VARIOUS    HEADS. 


Formula : 


P  =  H'  X  -4334  =  Pounds. 
P  —  H'X  .0304  =  Kilos. 


Pressure, 

«.  * 

Pressure, 

»  "i 

Pressure, 

P, 

IN 

P, 

IN 

P,  IN 

S>8 

fill 

Pounds 

Kilos 

Pounds 

Kilos 

Pounds 

Kilos 

per 

per 

per 

per 

per 

per 

Sq.  In. 

Sq.  Cm. 

Sq.  In. 

Sq.  Cm. 

Sq.  In. 

Sq.  Cm. 

lin. 

.03608 

.002537 

27  ft. 

11.691 

.82196 

64  ft. 

27.712 

1.94836 

2 

.07216 

.005074 

28 

12.124 

.85240 

65 

28.145 

1.97880 

3 

.10824 

.007611 

29 

12.557 

.88284 

66 

28.578 

2.00925 

4 

.14432 

.010148 

30 

12.990 

.91329 

67 

29.011 

2.03969 

5 

.18040 

.012685 

31 

13.423 

.94373 

68 

29.444 

2.07013 

6 

.21648 

.015222 

32 

13.856 

.97417 

69 

29.877 

2.10057 

7 

.25256 

.017759 

33 

14.289 

1.00462 

70 

30.310 

2.13102 

8 

.28864 

.020296 

34 

14.722 

1.03406 

71 

30.743 

2.16146 

9 

.32472 

.022833 

35 

15.155 

1.06450 

72 

31.176 

2.19190 

10 

.36080 

.025370 

36 

15.588 

1.09495 

73 

31.609 

2.22235 

11 

.39688 

.027907 

37 

16.021 

1.12539 

74 

32.042 

2.25279 

1ft. 

.433 

.030443 

38 

16.454 

1.15583 

75 

32.475 

2.28323 

2 

.866 

.060886 

39 

16.887 

1.18627 

76 

32.908 

2.31368 

3 

1.299 

.091329 

40 

17.320 

1.21773 

77 

33.341 

2.34412 

4 

1.732 

.121773 

41 

17.753 

1.24817 

78 

33.774 

2.37456 

5 

2.165 

.152216 

42 

18.186 

1.27861 

79 

34.207 

2.40500 

6 

2.598 

.182659 

43 

18.619 

1.30906 

80 

34.640 

2.43545 

7 

3.031 

.213102 

44 

19.052 

1.33950 

81 

35.073 

2.46589 

8 

3.464 

.243545 

45 

19.485 

1.36994 

82 

35.506 

2.49633 

9 

3.897 

.273989 

46 

19.918 

1.40039 

83 

35.939 

2.52678 

10   ' 

4.330 

.30443 

47 

20.351 

1.43083 

84 

36.372 

2.55722 

11 

4.763 

.33487 

48 

20.784 

1.46127 

85 

36.805 

2.58766 

12 

5.196 

,36531 

49 

21.217 

1.49171 

86 

37.238 

2.61811 

13 

5.629 

.39576 

50 

21.650 

1.52216 

87 

37.671 

2.64855 

14 

6.062 

.42620 

51 

22.083 

1.55260 

88 

38.104 

2.67899 

15 

6.495 

.45664 

52 

22.516 

1.58304 

89 

38.537 

2.70943 

16 

6.928 

.48709 

53 

22.949 

1.61349 

90 

38.970 

2.73989 

17 

7.361 

.51753 

54 

23.382 

1.64393 

91 

39.403 

2.77033 

18 

7.794 

.54797 

55 

23.815 

1.67437 

92 

39.836 

2.80077 

19 

8.227 

.57841 

56 

24.248 

1.70482 

93 

40.269 

2.83122 

20 

8.660 

.60886 

57 

24.681 

1.73526 

94 

40.702 

2.86166 

21 

9.093 

.63930 

58 

25.114 

1.76570 

95 

41.135 

2.89210 

22 

9.526 

.66974 

59 

25.557 

1.79614 

96 

41.568 

2.92255 

23 

9.959 

.70019 

60 

25.980 

1.82659 

97 

42.001 

2.95299 

24 

10.392 

.73063 

61 

26.413 

1.85703 

98 

42.434 

2.98343 

25 

10.825 

.76107 

62 

26.846 

1.88747 

99 

42.867 

3.01387 

26 

11.258 

.79152 

63 

27.279 

1.91792 

100 

43.300 

3.04432 

The  above  table  is  calculated  for  f resb  water  at  a  temperature  of  62°  F. 


694 


The  Naval  Constructor 


UNIT   EQUIVALENTS.    * 

HEAT,  ELECTRICAL  AND  MECHANICAL. 


Unit. 

Equivalents. 

1  K.W.  hour= 

1,000  watt  hours. 

1 .  34  horse-power  hours. 
2,654,200  ft.-Ibs. 
3,600,000  joules. 
3,412  heat  units. 
367,000  kilogram  metres. 

0.235  lb.  carbon  oxidized  with  perfect  efficiency. 
3 .  53  lbs.  water  evaporated  from  and  at  212  degrees  F. 
22 .  75  lbs.  of  water  raised  from  62  degrees  to  212  degrees  F. 

1  H.P.  hour= 

0.746  K.W.  hour. 
1,980,000  ft.-lbs. 
2,545  heat-units. 
273,740  k.g.m. 

0.175  lb.  carbon  oxidized  with  perfect  efficiency. 
2.64  lbs.  water  evaporated  from  and  at  212  degrees  F. 
17.0  lbs.  water  raised  from  62  degrees  to  212  degrees  F. 

1  kilowatt  =     • 

1,000  watts. 

1 .  34  horse-power. 
2,654,200  ft.-lbs.  per  hour. 
44,240  ft.-lbs.  per  minute. 

737.3  ft.-lbs.  per  second. 
3,412  heat-units  per  hour. 
56.9  heat-units  per  minute. 
0.948  heat-unit  per  second. 
0.2275  lb.  carbon  oxidized  per  hour. 
3.53  lbs.  water  evaporated  per  hour  from  and  at 
212  degrees  F. 

1H.P.= 

746  watts. 
0.746  K.W. 
33,000  ft.-lbs.  per  minute. 
550  ft.-lbs.  per  second. 
2,455  heat-units  per  hour. 
42.4  heat-units  per  minute. 
0. 707  heat-unit  per  second. 
0.175  lb.  carbon  oxidized  per  hour. 
2.64  lbs.   water  evaporated  per  hour  from  and  at 
212  degrees  F. 

Unit  Equivalents 


695 


UNIT  EQUIVALENTS.—  (Continued.) 
HEAT,  ELECTRICAL  AND  MECHANICAL. 


Unit. 

Equivalents. 

1  Joule = 

1  watt  second. 
0.000000278  K.W.  hour. 
0.102k.g.m. 
0.0009477  heat-unit. 
0.7373  ft.-lbs. 

1  f  t.-lb.  =       • 

1.356  joules. 
0.1383  k.g.m. 
0.000000377  K.W.  hour. 
0.001285  heat-unit. 
0.0000005  H.P.  hour. 

1  watt= 

1  joule  per  second. 
0.00134  H.P. 
3.412  heat-units  per  hour. 
0.7373  ft.-lb.  per  second. 
0.0035  lb.  water  evaporated  per  hour. 
44.24  ft.-lbs.  per  minute. 

1  watt  per     J 
sq.  in.= 

8.19  heat-units  per  square  foot  per  minute. 
6371  ft.-lbs.  per  square  foot  per  minute. 
0. 193  H.P.  per  square  foot. 

1  heat  unit  =  ■ 

1,055  watt  seconds. 
778  ft.-lbs. 

107.6  kilogram  metres. 
0.000293  K.W.  hour. 
0.000393  H.P.  hour. 
0.0000688  lb.  carbon  oxidized. 

0.001036    lb.    water    evaporated    from   and  at  212 
degrees  F. 

1  heat  unit      1 

per  sq.  ft.  per  < 

min.  =          | 

0. 122  watt  per  square  inch. 
0.0176  K.W.  per  square  foot. 
0.0236  H.P.  per  square  foot. 

1  kilogram 
metre = 

7.233  ft.-lbs. 
0.00000365  H.P.  hour. 
0.00000272  K.W.  hour. 
0.0093  heat-unit. 

696 


The   Naval  Constructor 


UNIT  EQUIVALENTS.—  (Continued.) 
HEAT,  ELECTRICAL  AND  MECHANICAL. 


Unit. 

Equivalents. 

1  lb.  carbon 
oxidized  with 
perfect  effi- 
ciency = 

14,544  heat-units. 

1.11  lbs.  anthracite  coal  oxidized. 
2.5  lbs.  dry  wood  oxidized. 
21  cubic  feet  illuminating-gas. 
4.26  K.W.  hours. 
5.71  H.P.  hours. 
11,315,000  ft.-lbs. 

15  lbs.  of  water  evaporated  from  and  at  212  degrees  F. 

1  lb.  water 
evaporated 
from  and  at 
212  degs.  F. 

0.283  K.W.  hour. 
0.379  H.P.  hour. 
965.7  heat-units. 
103,900  k.g.m. 
1,019,000  joules. 
61,300  ft.-lbs. 

0.0664  lb.  of  carbon  oxidized. 

Water  Notes 


697 


WATER   NOTES. 


1  United  States  gallon  : 

1  United  States  gallon  = 

1  United  States  gallon  : 

1  United  States  gallon  = 

1  British  gallon 

1  British  gallon  : 

1  British  gallon  : 

1  British  gallon  : 

1  cubic  foot  of  sea  water  = 

1  cubic  inch  of  sea  water  : 

1  cubic  foot  of  fresh  water       : 

1  cubic  inch  of  fresh  water       : 

1  ton  of  sea  water 

1  ton  of  fresh  water  : 

Weight  of  fresh  water  : 

1  cubic  foot  of  fresh  water 

1  cubic  foot  of  fresh  water       = 

1  cubic  foot  of  fresh  water 

1  litre  of  fresh  water 

1  litre  of  fresh  water  = 

1  litre  of  fresh  water  ■ 

1  litre  of  fresh  water 

Head  of  water  in  feet  X  .4334  : 

Head  of  water  in  feet  x  .0304 


231  cubic  inches. 

.83  British  gallon. 

3.8  litres. 

8^  pounds  fresh  water. 

277.274  cubic  inches. 

1.205  United  States  gallons. 

4.543  litres. 

10  pounds  fresh  water. 

64.05  pounds  =  .0286  ton. 

.037,035  pounds. 

62.39  pounds  =  .0279  ton. 

.0361  pound. 

34.973  cubic  feet. 

35.905  cubic  feet. 

weight  of  salt  water  x  .974. 

7.476  United  States  gallons. 

6.232  British  gallons. 

28.375  litres. 

.264  United  States  gallon. 

.22  British  gallon. 
!  61.0  cubic  inches. 

.0353  cubic  foot. 
;  Pressure  in  lbs.  per  sq.  in. 
:  Pressure  in  kilos  per  sq.  cm. 


AREAS    OF  CIRCLES. 


Diam- 

Area. 

Circum- 

Diam- 

Area. 

Circum- 

eter. 

ference. 

eter. 

ference. 

4 

.000767 

.09817 

ii 

.22166 

1.6690 

15 

.003068 

.19635 

ft 

.24850 

1.7671 

t 

.006903 
.012271 

.29452 

y 

.27688 

1.8653 

.39270 

t 

.30680 

1.9635 

A 

.019175 

.49087 

§4 

.33824 

2.0617 

3 
TB 

.027612 

.58905 

H 

.37122 

2.1598 

7 

.037583 

.68722 

M 

.40574 

2.2580 

.049087 

.78540 

i 

.44179 

2.3562 

ft 

.062126 

.88357 

if 

.47937 

2.4544 

ft 

.076699 

.98175 

11 

.51849 

2.5525 

§4 

.092806 

1.0799 

H 

.55914 

2.6507 

1 

.11045 

1.1781 

i 

.60132 

2.7489 

13 
3~S 

.12962 

1.2763 

.64504 

2.8471 

h 

.15033 

1.3744 

.69029 

9.9452 

¥ 

.17257 

1.4726 

H 

.73708 

3.0434 

.19635 

1.5708 

l 

.78540 

3.1416 

698 


The  Naval  Constructor 


AREAS    OF   CIRCLES 


And  Lengths  of  the  Sides  of  Squares  of  the 

Same  Area. 

Diam.  x  .8862  =  Side  of  Square. 


.  < 

< 

.< 

■ 

g   U   30 

■**  ^  « 

OH. 

■ 

M  ^  2 

o  w   . 

a  u  5 
5£m 

ft.         <» 

■<  u  A 

o  w  . 

© 

H«5 

$3t 

o 

»  a  & 

Qccg 

o 

S300 

_  - ■/. 

1 

.785 

.89 

21 

346.36 

18.61 

41 

1,320.26 

36.34 

1* 

1.767 

1.33 

21* 

363.05 

19.05 

41* 

1,352.66 

36.78 

2 

3.142 

1.77 

22 

380.13 

19.50 

42 

1,385.45 

37.22 

2* 

4.909 

2.22 

22* 

397.61 

19.94 

42* 

1,418.63 

37.66 

3 

7.069 

2.66 

23 

415.48 

20.38 

43 

1,452.20 

38.11* 

3* 

9.621 

3.10 

23* 

433.74 

20.83 

43* 

1,486.17 

38.55 

4 

12.566 

3.54 

24 

452.39 

21.27 

44 

1,520.53 

38.99 

4* 

15.904 

3.99 

24* 

471.44 

21.71 

44* 

1,555.29 

39.44 

5 

19.635 

4.43 

25 

490.88 

22.16 

45 

1,590.43 

39.88 

5* 

23.758 

4.87 

25* 

510.71 

22.60 

45* 

1,625.97 

40.32 

G 

28.274 

5.32 

26 

530.93 

23.04 

46 

1,661.91 

40.77 

6* 

33.183 

5.76 

26* 

551.55 

23.49 

46* 

1,698.23 

41.21 

7 

38.485 

6.20 

27 

572.56 

23.93 

47 

1,734.95 

41.65 

7* 

44.179 

6.65 

27* 

593.96 

24.37 

47* 

1,772.06 

42.10 

8 

50.266 

7.09 

28 

615.75 

24.81 

48 

1,809.56 

42.58 

8* 

56.745 

7.53 

28* 

637.94 

25.26 

48* 

1,847.46 

42.98 

9 

63.617 

7.98 

29 

660.52 

25.70 

49 

1,885.75 

43.43 

9* 

70.882 

8.42 

29* 

683.49 

26.14 

49* 

1,924.43 

43.87 

10 

78.540 

8.86 

30 

706.86 

26.59 

50 

1,963.50 

44.31 

10* 

86.590 

9.30 

30* 

730.62 

27.03 

50* 

2,002.97 

44.75 

11 

95.03 

9.75 

31 

754.77 

27.47 

51 

2,042.83 

45.20 

11* 

103.87 

10.19 

31* 

779.31 

27.92 

51* 

2,083.08 

45.64 

12 

113.10 

10.63 

32 

804.25 

28.36 

52 

2,123.72 

46.08 

12* 

122.72 

11.08 

32* 

829.58 

'28.80 

52* 

2,164.76 

46.53 

13 

132.73 

11.52 

33 

855.30 

29.25 

53 

2,206.19 

46.97 

13* 

143.14 

11.96 

33* 

881.41 

29.69 

53* 

2,248.01 

47.41 

14 

153.94 

12.41 

34 

907.92 

30.13 

54 

2,290.23 

47.86 

14* 

165.13 

12.85 

34* 

934.82 

30.57 

54*« 

2,332.83 

48.30 

15 

176.72 

13.29 

35 

962.11 

31.02 

55 

2,375.83 

48.74 

15* 

188.69 

13.74 

35* 

989.80 

31.46 

55* 

2,419.23 

49.19 

16 

201.06 

14.18 

36 

1,017.88 

31.90 

56 

2,463.01 

49.63 

16* 

213.83 

14.62 

36* 

1,046.35 

32.35 

56* 

2,507.19 

50.07 

17 

226.98 

15.07 

37 

1,075.21 

32.79 

57 

2,551.76 

50.51 

17* 

240.53 

15.51 

37* 

1,104.47 

33.23 

57* 

2,596.73 

50.96 

18 

254.47 

15.95 

38 

1,134.12 

33.68 

58 

2,642.09 

51.40 

18* 

268.80 

16.40 

38* 

1,164.16 

34.12 

58* 

2,687.84 

51.84 

19 

283.53 

16.84 

39 

1,194.59 

34.56 

59 

2,733.98 

52.29 

19* 

298.65 

17.28 

39* 

1,225.42 

35.01 

59* 

2,780.51 

52.73 

20 

314.16 

17.72 

40 

1,256.64 

35.45 

60 

2,827.74 

53.17 

20* 

330.06 

18.17 

40* 

1,288.25 

35.89 

60* 

2,874.76 

53.62 

Squares,  Cubes,  etc.,  of  Fractions 


699 


SQUARES, 


CUBES,   AND   FOURTH   POWERS 
OP  FRACTIONS. 


No. 

Square. 

Cube. 

Fourth  Power. 

No. 

Square. 

Cube. 

Fourth 
Power. 

A 

0.0002441 

0.000003815 

0.00000005961 

fi 

0.4104 

0.2629 

0.1684 

A 

0.0009766 

0.00003052 

0.0000009537 

14 

0.4307 

0.2826 

0.1855 

^¥ 

0.002197 

0.0001030 

0.000001922 

II 

0.4514 

0.3033 

0.2038 

A 

0.003906 

0.0002441 

0.00001526 

ft 

0.4727 

0.3250 

0.2234 

A 

0.006104 

0.0004768 

0.00003725 

n 

0.4944 

0.3476 

0  2444 

3 
32 

0.008789 

0.0008240 

0.00007725 

ti 

0.5166 

0.3713 

0.2669 

A 

0.01196 

0.001308 

0.0001431 

u 

0.5393 

0.3961 

0.2909 

1 
8 

0.01563 

0.001953 

0.0002441 

I 

0.5625 

0.4219 

0.3164 

A 

0.01978 

0.002781 

0.0003911 

n 

0.5862 

0.4488 

0.3436 

5 
32 

0.02441 

0.003815 

0.0005961 

H 

0.6104 

0.4768 

0.3725 

H 

0.02954 

0.005077 

0.0008727 

fi 

0.6350 

0.5060 

0.4032 

A 

0.03516 

0.006592 

0.001236 

H 

ff 

0.6602 

0.5364 

0.4358 

1  3 
6  4 

0.04126 

0.008381 

0.001702 

0.6858 

0.5679 

0.4703 

A 

0.04785 

0.01047 

0.002290 

H 

0.7119 

0.6007 

0.5068 

U 

0.05493 

0.01287 

0.003018 

55 
6¥ 

0.7385 

0.6347 

0.5454 

i 
4 

0.06250 

0.01563 

0.003906 

I 

8 

0.7656 

0.6699 

0.5862 

H 

0.07056 

0.01874 

0.004978 

fl 

0.7932 

0.7065 

0.6290 

A 

0.07910 

0.02225 

0.006257 

fj 

0.8213 

0.7443 

0.6745 

H 

0.08813 

0.02617 

0.007768 

fi 

0.8499 

0.7835 

0.7223 

5 

0.09766 

0.03052 

0.009537 

« 

0.8789 

0.8240 

0.7725 

u 

0.1077 

0.03533 

0.01159 

fi 

0.9084 

0.8659 

0.8253 

u 

0.1182 

0.04062 

0.01396 

fi 

0.9385 

0.9091 

0.8807 

8 

0.1292 

0.04641 

0.01668 

If 

0.9690 

0.9539 

0.9390 

0.1406 

0.05273 

0.01978 

l 

1.000 

1.000 

1.000 

If 

0.1526 

0.05960 

0.02328 

1A 

1.031 

1.048 

1.064 

13 

0.1650 

0.06705 

0.02724 

i  l 

1.063 

1.097 

1.131 

0.1780 

0.07508 

0.03168 

h\ 

1.096 

1.147 

1.201 

A 

0.1914 

0.08374 

0.03664 

1A 

1.129 

1.199 

1.274 

It 

0.2053 

0.09304 

0.04216 

1A 

1.162 

1.253 

1.351 

if 

0.2197 

0.1030 

0.04828 

lj2 

1.196 

1.308 

1.431 

fi 

0.2346 

0.1136 

0.05505 

1A 

1.231 

1.365 

1.515 

2 

0.2500 

0.1250 

0.06250 

a 

1.266 

1.424 

1.602 

6? 

0.2659 

0.1371 

0.07069 

1A 

1.301 

1.484 

1.693 

if 

0.2822 

0.1499 

0.07965 

1    5 
i32" 

Hi 

1.337 

1.546 

1.787 

M 

0.2991 

0.1636 

0.08944 

1.373 

1.609 

1.996 

9 

0.3164 

0.1780 

0.1001 

1A 

1.410 

1.675 

1.989 

H 

0.3342 

0.1932 

0.1117 

Hi 

1.448 

1.742 

2.095 

19 
32 

0.3526 

0.2093 

0.1243 

1A 

1.485 

1.810 

2.206 

II 

0.3713 

0.2263 

0.1379 

m 

1.524 

1.881 

2.322 

5 

8 

0.3906 

0.2441 

0.1526 

n 

1.563 

1.953 

2.441 

700 


The  Naval   Constructor 


SQUARES,    CUBES,    AND 

FOURTH 

POWERS 

OF   FRACTIONS 

—  (Continued.) 

No. 

"IS 

Square. 

Cube. 

Fourth 
Power. 

No. 

Square. 

Cube. 

Fourth 
Power. 

1.602 

2.027 

2.566 

Iff 

2.692 

4.416 

7.245 

1  n 

1.642 

2.103 

2.695 

ill 

2.743 

4.543 

7.525 

HI 

1.682 

2.181 

2.829 

Iff 

2.795 

4.673 

7.813 

if\ 

1.723 

2.261 

2.968 

iff 

2.848 

4.805 

8.109 

lf| 

1.764 

2.343 

3.111 

L« 

2.901 

4.940 

8.414 

l|I 

1.806 

2.426 

3.260 

2.954 

5.077 

8.727 

in 

1.848 

2.512 

3.415 

ill 

3.008 

5.217 

9.048 

it 

1.891 

2.600 

3.575 

l! 

3.063 

5.359 

9.379 

it! 

1.934 

2.689 

3.740 

Iff 

3.117 

5.504 

9.718 

iff 

1.978 

2.781 

3.911 

125 
*8? 

3.173 

5.652 

10.07 

in 

2.022 

2.875 

4.087 

Iff 

3.229 

5.802 

10.43 

if* 

2.066 

2.970 

4.270 

iff 

3.285 

5.954 

10.79 

iff 

2.112 

3.068 

4.459 

HI 

3.342 

6.110 

11.17 

Hi 

2.157 

3.168 

4.654 

1« 

3.399 

6.268 

11.56 

Hi 

2.203 

3.271 

4.855 

HI 

3.457 

6.428 

11.95 

If 

2.250 

3.375 

5.063 

H 

3.516 

6.592 

12.36 

Iff 

2.297 

3.482 

5.277 

Iff 

3.574 

6.758 

12.78 

iff 

iff 

2.345 

3.590 

5.498 

H! 

3.634 

6.927 

13.20 

2.393 

3.701 

5.726 

iff 

3.694 

7.099 

13.64 

lft 

2.441 

3.815 

5.961 

iff 

3.754 

7.273 

14.09 

H£ 

2.490 

3.930 

6.203 

Iff 

3.815 

7.451 

14.55 

Hi 

2.540 

4.048 

6.452 

1« 

3.876 

7.631 

15.02 

ill 

2.590 

4.168 

6.709 

HI 

3.938 

7.814 

15.51 

if 

2.641 

4.291 

6.973 

2 

4.000 

8.000 

16.00 

POWERS 

AND    ROOTS    OF   USEFUL   FACTORS. 

n 

1 
n 

n* 

n* 

Vn 

l 
0.564 

</n 

l 

IT  = 

3.142 

0.318 

9.870 

31.006 

1.772 

1.465 

0.683 

2tt  = 

6.283 

0.159 

39.478 

248.050 

2.507 

0.399 

1.845 

0.542 

7t/2  = 

1.571 

0.637 

2.467 

3.878 

1.253 

0.798 

1.162 

0.860 

7t/3  = 

1.047 

0.955 

1.097 

1.148 

1.023 

0.977 

1.016 

0.985 

4/3  ir  = 

4.189 

0.239 

17.546 

73.496 

2.047 

0.489 

1.612 

0.622 

r/4- 

0.785 

1.274 

0.617 

0.484 

0.886 

1.128 

0.923 

1.084 

Tt/6  = 

0.524 

1.910 

0.274 

0.144 

0.724 

1.382 

0.806 

1.241 

7T2  = 

9.870 

0.101 

97.409 

961.390 

3.142 

0.318 

2.145 

0.466 

»*  = 

31.006 

0.032 

961.390 

29,809.910 

5.56S 

1.796 

3.142 

0.318 

tt/32  = 

0.098 

10.186 

0.0096 

0.001 

0.313 

3.192 

0.461 

2.168 

g= 

32.2 

0.031 

1036.84 

33,386.24 

5.674 

0.176 

3.181 

0.314 

2g  = 

64.4 

0.015 

4147.36 

267,090 

8.025 

0.125 

4.007 

0.249 

Speed  Tables 


701 


SPEED  TABLES. 

{Based  on  the  Admiralty  Knot  of  6,080  Feet.*) 


1  Knot 

Admi- 
ralty 

1  Knot 

Admi- 
ralty 

1  Knot 

Admi- 
ralty 

1  Knot 

Admi- 

.  RALTY 

IN     := 
Min.  Sec. 

Knots 
PerHr. 

IN      = 

Min.  Sec. 

Knots 
Per  Hr. 

IN    = 

Min.  Sec. 

Knots 
Per  Hr. 

IN      ~ 

Min.  Sec. 

"  Knots 
Per  Hr. 

1    30 

40.000 

1    38 

36.734 

1    46 

33.962 

1 

54 

31.578 

1    30.2 

39.911 

1    38.2 

36.659 

1    46.2 

33.898 

1 

54.2 

31.523 

1    30.4  • 

39.823 

1    38.4 

36.585 

1    46.4 

33.834 

1 

54.4 

31.468 

1    30.6 

39.735 

1    38.6 

36.511 

1    46.6 

33.771 

1 

54.6 

31.413 

1    30.8 

39.647 

1    38.8 

36.437 

1    46.8 

33.707 

1 

54.8 

31.358 

1    31 

39.560 

1    39 

36.363 

1    47 

33.644 

1 

55 

31.304 

1    31.2 

39.473 

1    39.2 

36.290 

1    47.2 

33.581 

1 

55.2 

31.250 

1    31.4 

39.387 

1    39.4 

36.217 

1    47.4 

33.519 

1 

55.4 

31.195 

1    31.6 

39.301 

1    39.6 

36.144 

1    47.6 

33.457 

1 

55.6 

31.141 

1    31.8 

39.215 

1    39.8 

36.072 

1    47.8 

33.395 

1 

55.8 

31.088 

1    32 

39.130 

1    40 

36.000 

1    48 

33.333 

! 

56 

31.034 

1    32.2 

39.045 

1    40.2 

35.928 

1    48.2 

33.271 

1 

56.2 

30.981 

1    32.4 

38.961 

1    40.4 

35.856 

1    48.4 

33.210 

1 

56.4 

30.927 

1    32.6 

38.876 

1     40.6 

35.785 

1    48.6 

33.149 

1 

56.6 

30.874 

1    32.8 

38.793 

1    40.8 

35.714 

1    48.8 

33.088 

1 

56.8 

30.821 

1    33 

38.710 

1    41 

35.643 

1    49 

33.027 

1 

57 

30.768 

1    33.2 

38.626 

1    41.2 

35.573 

1    49.2 

32.966 

1 

57.2 

30.716 

1    33.4 

38.543 

1    41.4 

35.503 

1    49.4 

32.906 

1 

57.4 

30.664 

1    33.6 

38.461 

1    41.6 

35.433 

1    49.6 

32.846 

1 

57.6 

30.612 

1    33.8 

38.379 

1    41.8 

35.363 

1    49.8 

32.786 

1 

57.8 

30.560 

1    34 

38.300 

1    42 

35.294 

1    50 

32.727 

1 

58 

30.508 

1    34.2 

38.216 

1    42.2 

35.225 

1    50.2 

32.668 

1 

58.2 

30.456 

1    34.4 

38.135 

1    42.4 

35.156 

1    50.4 

32.608 

1 

58.4 

30.405 

1    34.6 

38.054 

1    42.6 

35.087 

1    50.6 

32.549 

1 

58.6 

30.354 

1    34.8 

37.974 

1    42.8 

35.019 

1    50.8 

32.490 

1 

58.8 

30.303 

1    35 

37.894 

1    43 

34.951 

1    51 

32.432 

1 

59 

30.252 

1    35.2 

37.815 

1    43.2 

34.883 

1    51.2 

32.365 

1 

59.2 

30.201 

1    35.4 

37.736 

1    43.4 

34.816 

1    51.4 

32.315 

1 

59.4 

30.150 

1    35.6 

37.657 

1    43.6 

34.749 

1    51.6 

32.258 

1 

59.6 

30.100 

1    35.8 

37.578 

1    43.8 

34.682 

1    51.8 

32.200 

1 

59.8 

30.050 

1    36 

37.500 

1    44 

34.614 

1    52 

32.142 

2 

0 

30.000 

1    36.2 

37.422 

1    44.2 

34.548 

1    52.2 

32.085 

2 

0.2 

29.950 

1    36.4 

37.344 

1    44.4 

34.482 

1    52.4 

32.028 

2 

0.4 

29.900 

1    36.6 

37.267 

1    44.6 

34.416 

1    52.6 

31.971 

2 

0.6 

29.850 

1    36.8 

37.190 

1    44.8 

34.351 

1    52.8 

31.914 

2 

0.8 

29.801 

1    37 

37.113 

1    45 

34.285 

1    53 

31.858 

2 

! 

29.752 

1    37.2 

37.037 

1    45.2 

34.220 

1    53.2 

31.802 

2 

1.2 

29.702 

1    37.4 

36.961 

1    45.4 

34.155 

1    53.4 

31.746 

2 

1.4 

29.654 

1    37.6 

36.885 

1    45.6 

34.090 

1    53.6 

31.690 

2 

1.6 

29.605 

1    37.8 

36.809 

1    45.8 

34.026 

1    53.8 

31.634 

2 

1.8 

29.556 

*  The  knot,  or  nautical  mile,  is  actually 
The  statute,  or  land,  mile  is  5,280  feet. 


,082.66  feet. 


702 


The  Naval  Constructor 


SPEED   TABLES.—  (Continued.) 


1  Knot 

in  = 
Min.  Sec 

Admi- 
ralty 
Knots 
Per  Hr. 

1  Knot 

in    = 

Min.  Sec. 

Admi- 
.  RALTY 

■  Knots 
Per  Hr. 

1  Knot 
in    = 

Min.  Sec 

ADMI- 
RALTY 

Knots 
Per  Hr. 

1  Knot 
in    = 
Min.  Sec 

Admi- 
ralty 
Knots 
Per  Hr. 

2      2 
2      2.2 
2      2.4 
2      2.6 
2      2.8 

29.508 
29.459 
29.411 
29.363 
29.315 

2 
2 
2 
2 
2 

11 

11.2 

11.4 

11.6 

11.8 

27.480 
27.438 
27.396 
27.355 
27.314 

2 

2 
2 
2 
2 

20 

20.2 

20.4 

20.6 

20.8 

25.714 
25.677 
25.641 
25.604 
26.568 

2 

2 
2 
2 
2 

29 

29.2 

29.4 

29.6 

29.8 

24.161 
24.128 

24.096 
24.064 
24.032 

2      3 
2      3.2 
2      3.4 
2      3.6 
2      3.8 

29.268 
2J.220 
29.173 
29.126 
29.079 

2 

2 
2 
2 
2 

12 

12.2 

12.4 

12.6 

12.8 

27.272 
27.231 
27.190 
27.149 
27.108 

2 
2 
2 
2 
2 

21 

21.2 

21.4 

21.6 

21.8 

25.532 
25.495 
25.459 
25.423 
25.387 

2 
2 
2 

2 

2 

30 

30.2 

30.4 

30.6 

30.8 

24.000 
23.968 
23.936 
23.904 
23.872 

2      4 
2      4.2 
2      4.4 
2      4.6 
2      4.8 

29.032 
28.985 
28.938 
28.892 
28.846 

2 
2 
2 

2 
2 

13 

13.2 
13.4 
13.6 
13.8 

27.066 
27.026 
26.986 
26.946 
26.905 

2 

2 
2 
2 
2 

22 

22.2 

22.4 

22.6 

22.8 

25.352 
25.316 
25.280 
25.245 
25.210 

2 
2 

2 
2 
2 

31 

31.2 

31.4 

31.6 

31.8 

23.840 
23.809 
23.778 
23.746 
23.715 

2      5 
2      5.2 
2      5.4 
2      5.6 
2      5.8 

28.800 
28.753 
28.708 
28.662 
28.616 

2 
2 
2 

2 

14 

14.2 

14.4 

14.6 

14.8 

26.864 
26.825 
26.785 
26.745 
26.705 

2 
2 

2 
'2 
2 

23 

23.2 

23.4 

23.6 

23.8 

25.174 
25.139 
25.104 
25.069 
25.034 

2 

2 
2 
2 
2 

32 

32.2 

32.4 

32.6 

32.8 

23.684 
23.653 
23.622 
23.591 
23.560 

2      6 
2      6.2 
2      6.4 
2      6.6 
2      6.8 

28.570 
28.526 
28.481 
28.436 
28.391 

2 
2 

•2 
2 
2 

15 

15.2 

15.4 

15.6 

15.8 

26.666 
26.627 
26.687 
26.548 
26.509 

2 
2 
2 
2 
2 

24 

24.2 

24.4 

24.6 

24.8 

25.000 
24.965 
24.930 
24.896 
24.861 

2 
2 
2 

2 
2 

33 

33.2 

33.4 

33.6 

33.8 

23.529 
23.498 
23.468 
23.437 
23.407 

2      7 
2      7.2 
2      7.4 
2      7.6 

2      7.8 

28.346 
28.301 
28.257 
28.213 
28.169 

2 
2 
2 
2 
2 

16 

16.2 

16.4 

16.6 

16.8 

26.470 
26.431 
26.392 
26.354 
26.315 

2 

2 
2 
2 

2 

25 

25.2 

25.4 

25.6 

25.8 

24.827 
24.793 
24.759 
24.725 
24.691 

2 
2 
2 
2 
2 

34 

34.2 

34.4 

34.6 

34.8 

23.376 
23.334 
23.316 
23.285 
23.255 

2      8 
2      8.2 
2      8.4 
2      8.6 
2      8.8 

28.126 
28.081 
28.037 
27.993 
27.950 

2 
2 
2 
2 
2 

17 

17.2 

17.4 

17.6 

17.8 

26.278 
26.239 
26.200 
26.162 
26.124 

2 
2 
2 
2 
2 

26 

26.2 

26.4 

26.6 

26.8 

24.657 
24.623 
24.590 
24.556 
24.523 

2 
2 
2 
2 
2 

35 
35.2 
35.4 
35.6 

35.8 

23.225 
23.195 
23.166 
23.136 
23.106 

2      9 
2      9.2 
2      9.4 
2      9.6 
2      9.8 

27.906 
27.863 
27.820 
27.777 
27.734 

2 

2 
2 
2 

2 

18 

18.2 

18.4 

18.6 

18.8 

26.086 
26.048 
26.011 
25.973 
25.936 

2 
2 

2 
2 

2 

27 

27.2 

27.4 

27.6 

27.8 

24.489 
24.456 
24.423 
24.390 
24.357 

2 
2 
2 
2 
2 

36 

36.2 

36.4 

36.6 

36.8 

23.076 
23.334 
23.017 
22.988 
22.959 

2    10 
2    10.2 
2    10.4 
2    10.6 
2    10.8 

27.692 
27.649 
27.607 
27.565 
27.522 

2 
2 
9 
2 

2 

19 

19.2 

19.4 

19.6 

19.8 

25.899 
25.862 
25.824 
25.787 
25.750 

2 
2 
2 
2 

2 

28 

28.2 

28.4 

28.6 

28.8 

24.324 
24.291 
24.258 
24  226 
24.193 

2 
2 
2 
2 
2 

37 

37.2 

37.4 

37.6 

37.8 

22.930 
22.900 
22.871 
22  842 
22.813 

Speed  Tables 


703 


SPEED  TABLES.  —  (Continued.) 


1  Knot 

IN     = 

Min.  Sec 

Admi- 
.  BALTY 

1  Knot 

Admi- 

.  RALTY 

1  Knot 

in   = 

Min.  Sec 

Admi- 

_  BALTY 

1  Knot 

Admi- 

.  RALTY 

"  Knots 
'  Per  Hr. 

M 

n.  Sec 

"  Knots 
•  Per  Hr. 

"  Knots 
•  Per  Hr 

in    ~ 
Min.  Sec 

"  Knots 
•  Per  Hr 

2    38 

•22.784 

2 

47 

21.556 

2 

56 

20.454 

3    25 

17.560 

2    38.2 

22.756 

2 

47.2 

21531 

2 

56.2 

20.431 

3    26 

17.475 

2    38.4 

22.727 

2 

47.4 

21.505 

2 

56.4 

20.408 

3    27 

17.391 

2    38.6 

22.698 

2 

47.6 

21.479 

2 

56.6 

20.385 

3    28 

17.307 

2    38.8 

22.670 

2 

47.8 

21.454 

2 

56.8 

20.361 

3    29 

17.225 

2    39 

22.646 

2 

48 

21.428 

2 

57 

20.338 

3    30 

17.142 

2    39.2 

22.613 

2 

48.2 

21.403 

2 

57.2 

20.316 

3    31 

17.061 

2    39.4 

22.584 

2 

48.4 

21.377 

2 

57.4 

20.293 

3    32 

16.981 

2    39.6 

22.556 

2 

48.6 

21,352 

2 

57.6 

20.270 

3    33 

16.901 

2    39.8 

22.528 

2 

48.8 

21.327 

2 

57.8 

20.247 

3    34 

16.822 

2    40 

22.500 

2 

49 

21.302 

2 

58 

20.224 

3    35 

16.744 

2    40.2 

22.471 

2 

49.2 

21.276 

2 

58.2 

20.202 

3    36 

16.667 

2    40.4 

22.443 

2 

49.4 

21.251 

2 

58.4 

20.179 

3    37 

16.590 

2    40.6 

22.415 

2 

49.6 

21.226 

2 

58.6 

20.156 

3    38 

16.514 

2    40.8 

22.388 

2 

49.8 

21.201 

2 

58.8 

20.134 

3    39 

16.438 

2    41 

22.360 

2 

50 

21.176 

2 

59 

20.111 

3    40 

16.363 

2    41.2 

22.332 

2 

50.2 

21.151 

2 

59.2 

20.089 

3    41 

16.289 

2    41.4 

22.304 

2 

50.4 

21.126 

2 

59.4 

20.066 

3    42 

16.216 

2    41.6 

22.277 

2 

50.6 

21.101 

2 

59.6 

20.044 

3    43 

16.143 

2    41.8 

22.249 

2 

50.8 

21.077 

2 

59.8 

20.022 

3    44 

16.071 

2    42 

22.222 

2 

51 

21.052 

3 

0 

20.000 

3    45 

16.000 

2    42.2 

22.194 

2 

51.2 

21.028 

3 

1 

19.890 

3    46 

15.929 

2    42.4 

22.167 

2 

51.4 

21.003 

3 

2 

19.780 

3    47 

15.859 

2    42.6 

22.140 

2 

51.6 

20.978 

3 

3 

19.672 

3    48 

15.789 

2    42.8 

22.113 

2 

51.8 

20.954 

3 

4 

19.564 

3    49 

15.721 

2    43 

22.086 

2 

52 

20.930 

3 

5 

19.460 

3    50 

15.652 

2    43.2 

22.058 

2 

52.2 

20.905 

3 

6 

19.355 

3    51 

15.584 

2    43.4 

22.031 

2 

52.4 

20.881 

3 

7 

19.251 

3    52 

15.517 

2    43.6 

22.004 

2 

52.6 

20.857 

3 

8 

19.150 

3    53 

15.450 

2    43.8 

21.978 

2 

52.8 

20.833 

3 

9 

19.047 

3    54 

15.384 

2    44 

21.951 

2 

53 

20.808 

3 

10 

18.947 

3    55 

15.319 

2    44.2 

21.924 

2 

53.2 

20.784 

3 

11 

18.848 

3    56 

15.254 

2    44.4 

21.897 

2 

53.4 

20.761 

3 

12 

18.750 

3    57 

15.190 

2    44.6 

21.871 

2 

53.6 

20.737 

3 

13 

18.652 

3    58 

15.126 

2    44.8 

21.844 

2 

53.8 

20.713 

3 

14 

18.556 

3    59 

15.062 

2    45 

21.818 

2 

54 

20.689 

3 

15 

18.461 

4    00 

15.000 

2    45.2 

21.791 

2 

54.2 

20.665 

3 

16 

18.367 

4      1 

14.938 

2    45.4 

21.765 

2 

54.4 

20.642 

3 

17 

18.274 

4      2 

14.876 

2    45.6 

21.739 

2 

54.6 

20.618 

3 

18 

18.181 

4      3 

14.815 

2    45.8 

21.712 

2 

54.8 

20.594 

3 

19 

18.090 

4      4 

14.754 

2    46 

21.686 

2 

55 

20.571 

3 

20 

18.000 

4      5 

14.694 

2    46.2 

21.660 

2 

55.2 

20.547 

3 

21 

17.910 

4      6 

14.634 

2    46.4 

21.634 

2 

55.4 

20.524 

3 

22 

17.823 

4      7 

14.575 

2    46.6 

21.608 

2 

55.6 

20.501 

3 

23 

17.734 

4      8 

14.516 

2    46.8 

21.582 

2 

55.8 

20.477 

3 

24 

17.647 

4      9 

14.457 

704 


The  Naval  Constructor 


SPEED   TABLES.  —  (Continued.) 


1  Knot 

Admi- 

.  BALTY 

1  Knot 

Admi- 

.  BALTY 

1  Knot 

Admi- 
.  BALTY 

1  Knot 

Admi- 

.  BALTY 

in   = 
Min.  Sec 

"  Knots 
•  Per  Hr. 

IN     — 

Min.  Sec 

"  Knots 
'  Per  Hr. 

IN     ~ 

Min.  Sec 

"  Knots 
•  Per  Hr. 

IN     — 

Min.  Sec 

"  Knots 
'  Per  Hr. 

1     10 

14.400 

\ 

55 

12.203 

B 

40 

10.588 

6 

25 

9.350 

4    11 

14.342 

1 

56 

12.162 

B 

41 

10.557 

8 

26 

9.828 

4    12 

14.285 

t 

57 

12.121 

B 

42 

10.526 

<; 

27 

9.302 

4    13 

14.220 

l 

58 

12.080 

B 

43 

10.495 

B 

28 

9.278 

4    14 

14.173 

l 

59 

12.040 

B 

44 

10.465 

G 

29 

9.254 

4    15 

14.118 

S 

00 

12.000 

r. 

45 

10.434 

G 

30 

9.230 

4    16 

14.063 

r. 

1 

11.960 

B 

46 

10.404 

a 

31 

9.207 

4    17 

14.008 

B 

2 

11.920 

B 

47 

10.375 

g 

32 

9.183 

4    18 

13.953 

B 

3 

11.880 

B 

48 

10.345 

a 

33 

9.160 

4    19 

13.900 

B 

4 

11.841 

B 

49 

10.315 

B 

34 

9.137 

4    20 

13.846 

0 

5 

11.803 

B 

50 

10.286 

1 

35 

9.113 

4    21 

13.793 

B 

6 

11.764 

B 

51 

10.256 

a 

36 

9.090 

4    22 

13.740 

B 

7 

11.726 

s 

52 

10.227 

a 

37 

9.068 

4    23 

13.688 

B 

8 

11.688 

B 

53 

10.198 

a 

38 

9.044 

4    24 

13.636 

6 

9 

11.650 

B 

54 

10.169 

0 

39 

9.022 

4    25 

13.584 

B 

10 

11.613 

5 

55 

10.140 

G 

40 

9.000 

4    26 

13.533 

B 

11 

11.575 

B 

56 

10.112 

G 

41 

8.977 

4    27 

13.483 

B 

12 

11.538 

B 

57 

10.084 

a 

42 

8.955 

4    28 

13.432 

B 

13 

11.501 

B 

58 

10.055 

<; 

43 

8.933 

4    29 

13.383 

5 

14 

11.465 

B 

59 

10.027 

G 

44 

8.911 

4    30 

13.333 

B 

15 

11.428 

| 

00 

10.000 

G 

45 

8.889 

4    31 

13.284 

5 

16 

11.392 

G 

1 

9.972 

G 

46 

8.867 

4    32 

13.235 

B 

17 

11.356 

a 

2 

9.944 

G 

47 

8.845 

4    33 

13.186 

B 

18 

11.323 

B 

3 

9.917 

G, 

48 

8.823 

4    34 

13.138 

5 

19 

11.285 

0 

4 

9.890 

G 

49 

8.801 

4    35 

13.092 

5 

20 

11.250 

6 

5 

9.863 

G 

50 

8.780 

4    36 

13.043 

B 

21 

11.214 

6 

6 

9.830 

(i 

51 

8.759 

4    37 

12.996 

B 

22 

11.180 

G 

7 

9.809 

G 

52 

8.737 

4    38 

12.950 

5 

23 

11.146 

6 

8 

9.783 

G 

53 

8.716 

4    39 

12.903 

5 

24 

11.111 

6 

9 

9.756 

G 

54 

8.695 

4    40 

12.857 

5 

25 

11.077 

6 

10 

9.729 

G 

55 

8.675 

4    41 

12.811 

B 

26 

11.043 

I 

11 

9.703 

G 

56 

8.654 

4    42 

12.766 

5 

27 

11.009 

6 

12 

9.677 

G 

57 

8.633 

4    43 

12.720 

5 

28 

10.975 

g 

13 

9.651 

6 

58 

8.612 

4    44 

12.676 

5 

29 

10.942 

g 

14 

9.625 

6 

59 

8.591 

4    45 

12.631 

5 

30 

10.909 

6 

15 

9.600 

7 

00 

8.571 

4    46 

12.587 

5 

31 

10.876 

6 

16 

9.574 

7 

1 

8.551 

4    47 

12.543 

5 

32 

10.843 

B 

17 

9.549 

7 

2 

8.530 

4    48 

12.500 

5 

33 

10.810 

g 

18 

9.524 

7 

3 

8.510 

4    49 

12  456 

5 

34 

10.778 

G 

19 

9.490 

7 

4 

8.490 

4    50 

12.413 

5 

35 

10.746 

6 

20 

9.473 

7 

5 

8.470 

4    51 

12.371 

5 

36 

10.714 

6 

21 

9.448 

7 

6 

8.450 

4    52 

12.329 

5 

37 

10.682 

6 

22 

9.424 

7 

7 

8.430 

4    53 

12.287 

5 

38 

10.651 

G 

23 

9.399 

7 

8 

8.413 

4    54 

12.245 

5 

39 

10.619 

6 

21 

9.375 

7 

9 

8.392 

Speed  Tables 


705 


SPEED   TABLES.  —  (Concluded. ) 


1  Knot    Admi" 

TV    —  KALTi' 

tvt;.!  Bq7  Knots 

Mm.  Sec.  Per  Hr 

1  Knot    Admi" 

ivr;i  cT  Knots 
Mm.  Sec.  per  Hr 

1  Knot    Admi" 
tx    —  ralty 

Min  Se7  KlfOTS 
Min.  bee.  per  m. 

7    10 
7    11 
7    12 
7    13 
7    14  ' 

7    15 
7    16 
7    17 
7    18 
7    19 

7    20 
7    21 
7    22 
7    23 
7    24 

7    25 
7    26 
7    27 
7    28 
7    29 

7    30 
7    31 
7    32 
7    33 
7    34 

8.372 
8.353 
8.334 
8.315 
8.295 

8.276 
8.257 
8.228 
8.219 
8.200 

8.181 
8.163 
8.144 
8.127 
8.108 

8.090 
8.071 
8.053 
8.035 
8.017 

8.000 
7.982 
7.964 
7.947 
7.929 

7    35 
7    36 
7    37 
7    38 
7    39 

7    40 
7    41 
7    42 
7    43 
7    44 

7    45 
7    46 
7    47 
7    48 
7    49 

7    50 
7    51 
7    52 
7    53 
7    54 

7.912 
7.895 

7.877 
7.860 
7.843 

7.826 
7.809 
7.792 
7.775 
7.758 

7.741 
7.725 
7.708 
7.692 
7.675 

7.659 
7.643 
7.627 
7.611 
7.595 

7    55 
7    56 
7    57. 
7    58 

7  59 

8  0 
8      1 
8      2 
8      3 
8      4 

8      5 
8      6 
8      1 
8      8 
8      9 

8     10 
8    11 
8     12 
8    13 
8     14 

7.579 
7.563 
7.547 
7.531 
7.515 

7.500 
7.484 
7.468 
7.453 
7.438 

7.422 
7.407 
7.392 
7.377 
7.362 

7.346 
7.331 
7.317 

7.302 

7.287 

8    15 
8    16 
8    17 
8    18 
8    19 

8    20 
8    21 
8    22 
8    23 
8    24 

8    25 

8    26 
8    27 
8    28 
8    29 

8    30 
8    31 
8    32 
8    33 
8    34 

7.272 
7.258 
7.243 
7.229 
7.214 

7.200 
7.185 
7.171 
7.157 
7.142 

7.128 
7.114 
7.100 
7.086 
7.072 

7.059 
7.045 
7.031 
7.017 
7.004 

706 


The  Naval  Constructor 


FOREIGN   WEIGHTS    AND    MEASURES 
WITH   EQUIVALENTS. 


Denomination. 


Almude 

Ardeb 

Arobe 

Arratel  or  libra.. 
Arroba  (dry) 

Arroba  (liquid) . 

Arshine 

Arshine  (square) 

Artel 

Barrel 

Barril 

Berkovetz 

Bongkal 

Bouw 

Bu 

Butt 

Caffiso 

Candy 

Cantar 

Cantaro  (cantar) 
Carga 

Catty 

Centaro 


Where  Used. 


Portugal 

Egypt 

Paraguay 

Portugal 

Argentina 

Brazil 

Cuba 

Portugal 

Spain 

Venezuela 

Cuba,  Spain,  and  Vene- 
zuela   

Russia 

Morocco 

Malta  (customs) 

Spain  (raisins) 

Argentina  and  Mexico. . . . 

Russia 

India 

Sumatra 

Japan 

Spain  (wine) 

Malta 

India  (Bombay) 

India  (Madras) 

Egypt 

Morocco 

Syria  (Damascus) 

Turkey 

Malta 

Colombia 

Mexico  and  Salvador. .  . . 

China 

Japan 

Java,  Malacca,  and  Siam 

Sumatra 

Central  America 


American  Equivalent. 


4.422  gallons. 
7.6907  bushels. 
25  pounds. 

1.011  pounds. 
25.3175  pounds. 
32.38  pounds. 
25.3664  pounds. 
32.38  pounds. 
25.36  pounds. 
25.4024  pounds. 

[■4.263  gallons. 

28  inches. 

5.44  square  feet. 

1 .  12  pounds. 

11.4  gallons. 
100  pounds. 
20.0787  gallons. 
361.12  pounds. 
832  grains. 

7,096 . 5  square  metres. 

0.li9inch. 

140  gallons. 

5.4  gallons. 

529  pounds. 

500  pounds. 

99 . 5  pounds. 
113  pounds. 
575  pounds. 
124.7036  pounds. 
175  pounds. 

250  pounds. 

300  pounds. 

1.333  J  (1§)  pounds. 

1 .  32  pounds. 

1 .  35  pounds. 

2.12  pounds. 
4.2631  gallons. 


Foreign  Weights  and   Measures         707 


FOREIGN   WEIGHTS   AND    MEASURES 
WITH   EQUIVALENTS.  —  (Continued.) 


Denomination. 

Where  Used. 

Centner 

Bremen  and  Brunswick . . 

Darmstadt 

Denmark  and  Norway. . . 
Nuremberg k 

Zollverein 

Chih 

Siam  (Koyan) 

Argentina 

Paraguay 

Paraguay  (square) 

•< 

<< 

Cwt.  (hundredweight). 

Dun 

Asia  Minor  (wheat) 

Chile 

H 

.. 

,, 

,, 

.< 

Uruguay  (double) 

II 

II 

Frail 

American  Equivalent. 


117.5  pounds. 
110.24  pounds. 
110.11  pounds. 

112.43  pounds. 

113.44  pounds. 
93.7  pounds. 
123 . 5  pounds. 
110.24  pounds. 
5.7748  bushels. 
14  inches. 
3098  pounds. 
2667  pounds. 

4 . 2  acres. 
78.9  yards. 
8.077  square  feet. 
Nearly  2  acres. 
112  pounds. 
2.6997  acres. 
1.599  bushels. 

1  gram. 

1  inch. 

10.61  pounds. 

1.5745  bushels. 

2.575  bushels. 

1.599  bushels. 

1.54728  bushels, 
f Strike  fanega,  70  lbs.,  full 
I    fanega,  118  lbs. 

1 . 6  bushels. 

7.776  bushels. 

3.888  bushels. 

1.599  bushels. 

16  gallons. 

1 . 03  acres. 
50  pounds. 
2.5096  quarts. 
2.5  quarts. 

35  pounds. 


708 


The  Naval  Constructor 


FOREIGN  WEIGHTS    AND   MEASURES 
WITH   EQUIVALENTS.  —  (Continued.) 


Denomination. 


Where  Used. 


American  Equivalent. 


Fuder 

Funt 

Garnice 

Go 

Joch 

Ken 

Klafter 

Koku  (dry)... 
Koku  (liquid). 

Korree 

Kota 

Kwan 

Last 


League 

Li 

Libra  (pound). 


Libra. 


Livre  (pound). 


Load 

Manzana . 


Luzemburg 

Russia 

Russian  Poland . . 

Japan 

Austria- Hungary. 

Japan 

Russia 

Japan 


Russia. 
Japan.. 


Belgium  and  Holland. 
England  (dry  malt) . . . 

Germany 

Prussia 

Russian  Poland 

Spain  (salt) 

Paraguay  (land) 

China 

Argentina 

Castilian 

Central  America 

Chile 

Cuba 

Mexico 

Peru 

Portugal 

Spain 

Uruguay 

Venezuela 

Greece 

Guiana 


England  (timber). 


Costa  Rica 

Nicaragua  and  Salvador 


264. 17  gallons. 
0.9028  pound. 
0.88  gallon. 
0.0000817  acre. 
1.422  acres. 
5.965  feet. 
216  cubic  feet. 
5.118  bushels. 
47.653  gallons. 
3.5  bushels. 

5.13  bushels. 
8.27  pounds. 
85.134  bushels. 
82.52  bushels. 

2  metric  tons  (4409.2  lbs.) 

112.29  bushels. 

11|  bushels. 

4760  pounds. 

4633  acres. 

2115  feet. 

1.0127  pounds. 

7100  grains  (troy). 

1 .  043  pounds. 

1.014  pounds. 
1.0161  pounds. 
1.01467  pounds. 

1.0143  pounds. 
1.011  pounds. 

1.0144  pounds. 
1.0143  pounds. 
1.0161  pounds. 
1 . 1  pounds. 
1.0791  pounds. 

Square,  50  cubic  feet;  un- 
hewn, 40  cubic  feet;  inch 
planks,  600  superficial 
feet. 

1|  acres. 

1 .  727  acres. 


Foreign  Weights  and  Measures         709 


FOREIGN   WEIGHTS   AND   MEASURES 
WITH  EQUIVALENTS.  —  {Continued.) 


Denomination. 


Where  Used. 


American  Equivalent. 


Marc 

Maund 

Mil 

Milla 

Morgen 

Oke 

Pic 

Picul 

I  i 

■ ::::::] 
•■ I 

Pie 

Pik 

Pood 

Pund  (pound) 

Quarter 

Quintal 

Rottle 

Rottle 


Bolivia 

India 

Denmark 

Denmark  (geographical). 
Honduras  and  Nicaragua. 

Prussia 

Egypt 

Greece 

Hungary 

Hungary  and  Wallachia. . 

Turkey 

Egypt 

Borneo  and  Celebes 

China,  Japan,  and  Suma-  i 

tra \ 

Java 

Philippine  Islands 

(hemp) 

Philippine  Islands  ) 

(sugar) ) 

Argentina 

Spain 

Turkey 

Russia 

Denmark  and  Sweden . . . 

Great  Britain 

London  (coal) 

Argentina 

Brazil 

Castile,      Chile,      and ) 

Peru ? 

Greece 

Mexico 

Newfoundland  (fish) 

Paraguay 

Syria 

Palestine 

Syria 

Russia 


0.507  pound. 
82?. 

4.68  miles. 
4.61  miles. 
1 .  1493  miles. 
0.63  acre. 
2.7225  pounds. 
2.75578  pounds. 
3.0817  pounds. 
2 . 5  pints. 
2.81857  pounds. 
21^  inches. 
135.64  pounds. 

133    pounds. 

135 . 1  pounds. 

139.45  pounds. 

140  pounds. 

0.9478  foot. 
0.91407  foot. 
27.9  inches. 
36.112  pounds. 
1 .  102  pounds. 
8.252  bushels. 
36  bushels. 
101.42  pounds. 
130.06  pounds. 

101.41  pounds. 

123.2  pounds. 

101.46  pounds. 
112  pounds. 
100  pounds. 
125  pounds. 

6  pounds. 
5|  pounds. 

7  feet. 


10 


The  Naval   Constructor 


FOREIGN    WEIGHTS    AND    MEASURES 
WITH   EQUIVALENTS.  —  (Concluded.) 


Denomination. 


Where  Used. 


American  Equivalent. 


Salm.. 

Se 

Seer... 
Shaku. 
Sho... 


Standard . 


Stone 

Suerte 

Sun 

Tael 

Tan 

Tierce 

To 

Tola 

Tonde 

Tondeland . 

Tsubo 

Tsun 

Tun 

Tunna 

Tunnland . . 
Vara 


Yedro 

Venetian  pound. 

Vergees 

Verst 

Vlocka  


Malta 

Japan 

India 

Japan 

Japan 

St.  Petersburg  (lumber  ) 

measure) ) 

Great  Britain 

Uruguay 

Japan 

Cochin  China 

Japan 

Newfoundland 

Japan 

Denmark  (cereals) 

Denmark 

Japan 

China 

Newfoundland  (cod  oil) . . 
Sweden 

Argentina i 

Central  America 

Chile  and  Peru 

Cuba 

Curacao 

Mexico 

Paraguay 

Spain 

Venezuela 

Russia 

Greece   and  Med i terra-) 

nean  countries ) 

Isle  of  Jersey 

Russia 

Russian  Poland 


490  pounds. 
0.02451  acre. 

1  pound,  13  ounces. 
11.9303  inches. 

1 . 6  dry  quarts. 

165  cubic  feet. 

14  pounds. 

2700  cuadras  (see  cuadra). 

1.193  inches. 

590.75  grains  (troy). 

0.245  acre. 

300  pounds. 

2  pecks. 
180  grains. 
3.94783  bushels. 
1.36  acres. 
35.581  square  feet. 
1.41  inches. 

306  gallons. 
4.5  bushels. 
1.22  acres. 
34.1208  inches. 
32.87  inches. 
33.367  inches. 
33.384  inches. 
33.375  inches. 
32.992  inches. 
34  inches. 
0.99081  yard. 
33.384  inches. 
2 .  707  gallons. 

1 .  05  pounds. 

71 . 1  square  rods. 
0.663  mile. 
41.98  acres. 


Stowages  of  Merchandise  711 

STOWAGES    OF   MERCHANDISE. 

Cubic  Feet 
per  Ton. 

Acid,  sulphuric 24 

Alcohol  in  casks 80 

Almonds,  shelled,  in  bags 70 

Almonds  in  bales 108 

Almonds  in  hogsheads 120 

Aniseed  in  bags 120 

Apparel 50 

Apples  in  boxes 90 

Arrowroot  in  boxes 70 

Arrowroot  in  bags 52 

Arrowroot  in  cases 50 

Asbestos  in  cases 53 

Ashes  in  casks 53 

Ashes,  some  sorts 40-45 

Asphalt 17 

Bacon  in  cases 64-66 

Bales,  Manchester  well  pressed 48-50 

Bales,  canvas 42-45 

Ballast,  Thames  shingle 22 

Ballast,  sand 19 

Ballast,  sand,  coarse 20 

Ballast,  loose  earth 24-25 

Ballast,  clay. 17 

Ballast,  clay  with  gravel 18 

Ballast  (Thames) 22 

Barley  in  bulk 47 

Barley  in  bags 58-60 

Beans,  Haricot  in  bags 68 

Beans  in  bulk 47 

Beef  (see  Meat) 

Beer  in  bulk,  hogsheads 54 

Beer  in  bottles,  in  cases  and  casks 80 

Beeswax 74 

Beeswax  in  India 50 

Blackwood 50 

Bone  meal 45 

Bones,  crushed 60 

Bones,  loose 85 

Bones,  calcined 106 

Bone  manure,  common 72 

Bone  manure,  best 53 

Books 50 

Borax  in  cases 50 


712  The   Naval  Constructor 


STOWAGES    OF  MERCHANDISE.  —  (Continued.) 

Cubic  Feet 
per  Ton. 

Borax  variable 42 

Borate  of  lime 52 

Bottles,  empty,  in  crates 85 

Bran  in  bags 110-104 

Bran,  compressed  bales  of 80 

Brandy  in  casks 80 

Brandy  bottled,  in  cases 52-60 

Bread  in  bulk 124 

Bread  in  bags 140 

Bread  in  casks 160 

Bread  in  cases 156 

Bricks  (absorb  about  15%  moisture) 20 

Bricks,  wet 19 

Bricks,  1000  new  bricks  about  3f  tons,  will  stow 

in  75  cubic  feet,  1000  old  bricks,  about  3  tons 

will  stow  in  68  to  70  cubic  feet 

Buckwheat  in  bags 65 

Bulbs  in  cases 80 

Butter  in  cases  or  kegs 70 

Camphor  in  cases .• 50 

Candles  in  boxes * 56 

Canvas 47 

Carpets  in  rolls 80 

Carpets  in  bales 140 

Casks,  empty  palm  oil 400 

Cassia  in  cases 184 

Cassia  in  bundles 130 

Cassia  buds  in  cases 130 

Cellulose •. 240 

Cement,  ordinary,  in  casks 46 

Cement,  Portland,  in  casks 35-37 

Chalk  in  barrels 38 

Charcoal  (absorbs  about  20%  moisture) 40 

Cheese 70 

Chicory  in  sacks 60 

Chloride  of  lime  in  casks 80 

Cider  in  casks *. 65 

Cigars  in  cases 180 

Cinnamon  in  bales 50 

Cinchona,  Peruvian  bark 130-150 

Cloth  goods  in  cases  (uncertain) 85-90 

Cloves  in  chests 50 

Coal,  Admiralty 48 


Stowages  of  Merchandise  713 

STOWAGES    OF   MERCHANDISE.  —  (Continued.) 

Cubic  Feet 
per  Ton. 

Coal,  American 43 

Coal,  Newcastle 45 

Coal,  New  River  (Gas) 50 

Coal,  Welsh 40 

Coal,  Japan 43-45 

Coal,  Pocahontas 40 

Cocoa  in  bags 80 

Cocoanuts  in  bulk 140 

Coffee  in  bags 61 

Coffee  in  tierces 70 

Coffee  in  parchment,  in  bags 80 

Coir,  yarn  in  bales 190 

Coir,  fibre 200 

Coir,  other  kinds 200-220 

Coke,  heaped 80 

Copper,  manufactured 10 

Copper  ore 10-20 

Copper  sulphate  in  casks 50 

Copperas,  casks 52 

Copra,  desiccated,  in  cases,  about 65 

Copra  in  bales 85 

Copra  in  cases 80-90 

Cork,  pressed  bales 200 

Cork,  bales  from  France 440 

Cork,  wood,  bales 270 

Cork,  shavings,  in  bales 290 

Cotton,  American,  pressed  (32  cubic  feet  per 

bale) 130 

Cotton,  American  unpressed 200 

Cotton,  East  Indian,  bales 57-60 

Cotton,  good  average,  bales 52 

Cotton,  ordinarily  pressed  bales 67 

Cotton,  Egyptian,  bales 58 

Cotton,  waste 170 

Cowrie  shells 40 

Cowrie  shells  in  bags ■ 65-80 

Creosote  in  casks 60 

Currents  in  cases 50 

Dates,  wet 40 

Dates,  dry 45 

Earth  mould 33 

Earthenware,  jars  in  crates 47 

Earthenware,  retorts,  loose 58 


714  The  Naval  Constructor 


STOWAGES    OF   MERCHANDISE.  —  (Continued.) 

Cubic  Feet 
per  Ton. 

Fish  in  cases 95 

Fish,  iced 60 

Fish,  oil,  in  cases 57 

Fish  manure 65 

Firewood 288 

Flax 88 

Flax  from  Baltic  ports 155 

Flax  from  New  York 108 

Flour  in  barrels 60 

Flour  in  bags 44-50 

Flour  bags,  Triest 52 

Forges,  portable,  carefully  packed 60 

Freestones 16 

Fruit: 

Currants 50 

Lemons 85 

Melons 80 

Onions 78 

Oranges,  boxes 90 

Raisins 52 

Fuel,  patent 30-35 

Fuel,  oil 39-40 

Furs,  skins,  in  cases 130 

Ginger 80 

Glass,  bottles 85 

Glass,  plate,  in  cases  (uncertain) 41 

Glassware  in  cases 110-200 

Glass  in  crates 130 

Granite,  stone 14 

Granite  dressed,  in  block 16 

Granite  in  cases 19 

Gravel,  coarse 23 

Grease 65 

Grindstones 57 

Guano 42 

Gum 50 

Gunny  bags 50 

Gunnies,  hard-pressed 48 

Gunnies,  ordinarily  pressed 57 

Gunpowder 50 

Hair,  pressed  horse 140-175 

Hair,  ordinary  horse 225 

Hair,  unpressed 360 


Stowages  of  Merchandise  715 

STOWAGES    OF   MERCHANDISE.  —  (Continued.) 

Cubic  Feet 
per  Ton. 

Hay  compressed 105-125 

Hay  uncompressed 140 

Hams,  smoked,  in  barrels 70 

Hemp  in  bales,  Manila 73 

Hemp  in  bales,  Calcutta 57 

Hemp,  American  and  New  Zealand 106 

Hemp  in  bales,  Italian 268 

Hemp  seed  in  bags 70 

Herrings,  cured,  in  barrels 60 

Herrings,  salted 45 

Herrings,  kippered  in  boxes 85 

Hides  in  bales,  dried  and  pressed 75-86 

Hides  in  barrels,  salted 50 

Hides  (dried  skins)  in  bales 120 

Hops  in  bales 260 

Horns  and  hoofs 90-95 

Ice 39 

India  rubber,  raw,  well-packed 68-70 

Indigo  in  cases 62-66 

Iron,  pig,  well-stowed 10 

Iron,  corrugated  galvanized  sheets 36 

Iron,  kegs  of  steel 21 

Ivory,  well-packed  loose 28 

Jaggery,  damp,  dirty  sugar 34 

Jute 58 

Kaolin,  China  clay,  in  bags 40 

Lard 70 

Lard  stearine,  in  bags 52 

Lead,  pig 8 

Lead,  pipes,  variable 12 

Leather  in  rolls 224 

Leather  in  bales 90 

Leather,  tannery  waste,  in  bales 185 

Lemons  (see  Fruit) 

Lemon  peel  in  casks 65 

Linseed  in  bags 56-57 

Locust  beans  in  bulk 80-84 

Logwood  in  bundles 92 

Madder 75 

Manure,  phosphate 46 

Manure,  manufactured 40 

Maize  in  bags 49-52 

Maize  in  bulk 46-50 


716  The  Naval  Constructor 

STOWAGES    OF   MERCHANDISE.  —  (Continued.) 

Cubic  Feet 
per  Ton. 

Marl 28 

Marble 14 

Marble  in  slabs 17 

Margarine  in  tubs 65-70 

Matches 120 

Meat: 

Beef,  American  salt,  in  tierces 52 

Beef,  packed,  frozen 90-95 

Beef,  hung  in  quarters 120-130 

Mutton,  New  Zealand 105-110 

Mutton,  River  plate 115 

Milk,  condensed,  in  cases 45 

Millet  in  bags 44-51 

Mineral  waters  in  cases 70 

Mohair  in  bags 240 

Molasses  in  puncheons 60-70 

Molasses  in  bulk 25£ 

Mother-of-Pearl  shells 45 

Nitrate  of  soda 32 

Nuts,  shelled  almonds,  in  bags 70 

Nuts,  shelled  nuts,  in  casks 80 

Nuts,  shelled  nuts,  in  casks 64 

Brazil  in  barrels 90 

Pistachio  in  cases 72 

Walnuts  in  bales 182 

Oak  logs,  planks  of  50  feet 48 

Oats  in  bags 75-80 

Oats  in  bulk 61 

Oatmeal  in  sacks 65 

Oil,  lubricating,  in  casks 60 

Oil,  sperm,  in  barrels 55 

Oil,  vegetable * 66 

Oil  in  bottles  and  baskets 96 

Oil  in  drums 49 

Oil  in  bottles,  in  cases 75 

Oil  in  large  drums 40 

Oil  cake  in  bags 46 

Oil  cake  in  bags,  East  Indian 60 

Oil  cake  in  bags,  Mediterranean 54 

Olives  in  casks 68 

Onions  in  cases 78 

Onions  in  bags 75 

Opium  in  chests 96 


Stowages  of  Merchandise  717 

STOWAGES    OF   MERCHANDISE.  —  (Continued.) 

Cubic  Feet 
per  Ton. 

Oysters  in  barrels 60 

Paint  in  drums 16 

Paper  in  rolls 120 

Peas  in  bags 50 

Phosphate  of  lime 42 

Pineapple,  tinned,  in  cases 60 

Pitch  in  barrels 45 

Potatoes  in  bags 55 

Potatoes  in  barrels 68 

Prunes  in  casks 52 

Quebrach 48 

Rum  in  bottles  and  cases 66 

Rape  seed 61 

Rice  in  bags 45-50 

Rice  meal 62 

Rope. 135 

Rum  in  hogsheads 70 

Rum  in  casks 60 

Rye  in  bags 53 

Sago 55 

Salt  in  bulk 37 

Salt  in  barrels 52 

Saltpetre 36 

Sand,  pit  (building) 22 

Sand,  river 21 

Sandstone 14 

Semolina  in  bags 60 

Sewing  machines  in  cases 81 

Shellac 83 

Shingle,  clean 24 

Silk,  bales 100-128 

Silk  in  cases 110-112 

Slate. 13 

Slates  in  cases 24 

Soap  in  boxes 46 

Soda  in  bags 57 

Soda  in  casks 54 

Sponge 152 

Starch  in  cases 80 

Stone  cargoes: 

Bath 16-17 

Braigleith 15 

Dundee 13| 


718  The   Naval   Constructor 

STOWAGES    OF   MERCHANDISE.  —  (Continued.) 

Cubic  Feet 
per  Ton. 

Stone  cargoes: 

Granite,  Quincy 15 

Limestone,  marble  and  purbeck 13J 

Portland  stone 17 

Welsh  slate 13 

Paving  stone 15 

Sugar,  grape,  in  boxes 42 

Sugar,  Alexandria,  in  bags 46 

Sugar  in  casks 60 

Sugar  in  hogsheads 54 

Sugar,  refined,  in  bags 48 

Sugar,  ordinary,  in  bags 39-40 

Sugar,  raw,  in  baskets 50 

Sugar,  candy 54 

Sulphur  in  bulk 27 

Sulphur  in  cases 40 

Sulphur  in  kegs 60 

Sumac  in  bags 70 

Syrup 34 

Tallow  in  hogsheads 70 

Tallow  in  barrels  and  tierces 58 

Tamarinds  in  cases 40-47 

Tamarinds  in  casks  or  kegs 54 

Tan  extract .  . 48 

Tapioca 57 

Tar  in  barrels 54 

Tares  in  bags 50 

Tares  in  bulk 48 

Tea,  Indian  in  cases 100 

Tea,  China,  in  chests 100 

Ties  (steel  railroad) 22 

Ties  (cast-iron  pot) 37 

Ties  (steel  broad  gauge) 38 

Ties  (oak) 50 

Tiles,  roofing,  in  crates 85 

Tiles,  fire  clay,  in  crates 50 

Tiles,  fire  clay  retorts,  in  bulk 48 

Timber,  flooring  boards 75 

Timber,  oak 39 

Timber,  mahogany 34 

Timber,  ash 39 

Timber,  beech 51 

Timber,  elm 60 


Stowages  of  Merchandise  719 


STOWAGES    OF   MERCHANDISE.  —  (Concluded.) 

Cubic  Feet 
per  Ton. 

Timber,  fir 65 

Timber,  greenheart 34 

Timber,  Baltic  fir,  squared 50 

Timber,  North  American,  fir,  squared 51 

Timber,  deals,  or  battens 50 

Tobacco  in  bales,  Brazil 40 

Tobacco  in  Yokohama 74 

Tobacco,  Turkish,  in  small  bales 150 

Tumeric 65-80 

Turpentine  in  barrels 60 

Vermicelli 110 

Waste  (see  Cotton) 

Water,  fresh 36 

Water,  salt 35 

Wheat  in  bags 52 

Wheat  in  bulk 46-48 

Whitening  in  casks 39 

Wool  in  sheets 260 

Wool,  New  Zealand,  dumped  and  greasy 84 

Wool,  New  Zealand,  scoured 100 

Wool,  Australian,  undumped 236 

Wool,  Cape  of  Good  Hope,  in  bales  pressed, 

scoured 280 

Wool,  Australian,  in  bales 100 

Wool,  Australian,  in  double  bales 113 

Wool,  Mediterranean,  in  bales  half  pressed  and 

corded 200 

Wool,  Spanish  bales,  unpressed 212 

Wool  in  bales,  hydraulic  pressed 100 

Wool  in  bales,  pressed  wool  waste 75 


720 


The  Naval   Constructor 


COLD    STORAGE    TEMPERATURES    IN    DEGREES 
FAHRENHEIT. 


Ale 

Apples 

Apple  and  peach  butter 

Asparagus 

Bananas 

Beans 

Beef  (fresh) 

Beer  in  casks 

Beer  in  bottles 

Berries,  fresh 

Buckwheat  flour 

Butter 

Butterine 


Cantaloupes 

Carrots 

Celery 

Cheese 

Chestnuts 

Chocolate  to  cool. 

Cider 

Cigars 

Clarets 

Corn  meal 

Cranberries 

Cream 

Cucumbers 

Currants 

Dates 

Eggs 

Ferns 


Fish  (fresh) 

Fish  (frozen) 

Fish  (canned) .... 

Fish  (dried) 

Fish  (to  freeze) . . . 

Flour 

Fruits... 

Fruits  (dried) 

Fruits  (canned) .  . 
Furs  (dressed) .  .  . 
Furs  (undressed) . 


33-42      Grapes 

32-36      Ginger  ale 

40  Hams 

33-35      Hogs 

34-35      Hops.. 

32-40      Hops  (frozen) 

35-39      Honey 

32-42      Lard 

45  Lemons 

35-40      Liver 

40-42  Maple  syrup  and  sugar 

14-38      Margarine 

20-35      Meat  (brined) 

32-35      Meat  (canned) 

40  Meat  (fresh) 

33-35      Melons 

32-35      Milk 

28-35      Mutton 

33-40      Mutton  (frozen) 

40  Nuts  in  shell 

32-40      Oatmeal 

35-42      Oleomargarine 

45-50      Oil 

42  Onions 

32-36      Oysters  in  tubs 

35  Oysters  in  shells 

38-40      Oxtails 

32  Parsnips 

45-55      Peaches 

30-35      Pears 

28  Plums 

35-55      Porter 

20-30      Pork 

14-17      Potatoes 

35  Poultry  (frozen) 

35-40  Poultry  (to  freeze) .... 

5  Poultry  (long  storage) . 

36-46      Sardines 

26-55      Sauerkraut 

35-40      Sausage  casings 

30-35      Sugar 

25-32      Syrup 

35  Tenderloin 


32-40 
35-36 
20-35 
30-35 
32-40 
28 

36-45 
34-35 
33-45 
30 

40-45 
18-35 
35-40 
30-35 
34-40 
35 
32 

33-36 
25-28 
35-40 
40-42 
20-35 
35-45 
32-40 
25-35 
33-43 
32 

32-35 
34-55 
40-45 
32-40 
33-42 
34 

34-40 
20-30 
5-22 
10 

35-40 
35-38 
30-35 
40-45 
35-45 
30-35 


Distance  in   Nautical    Miles 


721 


COLD   STORAGE  TEMPERATURES.  —  (Continued.) 

omatoes 32-42      Watermelons 34-40 

bbacco 35-42      Wheat  Flour 40-42 

eal 32-36      Wines 40-50 

egetables 34-40      Woolens 25-35 


HE   DISTANCE  IN   NAUTICAL   MILES   BETWEEN 
COLON  AND 


Miles. 

Acapulco 1426 

Antofagasta 2140 

Bahia 3928 

Baltimore 1903 

Boston 2144 

Buenos  Aires 5768 

Callao 1346 

Caracas 841 

Cartagena 281 

Cayenne 1930 

Charleston 1566 

Desterro 4925 

Galveston 1499 

Georgetown 1864 

Guayaquil 793 

Halifax 2570 

Havana... 1007 

Iquique 1987 

Jacksonville 1518 

Juneau 4945 

Key  West 1070 

Kingston 546 

Les  Cayes 647 

Liverpool 4548 

Manzanillo 1760 

Mazatlan 2060 

Montevideo 5646 


Miles. 

New  Orleans 1395 

New  York 1970 

Norfolk 1781 

Para 2629 

Parahiba 3250 

Paramaribo 1750 

Pernambuco 3529 

Philadelphia 1949 

Port  au  Prince ....  774 

Portland 3895 

Quebec 3295 

Rio  de  Janeiro ....  4609 

Sabanilla 315 

St.  Thomas 1029 

Salina  Cruz 1170 

San  Diego 2843 

San  Francisco 3245 

San  Salvador 840 

Savannah 1565 

Seattle 4076 

Sitka 4547 

Tampico 1491 

Valdivia 2983 

Valparaiso 2616 

Vera  Cruz 1426 

Victoria,  B.  C 4154 


Section  VII. 

MATHEMATICAL  TABLES. 


(Reproduced  by  permission  of  Messrs.  Lippincott  from 
"  Suplee's  Mechanical  Engineers  Reference  Book.") 


723 


The  Metric  System. 


725 


THE   METRIC   SYSTEM. 


The  principal  advantage  of  the  metric  system  consists  in  its  use  of  the 

decimal  subdivisions.    The  attempt  to  consider  the  metre  as of 

10,000,000 
a  quadrant  of  the  earth's  surface  has  been  abandoned,  and  it  is  now  held 
only  to  be  the  length  of  the  standard  known  as  the  Metre  des  Archives, 
copies  of  which  are  issued  by  the  Bureau  Internationale  des  Poids  et  M&sures, 
at  Breteuil,  near  Paris. 

The  kilogramme  was  originally  intended  to  be  the  weight  of  a  cubic 
decimetre  or  litre  of  pure  water  at  the  temperature  of  maximum  density, 
but  it  is  really  now  considered  only  as  the  weight  of  a  platinum  standard. 
At  the  same  time,  this  relation  between  the  unit  of  weight  and  a  standard 
volume  of  water  is  sufficiently  close  for  the  specific  gravity  of  any  sub- 
stance to  be  considered  as  equal  to  the  weight  of  a  cubic  decimetre  of  that 
substance.  In  all  hydraulic  measurements  a  cubic  metre  of  water  is  equal 
in  weight  to  the  metric  tonne  of  1000  kilogrammes,  a  most  convenient  fact 
in  the  determination  of  the  power  developed  by  a  given  fall  and  volume 
of  water, 

The  French  Metrical  System. 


The  French  units  of  weight,  measure,  and 
feet  decimal  system,  except  those  of  time  and 
multiplication  of  the  units  are  expressed  by 
follows : 

Latin,  Division. 
Milli  =  1000th  of  the  unit.  Deca 

Centi  =  100th  of  the  unit.  Hecato 

Deci  =  10th  of  the  unit.  Kilio 

Metre,     litre,     stere,     are,     franc,    Myrio 
gramme. 


coin  are  arranged  into  a  per- 
the  circle.  The  division  and 
Latin  and  Greek  names,  as 

Greek,  Multiplication. 
=  10  times  the  unit. 
=  100  times  the  unit. 
=  1000  times  the  unit. 
=  10000  times  the  unit. 


French  Measure  of  Length. 


1  millimetre     =    0.03937  inch. 
1  centimetre     =   0.3937  inch. 
1  decimetre      =»   3.937  inches. 
1  metre  (unit)  =  39.37  inches. 
1  sea  mile         =  1853.25  metres. 
1  kilometre      =■  0.53959  sea  mile. 


1  metre  (unit)  =       3.28083  feet. 
1  decametre     =     32.8083  feet. 
1  hectometre    =   328.083  feet. 
1  kilometre       =  3280.83  ft.  =  0.62137 
mile. 
1  statute  mile  =       1.60935  kilomets. 
1  kilometre       =     49.7096  chains. 


French  Measure  of  Surface. 

1  square  metre  =  10.764  square  feet. 
1  are  =  100  square  metres, 

1  decare  =  10  ares. 

1  hectare  =  100  ares. 


1  are  =  1076.4  square  feet. 

1  decare  =   107.64  square  feet. 

1  hectare         =       2.471  Eng.  acres. 
1  square  mile  =  259  hectares. 


French  Measure  of  Volume. 


l8S(cubic}=10decMtere8. 

1  stere  =  1000  litres. 

1  litre  =  1  cubic  decimetre. 

1  decistere  =  3.5314  cubic  feet. 


1  stere 
1  litre 
1  gallon 
1  decistere 


35.314  Eng.  cubic  feet. 
61.023  Eng.  cub.  inches. 

3.7854  litres. 

2.838  bushels  (nearly). 


French  Measure  of  Weight. 


lton 


1  cubic  metre  dis- 
tilled water. 

1000  kilogrammes. 

1000  grammes. 

100  grammes. 

10  grammes. 

1  cubic  centimetre 
distilled  water. 
1  French  ton      —  0.9842  Eng.  ton. 


1  ton 

1  kilogramme 
1  hectogramme 
1  decagramme 
1  gramme 


1  gramme 
1  decigramme  ■ 
1  centigramme  = 
1  kilogramme   = 

1  Eng.  pound    ■ 

1  gramme 

1  English  ton    = 


10  decigrammes. 
10  centigrammes. 
10  milligrammes. 
2.20462  pounds  av- 
oirdupois. 

0.45359  kilograms. 
15.43  grains  trov. 

1.016  French  tons. 


726 


The  Metric  System. 


Conversion  of  English  Inches  into  Centimetres. 

Inches. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Cm. 

Cm. 

Cm. 

Cm. 

Cm. 

Cm. 

Cm. 

Cm. 

Cm. 

Cm. 

0 

0.000 

2.540 

5.080 

7.620 

10.16 

12.70 

15.24 

17.78 

20.32 

22.86 

10 

25.40 

27.94 

30.48 

83.02 

35.56 

38.10 

40.64 

43.18 

45.72 

48.26 

20 

50.80 

53.34 

55.88 

58.42 

60.% 

63.50 

66.04 

68.58 

71.12 

73.66 

30 

76.20 

78.74 

81.28 

83.82 

86.36 

88.90 

91.44 

93.98 

96.52 

99.06 

40 

101.60  104.14 

106.68 

109.22 

111.76 

114.30 

116.84 

119.38 

121.92 

121,16 

50 

127.00  129.54 

132.08 

134.62 

137.16 

139.70 

142.24 

144.78 

147.32 

149.86 

60 

152.40 

154.94 

157.48 

160.02 

162.56 

165.10 

167.64 

170.18 

172.72 

175.26 

70 

17730 

180.34 

182.88 

185.42 

187.96 

190.50 

193.01 

195.58 

198.12 

200.% 

80 

203.20 

205.74 

208.28 

210.82 

213.36 

215.90 

218.44 

220.98 

223.52 

226.06 

90 

228.60 

231.14 

233.68 

236.22 

238.76 

241.30 

243.84 

246.38 

248.92 

251.46 

100 

254.00 

256.54 

259.08 

261.62 

264.16 

266.70 

269.24 

271.78 

274.32 

276.85 

Conversion  of  Centimetres  Into  English  Inches. 

Cm. 

0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

0 

0.000 

0.394 

0.787 

1.181 

1.575 

1.969 

2.362 

2.756 

3.150 

3.543 

10 

3.937 

4.331 

4.742 

5.118 

5.512 

5.9% 

6.299 

6.693 

7.087 

7.480 

20 

7.874 

8.268 

8.662 

9.055 

9.449 

9.843 

10.236 

10.630 

11.024 

11.418 

30 

11.811 

12.205 

12.599 

12.992 

13.386 

13.780 

14.173 

14.567 

14.%1 

15.355 

40 

15.748 

16.142 

16.536 

16.929 

17.323 

17.717 

18.111 

18.504 

18.898 

19.292 

50 

19.685 

20.079 

20.473  20.867 

21.260 

21.654 

22.048 

22.441  22.835 

23.229 

60 

23.622 

24.016 

24.410 

24.804 

25.197 

25.591 

25.985 

26.378;  26.772 

27.166 

70 

27.560 

27.953 

28.347 

28.741 

29.134 

29.528 

29.922 

30.316!  30.709 

31.103 

80 

31.497 

31.8% 

32.284 

32.678 

33.071 

33.465 

33.859 

34.253  34.646 

35.040 

90 

35.434 

35.827 

36.221 

36.615 

37.009 

37.402 

37.7% 

38.1%  38.583 

38.977 

100 

39.370 

39.764 

40.158 

40.552 

40.945 

41.339 

41.733 

42.126  42.520 

42.914 

Conversion  of  English  Feet  into  Metres. 

Feet. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

0 

0.0% 

0.3048 

0.60% 

0.9144 

1.2192 

1.5239 

1.8287 

2.1335 

2.4383 

2.7431 

10 

8.0479 

3.3527 

3.6575 

3.%23 

4.2671 

4.5719 

4.8767 

5.1815 

5.4863 

5.7911 

20 

6.0359 

6.40% 

6.7055 

7.0102 

7.3150 

7.6198 

7.9246 

8.2294 

8.5342 

8.83% 

30 

9.1438 

9.4486 

9.7534 

10.058 

10.363 

10.668 

10.972 

11.277 

11.582 

11.887 

40 

12.192 

12.4% 

12.801 

13.1% 

13.411 

13.716 

14.020 

14.325 

14.630 

14.935 

60 

15.239 

15.544 

15.849 

16.154 

16.459 

16.763 

17.068 

17.373 

17.678 

17.983 

60 

18.287 

18.592 

18.897 

19.202 

19.507 

19.811 

20.116 

20.421 

20.726 

21.031 

70 

21.335 

21.640 

21.945 

22.250 

22.555 

22.859 

23.164 

23.469 

23.774 

24.079 

80 

24.383 

24.688 

24.%3 

25.298 

25.602 

25.%7 

26.212 

26.517 

26.822 

27.126 

% 

27.431 

27.736 

28.041 

28.346 

28.651 

28.955 

29.260J  29.565 

29.870 

30.174 

1% 

30.479 

30.784 

31.089 

31.394 

31.698 

32.%3 

32.308 

32.613 

32.918 

33.222 

Conversion  of  Metres  into  English  Feet. 

Metres. 

0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

0 

0.0% 

3.2809 

6.5618 

9.8427 

13.123 

16.404 

19.685 

22.%6 

26.247 

29.528 

10 

32.809 

36.0% 

39.371 

42.651 

45.932 

49.213 

52.494 

55.775 

59.056 

62.337 

20 

65.618 

68.899 

72.179 

75.461 

78.741 

82.022 

85.303 

88.584 

91.865 

95.146 

30 

98.427 

101.71 

104.99 

108.27 

111.55 

114.83 

118.11 

121.39 

124.67 

127.96 

40 

131.24 

134.52 

137.80 

141.08 

144.36 

147.64 

150.92 

154.20 

157.48;  160.76 

50 

164.04 

167.33 

170.61 

173.89 

177.17 

180.45 

183.73 

187.01 

1%.29I  193.57 

60 

1%.85 

2%.  13 

203.42 

2%.70 

209.98 

213.26 

216.54 

219.82 

223.101 226.38 

70 

229.66 

232.94 

236.22 

239.51 

242.79 

246.07 

249.35 

252.63 

255.91  259.19 

80 

262.47 

265.75 

269.03 

272.31 

275.60 

278.88 

282.16 

285.44 

288.72:  292.00 

% 

295.28 

298.56 

301.84 

305.12 

308.40 

311.69 

314.97 

318.25 

321. 53 j  324.81 

1% 

328.09 

331.37 

334.65 

337.931 341,21 

344.49 

347.78 

351.% 

354.34  357.  j2 

The  Metric  System. 


727 


Conversion  of  English  Statute 

-mile 

i  Into  Kilometres. 

Miles. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

0 

0.0000 

1.6093 

3.2186 

4.8279 

6.4372 

8.0465 

9.6558 

11.2652 

12.8745 

14.4848 

10 

16.093 

17.702 

19.312 

20.921 

22.530 

24.139 

25.749 

27.358 

28.967 

30.577 

20 

32.186 

33.795 

35.405 

37.014 

38.623 

40.232 

41.842 

43.451 

45.060 

46.670 

80 

48.279 

49.888 

51.498 

53.107 

54.716 

56.325 

57.935 

59.544 

61.153 

62.763 

40 

64.372 

65.981 

67.591 

69.200 

70.809 

72.418 

74.028 

75.637 

77.246 

78.856 

50 

80.465 

82.074 

83.684 

85.293 

86.902 

88.511 

90.121 

91.730 

93.339 

94.949 

60 

96.558 

98.167 

99.777 

101.39 

102.99 

104.60 

106.21 

107.82 

109.43 

111.04 

70 

112.65 

114.26 

115.87 

117.48 

119.08 

120.69 

122.30 

123.91 

125.52 

127.13 

80 

128.74 

130.35 

131.96 

133.57 

135.17 

136.78 

138.39 

140.00 

141.61 

143.22 

90 

144.85 

146.44 

148.05 

149.66 

151.26 

152.87 

154.48 

156.09 

157.70 

159.31 

100 

160.93 

162.53 

164.14 

165.75 

167.35 

168.96 

170.57 

172.18 

173.79 

175.40 

Conversion  of  Kilometres  into  English  Statute-miles. 

Kilom. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Miles. 

Miles. 

Miles. 

Miles. 

Miles. 

Miles. 

Miles. 

Miles. 

Miles. 

Miles. 

0 

0.0000 

0.6214 

1.2427 

1.8641 

2.4855 

3.1069 

3.7282 

4.3497 

4.9711 

5.5924 

10 

6.2138 

6.8352 

7.4565 

8.0780 

8.6994 

9.3208 

9.9421 

10.562 

11.185 

11.805 

20 

12.427 

13.049 

13.670 

14.292 

14.913 

15.534 

16.156 

16.776 

17.399 

18.019 

30 

18.641 

19.263 

19.884 

20.506 

21.127 

21.748 

22.370 

22.990 

23.613 

24.233 

40 

24.855 

25.477 

26.098 

26.720 

27.341 

27.962 

28.584 

29.204 

29.827 

30.447 

50 

31.069 

31.690 

32.311 

32.933 

33.554 

34.175 

34.797 

35.417 

36.040 

36.660 

60 

37.282 

37.904 

38.525 

39.147 

39.768 

40.389 

41.011 

41.631 

42.254 

42.874 

70 

43.497 

44.118 

44.739 

45.361 

45.982 

46.603 

47.225 

47.845 

48.468 

49.088 

80 

49.711 

50.332 

50.953 

51.575 

52.196 

52.817 

53.439 

54.059 

54.682 

55.302 

90 

55.924 

56.545 

57.166 

57.788 

58.409 

59.030 

59.652 

60.272 

60.895 

61.515 

100 

62.138 

62.759 

63.380 

64.002 

64.623 

65.244 

65.866 

66.486 

67.109 

67.729 

Conversion  of  Sea-miles  into  Kilometres. 

Sea-miles. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

0 

0.0000 

1.8532 

3.7046 

5.5596 

7.4128 

9.2660 

11.119 

12.972 

14.825 

16.788 

10 

18.532 

20.386 

22.237 

24.128 

25.945 

27.798 

29.6M 

31.504 

33.357 

35.320 

20 

37.064 

38.918 

40.769 

42.660 

44.477 

46.331 

48.183 

50.036 

51.889 

53.852 

30 

55.596 

57.450 

59.301 

61.192 

63.009 

64.863 

66.715 

68.568 

70.421 

72.384 

40 

74.128 

75.982 

77.833 

79.724 

81.541 

83.396 

85.247 

87.100 

88.953 

90.916 

50 

92.660 

94.514 

96.365 

98.256 

100.07 

101.92 

103.78 

105.63 

107.48 

109.45 

60 

111.19 

113.05 

114.90 

116.79 

118.61 

120.45 

122.21 

124.16 

126.01 

127.98 

70 

129.72 

131.58 

133.43 

135.32 

137.14 

139.98 

140.74 

142.69 

144.54 

146.51 

80 

148.25 

150.11 

151.96 

153.85 

155.67 

157.52 

159.27 

161.22 

163.07 

165.04 

90 

166.78 

168.64 

170.49 

172.38 

174.20 

176.05 

177.80 

179.75 

181.60 

183.57 

100 

185.32 

187.18 

189.03 

190.88 

192.73 

194.58 

196.44 

198.28 

200.14 

201.99 

Conversion  of  Kilometres  into  Sea-miles. 

Kilom. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Sea-m. 

Sea-m. 

Sea-m. 

Sea-m. 

Sea-m. 

Sea-m. 

Sea-m. 

Sea-m. 

Sea-m. 

Sea-m. 

0 

0.0000 

0.5396 

1.0792 

1.6188 

2.1584 

2.6880 

3.2375 

3.7771 

4.3167 

4.8563 

10 

5.3959 

5.9356 

6.4751 

7.0147 

7.5543 

8.0839 

8.6334 

9.1730 

9.7126 

10.252 

20 

10.792 

11.331 

11.870 

12.410 

12.950 

13.480 

14.029 

14.568 

15.108 

15.647 

30 

16.188 

16.727 

17.265 

17806 

18.345 

18.876 

19.424 

19.965 

20.504 

21.044 

40 

21.584 

22.123 

22.661 

23.202 

23.740 

24.271 

24.819 

25.360 

25.900 

26.439 

50 

26.980 

27.519 

28.059 

28.598 

29.135 

29.667 

30.214 

30.757 

31.296 

31.835 

60 

32.375 

32.915 

33.456 

33.994 

34.530 

35.063 

35.609 

36.151 

36.692 

37.231 

70 

37.771 

38.310 

38.852 

39.390 

39.925 

40.459 

41.004 

41.574 

42.088 

42.627 

80 

43.167 

43.705 

44.284 

44.786 

45.320 

45.855 

46.399 

46.943 

47.483 

48.023 

90 

48.563 

49.103 

49.644 

50.182 

50.715 

51.251 

51.794 

52.339 

52.879 

53.419 

100 

53.959 

54.498 

55.038 

55.575 

56.117 

56.658 

57.198 

57.737 

58.275 

58.816 

728 


The  Metric  System. 


Conversion  of  Square  Inches  into  Square  Centimetres. 

Square  in. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Cm2. 

Clll2. 

Cm2. 

Cm2. 

Cm2. 

Cms. 

Cm2. 

Cm2. 

Cm*. 

Cm2. 

0 

0.0000 

6.4515 

12.903 

19.354 

25.806 

32.257 

38.709 

45.160 

51.612 

58.063 

10 

64.515 

70.967 

77.418 

83.869 

90.321 

96.772 

103.22 

109.67 

116.12 

122.67 

20 

129.03 

135.48 

141.93 

148.38 

1.54.83 

161.29 

167.74 

174.19 

180.64 

187.09 

30 

193.54 

199.99 

20(5.44 

212.89 

219.34 

225.80 

231.25 

238.70 

245.15 

251.60 

40 

258.06 

264.51 

270.% 

277.41 

283.86 

290.32 

296.77 

303.22 

309.07 

316.12 

50 

322.57 

329.02 

886.47 

341.92 

348.37 

351.83 

361.28 

867.78 

374.18 

3.80.(53 

60 

387.09 

393.54 

399.99 

406.44 

412.89 

419.35 

425.80 

432.25 

438.70 

445.15 

70 

451.60 

4.58.05 

464.50 

470.95 

477.40 

483.86 

490.31 

496.76 

503.21 

509.66 

80 

516.12 

522.57 

529.02 

535.47 

541.92 

548.38 

554.83 

561.28 

567.73 

574.18 

90 

580.63 

587.08 

593.53 

599.98 

606.43 

612.89 

619.34 

625.79 

632.24 

638.69 

100 

645.15 

651.60 

658.05 

664.50 

670.95 

677.41 

683.86 

690.31 

696.76 

703.21 

Conversion  of  Square  Centimetres  into  Square  Inches. 

Square  cm. 

0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

In2. 

In2. 

In2. 

In2. 

In2. 

In*. 

In*. 

In*. 

In**, 

In2. 

0 

0.0000 

0.1550 

0.3100 

0.4650 

0.6200 

0.7750 

0.9300 

1.0850 

1.2400 

1.3950 

10 

1.5500 

1.7050 

1.8600 

2.0150 

2.1700 

2.3250 

2.4800 

2.6350 

2.7900 

2.9450 

20 

3.1000 

3.2550 

3.4100 

3.5650 

3.7200 

3.8750 

4.0300 

4.1850 

4.3400 

4.4950 

30 

4.6501 

4.8051 

4.9601 

5.1151 

5.2701 

5.4251 

5.5801 

5.7351 

5.8901 

6.0451 

40 

6.2001 

(5.3551 

6.5101 

6.6651 

6.8201 

6.9751 

7.1301 

7.2851 

7.4401 

7.5951 

50 

7.7501 

7.9051 

8.0601 

8.2151 

8.3701 

8.5251 

8.6801 

8.8351 

8.9901 

9.1451 

60 

9.3002 

9.4552 

9.6102 

9.7652 

9.9202 

10.075 

10.230 

10.385 

10.540 

10.695 

70 

10.850 

11.040 

11.160 

11.315 

11.470 

11.625 

11.780 

11.935 

12.090 

12.245 

80 

12.400 

12.555 

12.710 

12.865 

13.020 

13.175 

13.330 

13.485 

13.640 

13.795 

90 

13.9.50 

14.105 

14.260 

14.415 

14.570 

14.725 

14.880 

15.035 

15.190 

15.345 

100 

15.500 

15.655 

15.810 

15.965 

16.120 

16.275 

16.430 

16.585 

16.740 

16.895 

Conversion  of  Cubic  Inches  Into  Cubic  Centimetres. 


Cubic  in. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Cm3. 

Cm3. 

Cms. 

Cm3. 

Cm3. 

Cm3. 

Cm3. 

Cm3. 

Cm3. 

Cm3. 

0 

0.0000 

16.383 

32.773 

49.160 

65.546 

81.933 

98.320 

114.71 

131.01 

147.48 

10 

163.87 

180.26 

196.64 

213.03 

229.41 

245.80 

262.19 

278.58 

294.88 

311.35 

20 

327.73 

344.12 

360.50 

376.89 

393.27 

409.66 

426.05 

442.44 

458.74 

475.21 

30 

491.60 

507.99 

524.37 

540.76 

557.14 

573.53 

569.92 

606.31 

622.61 

639.08 

40 

655.46 

671.85 

688.23 

704.52 

721.00 

737.39 

753.78 

770.17 

786.47 

802.94 

50 

819.33 

835.72 

851.10 

868.49 

884.87 

901.26 

917.65 

934.04 

950.34 

966.81 

60 

983.20 

999.59 

1016.0 

1032.4 

1048.7 

1065.1 

1081.5 

1097.9 

1114.2 

1130.7 

70 

1147.1 

1163.5 

1179.9 

1196.3 

1212.6 

1229.0 

1245.4 

1261.8 

1278.1 

1294.6 

80 

1310.9 

1327.3 

1343.7 

1360.1 

1376.4 

1392.8 

1409.2 

1425.6 

1441.9 

1458.4 

90 

1474.8 

1491.2 

1507.6 

1524.0 

1540.3 

1556.7 

1573.1 

1589.51 1605.8 

1622.3 

100 

1638.7 

1655.1 

1671.5 

1687.9 

1704.2 

1720.6 

1737.0 

1753.4  1769.7 

1786.2 

Conversion  of  Cubic  Centimetres  into  Cubic  Inches. 


Cubic  cm. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

IU3. 

In3. 

In». 

In3. 

In3. 

In3. 

Ia» 

In3. 

ft3. 

In3. 

0 

0.0000 

0.0610 

0.1221 

0.1831 

0.2441 

0.3051 

0.3661 

0.4272 

0.4882 

0.5492 

10 

0.6102 

0.6712 

0.7323 

0.7933 

0.8543 

0.9153 

0.9763 

1.0374 

1.0984 

1.1594 

20 

1.2205 

1.2815 

1.3426 

1.4036 

1.4646 

1.5256 

1.5866 

1.6477 

1.7087 

1.7697 

30 

1.8308 

1.8918 

1.9529 

2.0139 

2.0749 

2.1&59 

2.1969 

2.2580 

2.3190 

2.3800 

40 

2.4410 

2.5020 

2.5631 

2.6241 

2.6851 

2.7461 

2.8071 

2.8682 

2.9292 

2.9902 

50 

3.0513 

3.1123 

3.1734 

3.2344 

3.2954 

3.3564 

3.4174 

3.4785 

3.5395 

3.6005 

60 

3.6615 

3.7225 

3.7836 

3.8446 

3.9056 

3.9666 

4.0276 

4.0887 

4.1497  4.2107 

70 

4.2718 

4.3328 

4.3939 

4.4549 

4.5159 

4.5769 

4.6379 

4.6990 

4.7600 

4.8210 

80 

4.8826 

4.9430 

5.0041 

5.0651 

5.1261 

5.1871 

5.2481 

5.3092 

5.3702 

5.4312 

90 

5.4923  5.5533 

5.6144 

5.6754  5.7364 

5.7974 

5.8584 

5.9195 

5.9805 

6.0415 

100 

6.1025 

6.1635 

6.2246 

6.2856 

6.3466 

6.4076 

6.4686 

6.5297 

6.5907 

6.6517 

Thei  Metric  System. 


729 


Conversion  of  Cubic  Yards  into  Cubic  Metres 

. 

Cubic  yds. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Met3. 

Met3. 

Met3. 

Met3. 

Met3. 

Met3. 

Met3. 

Met3. 

Met3. 

Met*. 

0 

0.0000 

0.7645 

1.5291 

2.2936 

3.0581 

3.8226 

4.5872 

5.3517 

6.1163 

6.8808 

10 

7.6453 

8.4098 

9.1744 

9.9389 

10.703 

11.468 

12.232 

12.997 

13.761 

14.526 

20 

15.291 

16.055 

16.820 

17.585 

18.349 

19.114 

19.878 

20.643 

21.407 

22.172 

30 

22.936 

23.700 

24.455 

25.230 

25.994 

26.759 

27.523 

28.288 

29.052 

29.817 

40 

30.581 

31.345 

32.110 

32.875 

33.639 

34.404 

35.168 

35.933 

36.797 

37.462 

50 

38.226 

38.990 

39.755 

40.520 

41.284 

42.049 

42.813 

43.578 

44.342 

45.107 

60 

45.872 

46.636 

47.401 

48.166 

48.930 

49.695 

50.459 

51.224 

51.988 

52.753 

70 

53.517 

54.281 

55.046 

55.811 

56.575 

57.340 

58.104 

58.869 

59.633 

60.398 

80 

61.163 

61.927 

62.692 

63.457 

64.221 

64.986 

65.750 

66.515 

67.279 

68.044 

90 

68.808 

69.572 

70.337 

71.102 

71.866 

72.631 

73.395 

74.160 

74.924 

75.689 

100 

76.453 

77.217 

77.982 

78.747 

79.511 

80.276 

81.040 

81.805 

82.569 

83.334 

Conversion  of  Cubic  Metres  into  Cubic  Yards. 

Cubic  met. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Yds3. 

Yds3. 

Yds3. 

Yds3. 

Yds3. 

Yds3. 

Yds3. 

Yds3. 

Yds3. 

Yds3. 

0 

0.0000 

1.3080 

2.6160 

3.9240 

5.2329 

6.5399 

7.8479 

9.1559 

10.464 

11.772 

10 

13.080 

14.388 

15.696 

17.004 

18.313 

19.620 

20.928 

22.236 

23.544 

24.852 

20 

26.160 

27.468 

28.776 

30.084 

31.393 

32.700 

34.008 

35.316 

36.624 

37.932 

30 

39.240 

40.548 

41.856 

43.164 

44.473 

45.780 

47.088 

48.396 

49.704 

51.012 

40 

52.319 

53.627 

54.935 

56.243 

57.552 

58.859 

60.167 

61.475 

62.783 

63.091 

50 

65.399 

66.707 

68.015 

69.323 

70.632 

71.939 

73.247 

74.545 

75.863 

77.171 

60 

78.479 

79.787 

81.095 

82.403 

83.712 

85.019 

86.327 

87.535 

88.943 

90.251 

70 

91.559 

92.867 

94.175 

95.483 

96.792 

98.099 

99.407 

100.71 

102.02 

103.33 

80 

104.63 

105.94 

107.25 

108.56 

109.87 

111.17 

112.48 

113.79 

115.10 

116.41 

90 

117.72 

119.03 

120.34 

121.64 

122.95 

124.26 

125.57 

126.88 

128.18 

129.49 

100 

130.80 

132.11 

133.42 

134.72 

136.03 

137.34 

138.65 

139.96 

141.26 

142.57 

Conversion  of  U.  S 

Gallons  into  Litres. 

Gallons. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Litres. 

Litres. 

Litres. 

Litres. 

Litres. 

Litrea 

Litrea 

Litrea 

Litrea 

Litrea 

0 

0.0000 

3.7853 

7.5706 

11.356 

15.141 

18.946 

22.712 

26.497 

30.282 

34.068 

10 

37.853 

41.638 

45.423 

49.209 

52.994 

56.799 

60.565 

64.350 

68.135 

71.921 

20 

75.706 

79.491 

83.276 

87.062 

90.847 

94.652 

98.418 

102.20 

105.99 

109.77 

30 

113.56 

117.34 

121.13 

124.92 

128.66 

132.50 

136.27 

140.06 

143.84 

147.63 

40 

151.42 

155.22 

158.99 

162.78 

166.56 

170.36 

174.13 

177.92 

181.70 

185.49 

50 

189.46 

193.24 

197.03 

200.82 

204.60 

208.40 

212.17 

215.96 

219.74 

223.53 

60 

227.12 

230.90 

234.69 

238.48 

242.26 

246.06 

249.83 

253.62 

257.40 

261.19 

70 

264.97 

268.75 

272.54 

276.33 

280.11 

283.91 

286.68 

291.47 

295.25 

299.04 

80 

302.82 

306.60 

310.39 

314.18 

317.96 

321.76 

324.53 

329.32 

333.10 

336.89 

90 

440.68 

444.46 

448.25 

452.04 

455.82 

459.62 

463.39 

467.18 

470.96 

474.75 

100 

478.53 

482.31 

486.10 

789.89 

493.67 

497.47 

501.24 

505.03 

508.81 

512.60 

Conversion  of  Litres  into  U.  S 

.  Gallons. 

Litres. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

Gal. 

0 

0.0000 

0.2642 

0.5284 

0.7925 

1.0567 

1.3209 

1.5851 

1.8492 

2.1134 

2.3776 

10 

2.6418 

2.9060 

3.1702 

3.4343 

3.6985 

3.9627 

4.2269 

4.4910 

4.7552 

5.0194 

20 

5.2836 

5.5478 

5.8120 

6.0761 

6.3403 

6.6045 

6.8687 

7.1328 

7.3970 

7.6612 

^30 

no 

7.9254 

8.1896 

8.4538 

8.7179 

8.9821 

9.2463 

9.5105 

9.8746 

10.030 

10.303 

10.567 

10.831 

11.095 

11.360 

11.624 

11.888 

12.152 

12.416 

12.680 

12.945 

50 

13.209 

13.473 

13.737 

14.002 

14.266 

14.530 

14.794 

15.058 

15.322 

15.587 

60 

15.851 

16.115 

16.379 

16.644 

16.908 

17.172 

17.436 

17.700 

17.964 

18.229 

70 

18.492 

18.756 

19.020 

19.284 

19.549 

19.813 

20.077 

20.341 

20.605 

20.870 

80 

21.134 

21.398 

21.662 

21.926 

22.191 

22.455 

22.719 

22.983 

23.247 

23.512 

90 

23.776 

24.040J  24.304 

24.568 

24.832 

25.097 

25.361 

25.625 

25.889 

26.154 

100 

26.418 

26.682 

26.946 

27.210 

27.475 

27.739 

28.003 

28.267 

28.531 

28.796 

730 


The  Mettiic  System. 


Conversion  of  Yards  into  Metres 

Tarda. 

0 

1 

2 

3 

4  • 

5 

6 

7 

8 

9 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

Met. 

0 

0.0000 

0.9144 

1.8288 

2.7432 

3.6576 

4.5719 

5.4863 

6.4007 

7.3151 

8.2295 

10 

9.1439 

10.058 

10.973 

11.887 

12.801 

13.716 

14.630 

15.544 

16.4.58 

17.373 

20 

18.288 

19.202 

20.117 

21.031 

21.945 

22.860 

23.774 

24.689 

25.603 

26.518 

30 

27.432 

28.346 

29.260 

30.174 

31.088 

32.003 

32.917 

33.832 

34.746 

35.661 

40 

36.576 

37.490 

38.404 

89.818 

40.232 

41.147  42.061 

42.976 

43.890 

44.805 

50 

45.719 

46.634 

47.548 

48.462 

49.376 

50.291 

51.205 

52.120 

68.034 

53.949 

60 

54.863 

55.778 

56.692 

57.606 

58.520 

59.435 

60.349 

61.264 

62.178 

63.093 

70 

64.007 

64.922 

65.886 

66.750 

67.664 

68.578 

69.493 

70.408 

71.322 

72.237 

80 

73.151 

74.066 

71.980 

75.894 

76.808 

77.723 

78.637 

79.552 

80.466 

81.381 

90 

82.295 

83.210 

84.124 

85.0:38 

85.952 

86.867 

87.781 

88.696 

89.610 

90.525 

100 

91.439 

92.353 

93.267 

94.181 

95.095 

96.010 

96.924 

97.839 

98.753 

99.668 

Conversion  of  Metres  into  Yards 

Metres. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Yds. 

Yds. 

Yds. 

Yds. 

Yds. 

Yds. 

Yds. 

Yds. 

Yds. 

Yds. 

0 

0.0000 

1.0936 

2.1872 

3.2809 

4.3745 

5.4681 

6.5617 

7.6553 

8.7490 

9.8426 

10 

10.936 

12.029 

13.122 

14.217 

15.310 

16.404 

17.498 

18.591 

19.685 

20.778 

20 

21.872 

22.966 

24.059 

25.153 

26.247 

27.340 

28.434 

29.527 

30.621 

31.715 

30 

32.809 

33.900 

34.993 

36.090 

37.184 

38.277 

39.371 

40.464 

41.558 

42.652 

40 

43.745 

44.839 

45.932 

47.026 

48.120 

49.213 

50.307 

51.400!  52.544|  53.588 

50 

54.681 

55.775 

56.868 

57.962 

59.056 

60.149 

61.243 

62.336 

63.430 

64.524 

60 

65.617 

66.711 

67.804 

68.898 

69.992 

71.085 

72.179 

73.272 

74.366 

75.460 

70 

76.553 

77.647 

78.740 

79.834 

80.928 

82.021 

83.115 

84.208 

85.302 

86.396 

80 

87.490 

88.584 

89.677 

90.771 

91.865 

92.958 

94.052 

95.145 

96.239 

97.333 

90 

98.426 

99.520 

100.61 

101.71 

102.80 

103.89 

104.99 

106.08 

107.17 

108.27 

100 

109.36J  110.45 

111.55 

112.64 

113.73 

114.83 

115.92 

117.02  118.11 

119.20 

Conversion  of  Square  Yards  into  Square  Metres. 

Sq.  yards. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Met*. 

Mets. 

Met*. 

Met*. 

Met2. 

Met2. 

Met2. 

Met2. 

Met2. 

Met*. 

0 

0.0000 

0.8361 

1.6722 

2.5803 

3.3444 

4.1805 

5.0167 

5.8528 

6.6889 

7.5250 

10 

8.3611 

9.1972 

10.033 

10.941 

11.706 

12.542 

13.378 

14.214 

15.050 

15.886 

20 

16.722 

17.558 

18.394 

19.102 

20.066 

20.903 

21.739 

22.575 

23.411 

24.247 

30 

25.083 

25.919 

26.755 

27.663 

28.431 

29.264 

30.100 

30.936 

31.772 

32.608 

40 

33.444 

34.280 

35.116 

36.024 

36.788 

37.625 

38.461 

39.297 

40.133  40.969 

50 

41.805 

42.641 

43.477 

44.385 

45.149 

45.986 

46.822 

47.658 

48.494149.330 

60 

50.167 

51.003 

51.839 

52.747 

53.511 

54.348 

55.184 

56.020 

56.856 

57.692 

70 

58.528 

59.364 

60.190 

61.108 

61.872 

62.709 

63.545 

64.381 

65.217 

66.053 

80 

66.889 

67.725 

68.561 

69.469 

70.233 

71.070 

71.906 

72.742 

73.578 

74.414 

90 

75.250 

76.086 

76.922 

77.830 

78.594 

79.431 

80.267 

81.103 

81.939 

82.775 

100 

83.611 

84.447 

85.283 

86.191 

86.955 

87.792 

88.628 

89.464 

90.300 

91.136 

Conversion  of  Square  Metres  into  Square  Yards. 

Sq.  metres. 

0 

1 

2 

3          4 

5 

6 

7 

8 

9 

Yds2. 

Yds2. 

Yds2. 

Yds2.  1  Yds2. 

Yds2. 

Yds2. 

Yds2. 

Yds*. 

Yds*. 

0 

0.0000 

1.1960 

2.3920 

3.5880  4.7840 

5.9800 

7.1760 

8.3720 

9.5681 

10.764 

10 

11.960 

13.156 

]  1.352 

15.548  16.744 

17.940 

19.136 

20.332 

21.528  22.724 

20 

23.920 

25.116 

26.312 

27.508 

28.704 

29.900 

31.096 

32.292 

33.488!  34.684 

30 

35.880 

37.076 

38.272;  39.468 

40.664 

41.860 

43.056 

44.252 

45.448  46.644 

40 

47.840 

49.036 

50.232  51.42S 

52.624 

53.820 

55.016 

56.212 

57.408,58.604 

50 

59.800 

60.996 

62.1921  63.388 

63.584 

65.780 

66.976 

68.172 

69.368(70.564 

60 

71.760 

72.956 

74.152  75.348 

76.544 

77.740 

78.936 

80.132 

81.328  82.524 

70 

83.721 

84.917 

86.113 

87.309 

88.505 

89.701 

90.897 

92.093 

93.289  94.485 

80 

95.681 

96.877 

98.073 

99.269 

100.46 

101.66 

102.86 

104.06 

105.25  106.44 
117.21  118.40 

90 

107.64 

108.84  110.03 

111.24 

112.44 

113.62 

114.81 

116.01 

100 

119.60 

120.80 

121.99 

123.19 

124.38 

125.58 

126.77 

127.97 

129.17 

130.36 

The  Metric  System. 


731 


Conversion  of  Hectares  into  Acres 

. 

Hectares. 

0 

1 

2 

3     |     4 

5 

6 

7 

8 

9 

Acres. 

Acres. 

Acres. 

Acres.  Acres. 

Acres. 

Acres. 

Acres. 

Acres. 

Acres. 

0 

0.0000 

2.4711 

4.9422 

7.4133 

9.8844 

12.355 

14.836 

17.298 

19.769 

22.240 

10 

24.711 

27.182 

29.653 

32.124 

34.695 

37.046 

39.547 

42.009 

44.480 

46.951 

20 

49.422 

51.893 

54.364 

56.835 

59.306 

61.757 

64.258 

66.720 

68.191 

71.662 

30 

74.133 

76.604 

79.075 

81.546 

84.017 

86.468 

88.969 

91.431 

93.902 

96.373 

40 

98.844 

101.31 

103.79 

106.26 

108.73 

111.18 

113.68 

116.14 

118.61 

121.08 

50 

123.55 

126.02 

128.49 

130.96 

133.43 

135.88 

138.38 

140.85 

143.32 

145.79 

60 

148.36 

150.83 

153.30 

155.77 

158.24 

160.69 

163.19 

165.66 

168.13 

170.60 

70 

172.95 

175.45 

177.92 

180.39 

182.86 

185.31 

187.81 

190.28 

192.75 

195.22 

80 

197.69 

200.16 

202.63 

205.10 

207.57 

210.02 

212.52 

214.99 

217.46 

219.93 

90 

222.40 

224.87 

227.34 

229.81 

232.28 

234.73 

237.23 

239.70 

242.17 

244.64 

100 

247.11 

249.58 

252.05 

254.52 

256.99 

259.44 

261.94 

264.41 

266.88 

269.35 

Conversion  of  Acres  into  Hectares. 

Acres. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Hect. 

Hect. 

Hect. 

Hect. 

Hect. 

Hect. 

Hect. 

Hect. 

Hect. 

Hect. 

0 

0.0000 

0.4047 

0.8093 

1.2140 

1.6187 

2.0234 

2.4280 

2.8327 

3.2374 

3.6420 

10 

4.0468 

4.4515 

4.8561 

5.2608 

5.6655 

6.0702 

6.4748 

6.8795 

7.2782 

7.6888 

20 

8.0936 

8.4983 

8.9029 

9.3076 

9.7123 

10.117 

10.521 

10.926 

11.331 

11.735 

30 

12.140 

12.545 

12.949 

13.351 

13.759 

14.163 

14.568 

14.973 

15.377 

15.782 

40 

16.187 

16.592 

16.996 

17.401 

17.806 

18.210 

18.615 

19.020 

19.414 

19.829 

50 

20.234 

20.639 

21.043 

21.448 

21.853 

22.257 

22.662 

23.067 

23.471 

23.876 

60 

24.280  24.685 

25.089 

25.494 

25.899 

26.303 

26.708 

27.113 

27.517 

27.922 

70 

28.327 

28.732 

29.136 

29.541 

29.946 

30.350 

30.755 

31.160 

31.564 

31.969 

80 

32.374 

32.779 

33.183 

33.588 

33.993 

34.397 

34.802 

35.207 

35.611 

36.016 

90 

36.420 

36.825 

37.229 

37.634 

38.039 

38.443 

38.848 

39.253 

39.657 

40.062 

100 

40.468 

40.873 

41.277 

41.682 

42.087 

42.491 

42.896 

43.301 

43.695 

44.110 

Conversion  of  Square  Miles  into  Square  Kilometres. 

Sq.  miles. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Kil->. 

Kil2. 

Kil2. 

Kil-!. 

Kil-'. 

KIP. 

Kil2. 

Kil2. 

Kil2. 

Kil2. 

0 

0.0000 

2.5899 

5.1798 

7.7697 

10.359 

12.929 

15.539 

18.129 

20.718 

23.309 

10 

25.899 

28.490 

31.079 

33.669 

36.259 

38.829 

41.439 

44.029 

46.619 

49.209 

20 

51.798 

54.388 

56.978 

59.56S 

62.158 

64.728 

67.338 

69.928 

72.518 

75.108 

30 

77.697 

80.287 

82.877 

85.467 

88.057 

90.627 

93.238 

96.828 

98.417 

101.01 

40 

103.59 

106.18 

108.77 

111.36 

113.95 

116.52 

119.13 

121.72 

124.31 

126.90 

50 

129.29 

131.88 

134.47 

137.06 

139.65 

142.22 

144.83 

147.42 

150.01 

152.50 

60 

155.39 

157.98 

160.57 

163.16 

165.75 

168.32 

170.93 

173.52 

176.11 

178.70 

70 

181.29 

183.88 

186.47 

188.06 

191.65 

194.22 

196.83 

199.42 

202.01 

204.60 

80 

207.19 

209.77 

212.36 

214.95 

217.55 

220.11 

222.73 

225.31 

227.91 

230.50 

90 

233.09 

235.68 

238.27 

240.86 

243.45 

246.02 

248.63 

251.22 

253.81 

256.40 

100 

258.99 

261.58 

264.17 

266.76 

269.35 

271.92 

274.53 

277.12 

279.71 

282.20 

Conversion  of  Square  Kilometres  into  Square  Miles. 

Sq.  kllom. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Sq.  m. 

Sq.  m. 

Sq.  m. 

Sq.  m. 

Sq.  m. 

Sq.  m. 

Sq.  m. 

Sq.  m 

Sq.  m. 

Sq.  m. 

0 

0.0000 

0.3861 

0.7722 

1.1583 

1.5445 

1.9304 

2.3166 

2.7028 

3.0890 

3.4749 

10 

3.8612 

4.2471 

4.6334 

5.0195 

5.4057 

5.7916 

6.1778 

6.5640 

6.9502 

7.3362 

20 

7.7224 

8.1081 

8.4946 

8.8807 

9.2669 

9.6528 

10.039 

10.425 

10.811 

11.197 

30 

11.583 

11.969 

12.355 

12.741 

13.127 

13.513 

13.899 

14.286 

14.672 

15.058 

40 

15.445 

15.830 

16.217 

16.603 

16.989 

17.375 

17.761 

18.146 

18.534 

18.920 

50 

19.304 

19.691 

20.076 

20.462 

20.848 

21.234 

21.620 

22.007 

22.393 

22.779 

60 

23.166 

23.552 

23.938 

24.324 

24.710 

25.096 

25.482 

25.869 

26.245 

26.641 

70 

27.028 

27.413 

27.800 

28.186 

28.572 

28.958 

29.344 

29.731 

30.117 

30.503 

80 

30.890 

31.274 

31.662 

32.048 

32.434 

32.820 

33.206 

33.593 

33.979 

34.365 

90 

34.749 

35.135 

35.521 

35.907 

36.293 

36.679 

37.065 

37.452 

37.838 

38.224 

100 

38.612 

38.996 

39.384 

39.770 

40.156 

40.542 

40.928 

41.315 

41.701 

42.087 

732 


The  Metric  System. 


Conversion  of  Cubic  Feet  into  Cubic  Decimetres. 

Cubic  feet. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Dm3. 

Dm8. 

Dm3. 

Dm2. 

Dms. 

Dm3. 

Dm8. 

Dm3. 

Dm3. 

Dm8. 

0 

0.0000 

28.316 

56.632 

84.948 

113.26 

141.58 

169.90 

198.21 

226.53 

254.84 

10 

283.16 

311.47 

3:59.79 

268.11 

396.42 

424.74 

453.06 

481.37 

509.69 

538.00 

20 

566.32 

594.64 

622.96 

651.27 

679.58 

707.90 

736.22 

764.53 

792.85 

821.16 

30 

849.48 

877.80 

906.11 

934.43 

962.74 

991.06 

1019.4 

1047.7 

1076.0 

1104.3 

40 

1132.6 

1160.8 

1189.2 

1217.5 

1245.9 

1274.2 

1302.5 

1330.8 

1359.1 

1387.4 

60 

1415.8 

1444.0 

1472.4 

1500.7 

1529.1 

1557.4 

1688.7 

1614.0 

1642.3 

1670.6 

60 

1698.9 

1727.2 

1755.5 

1783.8 

1812.2 

1840.5 

1868.8 

1897.1 

1925.4 

1953.7 

70 

1982.1 

2010.3 

2038.7 

2067.0 

2095.4 

2123.7 

2152.0 

2180.3 

2208.6 

2236.9 

80 

2265.3 

2293.5 

2321.9 

2350.2 

2378.6 

2406.9 

2435.2 

2463.5 

2491.8 

2520.1 

90 

2548.4 

2576.6 

2605.0 

2633.3 

2661.6 

2690.0 

2718.3 

2746.6 

2774.9 

2803.2 

100 

2831.6  2859.8 

2888.2 

2916.5 

2944.9 

2973.2 

3001.5 

3029.8 

3058.1 

3086.4 

Conversion  of  Cubic  Decimetres  into  Cubic  Feet. 

Cubic  dm. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Fts. 

Fts. 

Ft8. 

Ft3. 

Ff. 

FR 

Fts. 

Ft-5. 

Fts. 

Ft3. 

0 

0.0000 

0.0353 

0.0706 

0.1059 

0.1413 

0.1766 

0.2119 

0.2472 

0.2825 

0.3178 

10 

0.3531 

0.3884 

0.4237 

0.4590 

0.4944 

0.5297 

0.5540 

0.6003 

0.6356 

0.6709 

20 

0.7063 

0.7416 

0.7766 

0.8122 

0.8476 

0.8829 

0.9182 

0.9535 

0.9888 

1.0241 

30 

1.0594 

1.0947 

1.1300 

1.1653 

1.2007 

1.2360 

1.2713 

1.3066 

1.3419 

1.3772 

40 

1.4126 

1.4479 

1.4832 

1.5185 

1.5539 

1.5892 

1.6245 

1.6608 

1.6951 

1.7304 

50 

1.7658 

1.8011 

1.8364 

1.8717 

1.9071 

1.9424 

1.9777 

2.0130 

2.0483 

2.0836 

60 

2.1189 

2.1542 

2.1895 

2.2248 

2.2602 

2.2955 

2.3308 

2.3661 

2.4014 

2.4367 

70 

2.4721 

2.5074 

2.5427 

2.5780 

2.6134 

2.6487 

2.6840 

2.7193 

2.7546 

2.7899 

80 

2.8252 

2.8605 

2.8958 

2.9311 

2.9665 

3.0018 

3.0371 

3.0724 

3.1077 

3.1430 

90 

3.1784 

3.2137 

3.2490 

3.2S43 

3.3197 

3.3550 

3.3903 

3.4256 

3.4609 

3.4962 

100 

3.5315 

3.5668 

3.6021 

3.6374 

3.6728 

3.7081 

3.7434 

3.7787 

3.8140 

3.8493 

Pounds 

per  Square  Foot  into  Kilogrammes  per  Square  Metre. 

LbS.  pr  fts. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

K.m2. 

K.m2. 

K.m2. 

K.m2. 

K.m2. 

K.m2. 

K.m2. 

K.m2. 

K.m2. 

K.m2. 

0 

0.0000 

4.8825 

9.7650 

14.647 

19.530 

24.413 

29.295 

34.177 

39.006 

43.943 

10 

48.825 

53.707 

58.590 

63.472 

68.355 

73.238 

78.120 

83.002 

87.831 

92.768 

20 

97.650 

102.53 

107.41 

112.30 

117.18 

122.06 

126.94 

131.83 

136.66 

141.59 

30 

146.47 

151.35 

156.23 

161.12 

165.90 

170.88 

175.76 

180.65 

185.47 

190.41 

40 

195.30 

200.13 

205.06 

209.95 

214.83 

219.71 

224.59 

229.48 

234.30 

239.24 

50 

244.13 

249.01 

253.89 

258.78 

263.66 

268.54 

273.42 

278.31 

283.13 

288.08 

60 

292.95 

297.83 

302.71 

307.60 

312.48 

317.36 

322.24 

327.13 

331.95 

336.89 

70 

341.77 

346.65 

351.53 

356.42 

361.20 

366.18 

371.06 

375.95 

880.77 

385.71 

80 

390.06 

394.94 

399.82 

404.71 

409.59 

414.47 

419.35 

424.24 

429.06 

434.00 

90 

439.43 

444.31 

449.19 

454.08 

458.96 

463.34 

468.72 

473.61 

478.43 

483.37 

100 

488.25  493.13  498.01 

502.90 

507.78 

512.66 

517.54 

522.43 

527.25  532.19 

Kilogra 

mmes  per  Square  Metre  into  Pounds  per  Square  Foot. 

K.  per  m*. 

0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

Lb.  ft2 

Lb.  ft* 

Lb.  ft2 

Lb.ft2Lb.ft2 

Lb.  ft2 

Lb.  ft2 

Lb.  W 

Lb.  ft2 

Lb.  ft* 

0 

0.0000 

0.2048 

0.4096 

0.6144  0.8192 

1.0240 

1.2289 

1.4337 

1.6385 

1.8433 

10 

2.0481 

2.2529 

2.4577 

2.6625 

2.8673 

3.0721 

3.2770 

3.4818 

3.6866 

3.8914 

20 

4.0962 

4.3010 

4.5058 

4.7106 

4.9154 

5.1202 

5.3251 

5.5299 

5.7347 

5.9395 

30 

6.1444 

6.3492 

6.5540 

6.7588 

6.9636 

7.1684 

7.3733 

7.5781 

7.7829 

7.9877 

40 

8.1925 

8.3973 

8.6021 

8.8069 

9.0117 

9.2165 

9.4214 

9.6262 

9.8310 

10.036 

50 

10.240 

10.445 

10.649 

10.854 

11.059 

11.264 

11.469 

11.674 

11.878 

12.083 

60 

12.289 

12.494 

12.698 

12.903 

13.108 

13.313 

13.518 

13.723 

13.927 

14.132 

70 

14.337 

14.542 

14.746 

14.951 

15.156 

15.361 

15.566 

15.771 

15.975 

16.180 

80 

16.385 

16.590 

16.794 

16.999 

17.204 

17.409 

17.614 

17.819 

18.023 

18.228 

90 

18.433 

18.638 

18.842 

19.047 

19.252 

19.457 

19.662 

19.867 

20.071 

20.276 

100 

20.481 

20.686 

20.890 

21.095 

21.300 

21.505 

21.710 

21.915 

22.119 

22.324 

The  Metric  System. 


733 


Pounds 

per  Square 

Inch  into  Atmospheric 

Press 

ure. 

Lbs.  pr  in2. 

0 

At. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

At. 

At. 

At. 

At. 

At. 

At. 

At. 

At. 

At. 

0 

0.0000 

0.0680 

0.1361 

0.2041 

0.2722 

0.3402 

0.4082 

0.4763 

0.5443 

0.6124 

10 

0.6804 

0.7484 

0.8165 

0.8845 

0.9526 

1.0206 

1.0886 

1.1567 

1.2247 

1.2928 

20 

1.3608 

1.4288 

1.4969 

1.5649 

1.6330 

1.7010 

1.7690 

1.8371 

1.9051 

1.9732 

30 

2.0413 

2.1093 

2.1774 

2.2454 

2.3135 

2.3814 

2.4495 

2.5176 

2.5856 

2.6537 

40 

2.7217 

2.7897 

2.8578 

2.9258 

2.9939 

3.0619 

3.1299 

3.1980 

3.2660 

3.3341 

50 

3.4021 

3.4701 

3.5382 

3.6062 

3.6743 

3.7423 

3.8103 

3.8784 

3.9464 

4.0145 

60 

4.0825 

4.1505 

4.2186 

4.2866 

4.3547 

4.4227 

4.4907 

4.5588 

4.6268 

4.6949 

70 

4.7630 

4.8310 

4.8991 

4.9671 

5.0352 

5.1031 

5.1712 

5.2393 

5.3073 

5.3754 

80 

5.4434 

5.5114 

5.5795 

5.6475 

5.7156 

5.7836 

5.8516 

5.9197 

5.9877 

6.0558 

90 

6.1238 

6.1918 

6.2599 

6.3279 

6.3960 

6.4640 

6.5320 

6.6001 

6.6681 

6.7362 

100 

6.8042 

6  8722 

6.9403 

7.0083 

7.0764 

7.1444 

7.2124 

7.2805 

7.3485 

7.4166 

Atmospheric  Pressure  into  Pounds  per  Square  Inch. 

Atm.  pres. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Lb.  in2 

Lb.  in2 

Lb.  in2 

Lb.  in2 

Lb.  in2 

Lb.in2 

Lb.in2 

Lb.in* 

Lb.in2 

Lb.in« 

0 

0.0000 

14.697 

29.393 

44.090 

58.787 

73.483 

88.180 

102.87 

117.57 

132.27 

10 

146.97 

161.67 

176.36 

191.06 

205.76 

220.45 

235.15 

249.84 

264.54 

279.24 

20 

293.93 

308.63 

323.32 

338.02 

352.72 

367.41 

382.11 

396.80 

411.50 

426.20 

30 

440.90 

455.60 

470.29 

484.99 

499.69 

514.38 

529.08 

543.77 

558.47 

573.17 

40 

587.87 

602.57 

617.26 

631.96 

646.66 

661.35 

676.05 

690.74 

705.44 

720.14 

50 

734.83 

749.53 

764.22 

778.92 

793.62 

808.31 

823.01 

837.70 

852.40 

867.10 

60 

881.80 

896.50 

911.19 

925.89 

940.59 

955.28 

969.98 

984.67 

999.37 

1014.1 

70 

1028.7 

1043.4 

1058.1 

1072.8 

1087.5 

1102.2 

1116.9 

1131.6 

1146.3 

1161.0 

80 

1175.7 

1190.4 

1205.1 

1219.8 

1234.5 

1249.2 

1263.9 

1278.6 

1293.3 

1308.0 

90 

1322.7 

1337.4 

1352.1 

1366.8 

1381.5 

1396.2 

1410.9 

1425.6 

1439.3 

1455.0 

100 

1469.7  1484.4  1499.1 

1513.8 

1528.5 

1543.2 

1557.9 

1572.6 

1586.3 

1602.0 

Pounds  per  Square  Inch  into  Kilogrammes  per  Square  Centimetre. 


Lbs.  prin2. 

o 

* 

2 

3 

4 

5 

6 

7 

8 

9 

K.cm2 

K.cm2 

K.cm2 

K.cm2 

K.cm2 

K.cm2 

K.cm2 

K.cm2 

K.cm2 

K.cm* 

0 

0.0000 

0.0703 

0.1406 

0.2109 

0.2812 

0.3515 

0.4218 

0.4921 

0.5625 

0.6328 

10 

0.7031 

0.7734 

0.8437 

0.9140 

0.9843 

1.0546 

1.1249 

1.1952 

1.2655 

1.3358 

20 

1.4062 

1.4765 

1.5468 

1.6171 

1.6874 

1.7577 

1.8280 

1.8983 

1.9686 

2.0389 

30 

2.1092 

2.1795 

2.2498 

2.3202 

2.3905 

2.4608 

2.5311 

2.6014 

2.6717 

2.7420 

40 

2.8123 

2.8826 

2.9529 

3.0232 

3.0935 

3.1639 

3.2342 

3.3045 

3.3748 

3.4451 

50 

3.5154 

3.5857 

3.6560 

3.7263 

3.7966 

3.8669 

3.9372 

4.0075 

4.0779 

4.1482 

60 

4.2185 

4.2888 

4.3591 

4.4294 

4.4997 

4.5700 

4.6403 

4.7106 

4.7809 

4.8512 

70 

4.9216 

4.9919 

5.0622 

5.1325 

5.2028 

5.2731 

5.3434 

5.4137 

5.4840 

5.5543 

80 

5.6246 

5.6949 

5.7652 

5.8356 

5.9059 

5.9762 

6.0465 

6.1168 

6.1871 

6.2574 

90 

6.3277 

6.3980 

6.4683 

6.5386 

6.6089 

6.6793 

6.7496 

6.8199 

6.8902 

6.9605 

100 

7.0308 

7.1011 

7.1714 

7.2417 

7.3120 

7.3823 

7.4526 

7.5229 

7.5933 

7.6636 

Kilogrammes  per  Square  Centimetre  into  Pounds 

per  Square  Inch. 

K.  per  cm2. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Lb.in2 

Lb.in2 

Lb.in2 

Lb.in2 

Lb.in2 

Lb.in'- 

Lb.in2 

Lb.in2 

Lb.in2 

Lb.in» 

0 

0.0000 

14.223 

28.446 

42.670 

56.893 

71.116 

85.339 

99.562 

113.78 

128.01 

10 

142.23 

156.45 

170.68 

184.90 

199.12 

213.35 

227.57 

241.79 

256.02 

270.24 

20 

284.46 

298.69 

312.91 

327.13 

341.36 

355.58 

369.80 

384.03 

398.25 

412.47 

30 

426.70 

440.92 

455.14 

469.36 

483.59 

497.81 

512.03 

526.26 

540.48 

554.70 

40 

568.93 

583.15 

597.37 

611.60 

625.82 

640.04 

654.27 

668.49 

682.71 

696.94 

50 

711.16 

725.38 

739.61 

753.83 

768.05 

782.28 

796.50 

810.72 

824.94 

839.17 

60 

853.39 

867.61 

881.84 

896.06 

910.28 

924.51 

938.73 

952.95 

967.18 

981.40 

70 

995.62 

1009.8 

1024.1 

1038.3 

1052.5 

1066.7 

1081.0 

1095.2 

1109.4 

1123.6 

80 

1137.8 

1152.1 

1166.3 

1180.5 

1194.7 

1209.0 

1223.2 

1237.4 

1251.6 

1265.9 

90 

1280.1 

1294.3 

1308.5 

1322.7 

1337.0 

1351.2 

1365.4 

1379.6 

1393.9 

1408.1 

100 

1422.3 

1436.5  1450.8  1465.0 

1479.2  1493.4 

1507.7 

1521.9 

1536.1 

1550.3 

7:  J 


The  Metis ic  System. 


Conversion  of  English  Pounds  into  Kilogrammes. 

£ug.  lbs. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

Kilo. 

0 

0.000 

0.453 

0.907 

1.361 

1.814 

2.268 

2.722 

3.175 

3.629 

4.082 

10 

4.536 

4.989 

5.443 

5.897 

6.350 

6.804 

7.258 

7.711 

8.165 

8.618 

20 

9.072 

9.525 

9.979 

10.43 

10.89 

11.34 

11.79 

12.25 

12.70 

13.15 

30 

13.61 

14.06 

14.52 

14.97 

1542 

15.88 

16.33 

16.78 

17.24 

17.09 

40 

18.14 

18.59 

19.05 

19.50 

19.95 

20.41 

20.86 

21.31 

21.77 

22.22 

50 

22.68 

23.13 

23.59 

24.04 

24.49 

24.95 

25.40 

25.85 

26.31 

26.76 

60 

27.22 

27.67 

28.13 

28.58 

29.03 

29.49 

29.94 

30.39 

30.85 

31.30 

70 

31.75 

32.20 

32.66 

33.11 

38.56 

34.02 

34.47 

34.92 

35.38 

80 

36.29 

36.74 

37.20 

37.65 

38.10 

38.56 

39.01 

39.46 

39.92 

40.87 

90 

40.82 

41.27 

41.73 

42.18 

42.63 

43.09 

43.54 

43.99 

44.45 

44.90 

100 

45.36 

45.81 

46.27 

46.72 

47.17 

47.63 

48.08 

48.53 

48.99 

49. 1 1 

Conversion  < 

»f  Kilogrammes  into  English  Pounds. 

Fr.  kilo. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

0 

0.000 

2.205 

4.410 

6.615 

8.820 

11.02 

13.23 

15.43 

17.64 

19.84 

10 

22.05 

24.25 

26.46 

28.67 

30.87 

33.07 

35.28 

37.48 

39.69 

41.89 

20 

44.10 

46.30 

48.51 

50.72 

52.92 

55.12 

57.33 

59.53 

61.74 

63.94 

30 

66.15 

68.35 

70.56 

72.77 

74.97 

77.17 

79.38 

81.58 

83.79 

85.99 

40 

88.20 

90.40 

92.61 

94.82 

97.02 

99.22 

101.4 

103.6 

105.8 

108.0 

50 

110.2 

112.5 

114.6 

116.8 

119.0 

121.2 

123.4 

125.6 

127.8 

130.0 

60 

132.3 

134.5 

136.7 

138.9 

141.1 

143.3 

145.5 

147.7 

149.9 

152.1 

70 

154.3 

156.5 

158.7 

160.9 

163.1 

165.3 

167.5 

169.7 

171.9 

174.1 

80 

176.4 

178.6 

180.8 

183.0 

185.2 

187.4 

189.6 

191.8 

194.0 

196.2 

90 

198.4 

200.6 

202.8 

205.0 

207.2 

209.4 

211.6 

213.8 

216.0 

218.2 

100 

220.5 

222.7 

224.9 

227.1 

229.3 

231.5 

233.7 

235.9 

238.1 

240.3 

Conversion  of  English  Tons  into  Metric  Tons. 


Eng.  tons. 

0    |     . 

2     |     3          4 

S 

6 

7 

8- 

9 

M.  ton  M.  ton 

M.  ton  M.  ton 

M.ton 

M.ton 

M.ton 

M.ton 

M.ton 

M.ton 

0 

0.000 

1.016 

2.032 

3.048 

4.064 

5.080 

6.096 

7.112 

8.128 

9.144 

10 

10.16 

11.18 

12.19 

13.21 

14.12 

15.24 

16.26 

17.27 

18.29 

19.30 

20 

20.32 

21.34 

22.35 

23.37 

24.38 

25.40 

26.42 

27.43 

28.45 

29.46 

50 

30.48 

31.50 

32.51 

33.53 

34.54 

35.56 

36.58 

37.59 

38.61 

39.62 

40 

40.64 

41.66 

42.67 

43.69 

44.70 

45.74 

46.74 

47.75 

48.77 

49.78 

50 

50.80 

51.82 

52.83 

53.85 

64.86 

55.88 

56.90 

57.90 

58.93 

59.94 

60 

60.96 

61.97 

62.99 

64.01 

65.02 

66.04 

67.06 

68.07 

69.09 

70.10 

70 

71.12 

72.14 

73.15 

74.17 

75.18 

76.20 

77.22 

78.23 

79.25 

80.26 

80 

81.28 

82.29 

83.31 

84.33 

85.34 

86.36 

87.38 

88.39 

89.41 

90.42 

90 

91.44 

92.46 

93.47 

94.49 

95.50 

96.52 

97.54 

98.55 

99.57 

100.6 

100 

101.6 

102.6 

103.6 

104.6 

105.7 

106.7 

107.7 

108.7 

109.7 

110.7 

Conversion  of  Metric  Tons  Into  English  Tons 

. 

Fr.  m.  ton. 

0 

1 

2 

3 

4 

5 

6         t 

8 

9 

E.  ton 

E.  ton 

E.  ton 

E.  ton 

E.  ton 

E.  ton 

E.  ton'E. ton 

E.  ton  E.  ton 

0 

0.000 

0.984 

1.969 

2.953 

3.937 

4.921 

5.906 

6.890 

7.874 

8.858 

10 

9.843 

10.83 

11.81 

12.79 

13.78 

14.76 

15.75 

16.73 

17.72 

18.70 

20 

19.69 

20.67 

21.66 

22.64 

23.63 

24.61 

25.60 

26.58 

27.56 

28.55 

30 

29.53 

30.51 

31.50 

32.48 

33.47 

34.45 

35.44 

36.42 

37.40 

38.39 

40 

39.37 

40.35 

41.34 

42.32 

43.31 

44.29 

45.28 

46.26 

47.24 

48.23 

50 

49.21 

50.19 

51.18 

52.16 

53.15 

54.13 

55.12 

56.10 

57.08 

58.07 

60 

59.06 

60.04 

61.03 

62.01 

63.00 

63.98 

64.97 

65.95 

66.93 

67.92 

70 

68.90 

69.88 

70.87 

71.85 

72.84 

73.82 

74.81 

75.79 

76.77 

77.76 

80 

78.74 

79.72 

80.71 

81.69 

82.68 

83.66 

84.65 

85.63 

86.61 

87.60 

90 

88.58 

89.56 

90.55 

91.53 

92.52 

93.50 

94.49 

95.47 

96.45 

97.44 

100 

98.43 

99.41 

100.4 

101.4 

102.4 

103.3 

104.3 

105.3 

106.3 

107.3 

The  Metric  System. 


735 


Conversion  of 

English  Ounces  Avoirdupois 

into  French  Grammes. 

Eng.  ozs. 

0 

1      |     2     |     3 

4     |     .     |     6 

' 

8     |     9 

Grams 

Grams, Grams  Grams 

Grams  Grams  Grams 

Grams 

Grams  Grams 

0 

0.0000 

28.348 

56.697  j  85.046 

113.39 

141.74 

170.09 

198.44 

226.79 

255.14 

10 

283.48 

311.83 

340.18 

368.52 

396.87 

425.22 

453.57 

481.92 

510.27 

538.62 

20 

566.97 

595.32 

623.67 

652.01 

680.36 

708.71 

737.06 

765.41 

793.76 

822.11 

30 

850.46 

878.81 

907.16 

935.50 

963.85 

992.20 

1020.5 

1048.9 

1077.2 

1105.6 

40 

1133.9 

1162.2 

1190.6 

1218.9 

1247.3 

1275.6 

1304.0 

1332.3 

1360.7 

1389.0 

50 

1417.4 

1445.7 

1474.1 

1502.4 

1530.8 

1559.1 

1587.5 

1615.8 

1644.2 

1672.5 

60 

1700.9 

1729.2 

1756.6 

1785.9 

1814.3 

1842.9 

1871.0 

1899.3 

1927.7 

1956.0 

70 

1984.4 

2012.7 

2041.1 

2079.4 

2097.8 

2126.1 

2154.5 

2182.8 

2211.2 

2239.5 

80 

2267.9 

2296.2 

2324.6  2352.9 

2381.3 

2409.6 

2438.0 

2466.3 

2494.7 

2523.0 

90 

2551.4 

2579.7 

2608.1  2636.4 

2664.8 

2693.1 

2721.5 

2739.8 

2778.2 

2806.5 

100 

2834.8  2863.1  2891.5)  2919.8 

2948.2 

2976.5 

3004.9 

3033.2 

3061.6 

3089.9 

Conversion  of  French  Grammes 

into  English  Ounces  Avoirdupois. 

Fr.  grams. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Ozs.      Ozs. 

Ozs. 

Ozs. 

Ozs. 

Ozs. 

Ozs. 

Ozs. 

Ozs. 

Ozs. 

0 

0.0000  0.0353 

0.0705 

0.1058 

0.1411 

0.1768 

0.2116 

0.2469 

0.2822 

0.3175 

10 

0.3527J  0.3880 

0.4232 

0.4585 

0.4938 

0.5295 

0.5643 

0.5996 

0.6349 

0.6702 

20 

0.7055  0.7408 

0.7760 

0.8113 

0.8466 

0.8823 

0.9171 

0.9524 

0.9877 

1.0230 

30 

1.0582, 1.0935 

1.1287 

1.1640 

1.1993 

1.2350 

1.2698 

1.3051 

1.3404 

1.3757 

40 

1.4110  1.4463 

1.4815 

1.5168 

1.5521 

1.5878 

1.6226 

1.6579 

1.6932 

1.7285 

50 

1.7687 

1.8040 

1.8392 

1.8745 

1.9098 

1.9455 

1.9803  2.01-56 

2.0509 

2.0862 

60 

2.1165 

2.1518 

2.1870 

2.2223 

2.2576 

2.2933 

2.3281 

2.3634 

2.3987 

2.4340 

70 

2.4692 

2.5045 

2.5397 

2.5750 

2.6103 

2.6460 

2.6808 

2.7161 

2.7514 

2.7867 

80 

2.8220 

2.8573 

2.8925 

2.9278 

2.9631 

2.9988 

3.0336 

3.0689 

3.1042 

3.1395 

90 

3.1747 

3.2100 

3.2452 

3.2805 

3.3158 

3.3515 

3.3863 

3.4216 

3.4569 

3.4922 

100 

3.5275 

3.5628 

3.5980 

3.6333 

3.6686 

3.7043 

3.7391 

3.7744 

3.8097 

3.8450 

Conversion  of  English  Grains  Troy  into  French  Grammes. 

Eng.  grains 

0          12 

3 

4 

5          6 

7 

8 

9 

Grams  Grams  Grams 

Grams  Grams 

Grams  Grams 

Grams 

Grams 

Grams 

0 

0.0000!  0.0648 

0.1296 

0.1944  0.2592 

0.3240 

0.3888 

0.4535 

0.5183 

0.5831 

10 

0.6479|  0.7127 

0.7775 

0.84231  0.9071 

0.9719 

1.0367 

1.1014 

1.1662 

1.2310 

20 

1.2959i  1.3607 

1.4255 

1.4903  1.5551 

1.6199 

1.6847 

1.7494 

1.8142 

1.8890 

30 

1.9438:  2.0086 

2.0734 

2.1382 

2.2030 

2.2678 

2.3326 

2.3973 

2.4621 

2.5269 

40 

2.5918!  2.6566 

2.7214 

2.7862 

2.8510 

2.9158 

2.9806 

3.0453 

3.1101 

3.1749 

50 

3.2398  3.3046 

3.3694 

3.4342 

3.4990 

3.5638 

3.6286 

3.6933 

3.7581 

3.8229 

60 

3.8877 1  3.9525 

4.0173 

4.0821 

4.1469 

4.2117 

4.2765 

4.3412 

4.4060 

4.4708 

70 

4.5357! 4.6005 

4.6653 

4.7301 

4.7949 

4.8597 

4.9245 

4.9892 

5.0540 

5.1188 

80 

5.18301  5.2484 

5.3132 

5.3780 

5.4428 

5.5076 

5.5724 

5.6371 

5.7019 

5.7667 

90 

5.8316 '  5.8964 

5.9612 

6.0260 

6.0908 

6.1556 

6.2204 

6.2851 

6.3499 

6.4147 

100 

6.4795  6.5443 

6.6091 

6.6739 

6.7387 

6.8035 

6.8683 

6.9330 

6.9978 

7.0626 

Conversion 

of  French  Grammes  into  English  Grains  Troy. 

Fr.  grams. 

0 

1 

2 

3 

4 

5          6 

7 

8 

9 

Grs. 

Grs. 

Grs. 

Grs. 

Grs. 

Grs.   j   Grs. 

Grs. 

Grs. 

Grs. 

0 

0.0000 

15.433 

30.866 

46.299 

61.732 

f 7.165  912.599 

108.03 

123.46 

138.90 

10 

154.33 

169.76 

185J9 

200.63 

216.06 

231.49!  246.93 

262.36 

277.79 

293.23 

20 

308.66 

324.09 

339.52 

354.96 

370.39 

385.82  401.26 

416.69 

432.12 

447.56 

30 

462.99 

478.42 

493.86 

509.29 

524.72 

540.15 

555.59 

571.02 

586.45 

601.89 

40 

617.65 

632.75 

648.18 

663.95!  679.38 

694.81 

709.92 

725.35 

740.78 

756.22 

50 

771.65  787.08 

802.52 

817.95  833.38 

848.82 

864.25 

879.68 

895.11 

910.55 

60 

925.99 

941.42 

956.85 

972.29 

987.72 

1003.1 

1018.6 

1034.0 

1049.4 

1064.9 

70 

1080.3 

1095.7 

1111.2 

1126.6 

1142.0J  1157.5 

1172.9 

1188.3 

1203.7 

1219.2 

80 

1234.6 

1250.0 

1265.5 

1280.1 

1296.311311.8 

1327.2 

1342.6 

1358.1 

1373.5 

90 

1389.0 

1404.4 

1419.8 

1435.3 

1450.7|  1466.1 

1481.6 

1497.0 

1512.4 

1527.9 

100 

1543.3 

1558.7 

1574.1 

1589.6 

1605.0 

1620.4 

1635.9 

1651.3 

1666.7 

1682.2 

736 


The  Metric  System. 


Horse-power  into  ChevaUvapeur 

H.-power. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

C.-v. 

C.-T. 

C.-v. 

C.-v. 

C.-v. 

C.-v. 

C.-v. 

C.-v. 

C.-v. 

C.-v. 

0 

0.0000 

1.0136 

2.0272 

3.0408 

4.0544 

5.0680 

6.0816  7.0952 

8.1088 

9.1224 

10 

10.136 

11.150 

12.163 

13.176 

14.190 

15.204 

16.218 

17.231 

18.245 

19.258 

20 

20.272 

21.308 

22.299 

23.313 

24.326 

25.240 

26.354 

27.367 

28.381 

29.394 

80 

30.408 

31.422 

32.435 

33.449 

34.462 

35.476 

36.490 

37.503 

38.517 

39.530 

40 

40.544 

41.557 

42.571 

43.585 

44.598 

45.612 

46.626 

47.639 

48.653 

49.666 

50 

50.680 

51.693 

52.707 

53.721 

54.734 

55.748 

56.762 

57.775 

58.789 

59.802 

60 

60.816 

61.829 

62.843 

63.857 

64.870 

65.884 

66.898 

67.911 

68.925 

69.938 

70 

70.952 

71.965 

72.979 

73.993 

75.006 

76.020 

77.034 

78.047 

79.061 

80.074 

80 

81.088 

82.102 

83.115 

84.129 

85.142 

86.156 

87.170 

88.183 

89.197 

90.210 

90 

91.224 

92.338 

93.251 

94.265 

95.278 

96.292 

97.306 

98.319 

99.333 

100.34 

100 

101.36 

102.37 

103.30 

104.40 

105.41 

106.43 

107.44 

108.45 

109.47 

110.48 

ChevaUvapeur  into  Horse-power 

Chev.-vap. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

H.-p. 

0 

0.0000 

0.9863 

1.9726 

2.9589 

3.9452 

4.9315 

5.9178 

6.9041 

7.8904 

8.8767 

10 

9.8630 

10.849 

11.835 

12.822 

13.808 

14.794 

15.781 

16.767 

17.753 

18.739 

20 

19.726 

20.712 

21.698 

22.685 

23.671 

24.657 

25.644 

26.630 

27.616 

28.602 

30 

29.589 

30.575 

31.561 

32.548 

33.534 

34.520 

35.507 

36.493 

37.479 

38.465 

40 

39.452 

40.438 

41.424 

42.411 

43.397 

44.383 

45.370 

46.356 

47.342 

48.328 

50 

49.315 

50.301 

51.287 

52.274 

53.260 

54.246 

55.233 

56.219 

57.205 

58.191 

60 

59.178 

60.164 

61.150 

62.137 

63.123 

64.109 

65.096 

66.082 

67.068 

68.054 

70 

69.041 

70.027 

71.013 

71.990 

72.986 

73.972 

74.959 

75.945 

76.941 

77.917 

80 

78.904 

79.890 

80.876 

81.863 

82.849 

83.835 

84.822 

85.808 

86.794 

87.780 

90 

88.767 

89.753 

90.739 

91.726 

92.712 

93.698 

94.785 

95.671 

96.657 

97.643 

100 

98.630 

99.616 

100.60 

101.59 

102.57 

103.56 

104.55 

105.53 

106.52 

107.50 

Foot-pounds  into  Kilogrammetres. 


Foot-lba. 

0 

1     |     2 

3 

4     I     5 

6 

7 

8 

9 

Kgm. 

Kgm.  1  Kgm. 

Kgm. 

Kgm. 

Kgm. 

Kgm. 

Kgm. 

Kgm. 

Kgm. 

0 

0.0000 

0.13820.2764 

0.4146 

0.5528 

0.6910 

0.8292 

0.9674 

1.1056 

1.2438 

10 

1.3820 

1.5202  1.6584 

1.7966 

1.9348 

2.0731 

2.2112 

2.3494 

2.4876 

2.6259 

20 

2.7640 

2.9022  3.0404 

3.1786 

3.3168 

3.4552 

3.5933 

3.7315 

3.8696 

4.0078 

30 

4.1400 

4.2842  4.4224 

4.5606 

4.6988 

4.8370 

4.9751 

5.1134 

5.2517 

5.3897 

40 

5.5280 

5.6666  5.8044 

5.9426 

6.0808 

6.2191 

6.3572 

6.4954 

6.6336 

6.7718 

50 

6.9100 

7.0482 

7.1864 

7.3246 

7.4628 

7.6010 

7.7393 

7.8775 

8.0155 

8.1538 

60 

8.2920 

8.4303 

8.5684 

8.7066 

8.8448 

8.9830 

9.1212 

9.2594 

9.3976 

9.5359 

70 

9.6740 

9.8122 

9.9504 

10.088 

10.227 

10.365 

10.503 

10.641 

10.779 

10.918 

80 

11.056 

11.194 

11.322 

11.570 

11.609 

11.747 

11.885 

12.023 

12.161 

12.300 

90 

12.438 

12.576 

12.714 

12.855 

12.991 

13.129 

13.267 

13.405 

13.544 

13.682 

100 

13.820 

13.958 

14.096 

14.235 

14.373 

14.511 

14.649 

14.787 

14.925 

14.064 

Kilogrammetres  into  Poot-pounds 

Kgm. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Ft. -lb. 

Ft.-lb. 

Ft.-lb. 

Ft.-lb. 

Ft. -lb. 

Ft. -lb. 

Ft.-lb. 

Ft.-lb. 

Ft. -lb. 

Ft.-lb. 

0 

0.0000 

7.2334 

14.467 

21.700 

28.934 

36.166 

43.400 

50.734 

57.868 

65.100 

10 

72.334 

79.567 

87.101 

94.034 

101.27 

108.50 

115.74 

123.07 

130.20 

137.43 

20 

144.67 

151.90 

158.43 

166.37 

173.60 

180.84 

188.08 

195.40 

202.54 

209.77 

30 

217.00 

224.23 

231.77 

238.70 

245.93 

253.17 

260.41 

267.73 

274.87 

282.10 

40 

289.34 

2%.  57 

304.11 

311.04 

318.27 

325.50 

332.75 

340.07 

347.21 

354.44 

50 

361.66 

368.89 

376.43 

383.36 

390.59 

397.82 

405.07 

412.39 

419.53 

426.76 

60 

434.00 

441.23 

448.77 

455.70 

462.93 

470.17 

477.41 

484.73 

491.87 

499.10 

70 

507.34 

514.57 

522.11 

529.04 

536.27 

543.50 

550.75 

558.07 

565.21 

572.44 

80 

578.68 

585.91 

593.45 

599.38 

607.61 

614.85 

622.09 

629.41 

636.55 

643.78 

90 

651.00 

658.23 

665.77 

672.70 

679.93 

687.17 

694.41 

701.73 

708.87 

716.10 

100 

723.34 

730.57 

738.11 

745.04 

752.27 

759.51 

76675 

774.07 

781.21 

788.44 

The  Metric  System. 


737 


Conversion  of  Foot-tons  into  Tonnes- metres 

Foot-tons. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

T.-m. 

0 

0.0000 

0.3097 

0.6194 

0.9291 

1.2382 

1.5484 

1.8581 

2.1678 

2.4775 

2.7872 

10 

3.0969 

3.3166 

3.7163 

4.0260 

4.3356 

4.6453 

4.9550 

5.2667 

5.5744 

5.8841 

20 

6.1938 

6.4135 

6.8132 

7.1229 

7.4325 

7.7422 

8.0519 

8.3636 

8.6713 

8.9810 

30 

9.2906 

9.6003 

9.9100 

10.219 

10.529 

10.839 

11.149 

11.460 

11.768 

12.078 

40 

12.387 

12.697 

13.006 

13.316 

13.626 

13.935 

14.245 

14.557 

14.864 

15.174 

50 

15.484 

15.794 

16.103 

16.413 

16.723 

17.032 

17.342 

17.654 

17.961 

18.271 

60 

18.581 

18.891 

19.200 

19.510 

19.820 

20.129 

20.439 

20.751 

21.058 

21.368 

70 

21.678 

21.988 

22.297 

22  607 

22.917 

23.226 

23.536 

23.848 

24.155 

24.465 

80 

24.775 

25.085 

25.394 

25.704 

26.014 

26.323 

26.633 

26.945 

27.252 

27.562 

90 

27.872 

28.182 

28.491 

28.801 

29.111 

29.420 

29.730 

30.042 

30.349 

30.659 

100 

30.969 

31.279 

31.588 

31.898 

32.208 

32.517 

32.827 

33.139 

33.446 

33.756 

Conversion  of  Tonnes 

-metres  into  Foot-tons 

T.-metre8. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

F.-tn. 

F.-tn. 

F.-tn. 

F.-tn. 

F.-tn. 

F.-tn. 

F.-tn. 

F.-tn. 

F.-tn. 

F.-tn. 

0 

0.0000 

3.2290 

6.4581 

9.6871 

12.916 

16.145 

19.374 

22.603 

25.832 

29.061 

10 

32.290 

35.519 

38.758 

41.977 

45.206 

48.435 

51.664 

54.893 

58.122 

61.351 

20 

64.581 

67.810 

71.049 

74.268 

77.497 

80.726 

83.955 

87.184 

90.413 

93.642 

30 

96.871 

100.10 

103.34 

106.56 

109.79 

113.01 

116.24 

119.47 

122.70 

125.93 

40 

129.16 

133.39 

135.63 

138.85 

142.07 

145.30 

148.53 

151.76 

154.99 

158.22 

50 

161.45 

164.68 

167.92 

171.14 

174.36 

177.59 

180.82 

184.05 

187.28 

190.51 

60 

193.74 

196.97 

200.21 

203.43 

206.65 

209.88 

213.11 

216.34 

219.57 

222.80 

70 

226.03 

229.26 

232.50 

235.72 

238.94 

242.17 

245.40 

248.63 

251.86 

255.09 

80 

258.32 

261.55 

264.79 

268.01 

271.23 

274.46 

277.69 

280.92 

284.15 

287.38 

90 

290.61 

293.84 

297.08 

300.30 

303.52 

306.75 

309.98 

313.21 

316.44 

319.67 

100 

322.90 

326.13  329.37 

332.59 

335.81 

339.04 

342.27 

345.50 

348.73 

351.96 

British  Thermal  Units  into  French  Calories. 

B.  T.  U. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Cal. 

Cal. 

Cal. 

Cal. 

Cal. 

Cal. 

Cal. 

Cal. 

Cal. 

Cal. 

0 

0.0000 

0.2520 

0.5040 

0.7560 

1.0080 

1.2600 

1.5120 

1.7640 

2.0160 

2.26SO 

10 

2  5200 

2.7720 

3.0240 

3.2760 

3.5280 

3.7800 

4.0320 

4.2840 

4.5360 

4.7880 

20 

5.0399 

5.2919 

5.5439 

5.7959 

6.0478 

6.2699 

6.5419 

6.8039 

7.0559 

7.3079 

30 

7.5600 

7.8120 

8.0640 

8.3160 

8.5680 

8.8200 

9.0720 

9.3340 

9.5760 

9.8280 

40 

10.080 

10.332 

10.584 

10.836 

11.088 

11.340 

11.512 

11.844 

12.096 

12.348 

50 

12.600 

12.852 

13.104 

13.356 

13.608 

13.860 

14.112 

14.364 

14.616 

14.868 

60 

15.120 

15.372 

15.624 

15.876 

16.128 

16.380 

16.632 

16.884 

17.136 

17.388 

70 

17.640 

17.892 

18.144 

18.396 

18.648 

18.900 

19.152 

19.404 

19.656 

19.908 

80 

20.160 

20.412 

20.664 

20.916 

21.168 

21.420 

21.672 

21.924 

22.176 

22.428 

90 

22.680 

22.932 

23.184 

23.436 

23.688 

23.940 

24.192 

24.444 

24.696 

24.948 

100 

25.200 

25.452 

25.704 

25.956 

26.208 

26.460 

26.712 

26.964 

27.216 

27.468 

French  Calories  Into  British  Thermal  Units. 

Calories. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

T.  U. 

T.  U. 

T.  U. 

T.  U. 

T.  U. 

T.  U. 

T.  U. 

T.  U. 

T.  U. 

T.  U. 

0 

0.0000 

3.9683 

7.9366 

11.905 

15.873 

19.842 

23.810 

27.778 

31.746 

35.715 

10 

39.683 

43.651 

47.620 

51.598 

55.520 

59.525 

63.493 

67.461 

71.429 

75.398 

20 

79.366 

83.334 

87.303 

91.271 

95.203 

99.208 

103.17 

107.14 

111.11 

115  08 

30 

119.05 

123.02 

126.98 

130.95 

134.89 

138.89 

142.86 

146.83 

150.80 

154.7? 

40 

158.73 

162.70 

166.66 

170.62 

174.57 

178.57 

182.54 

186.51 

190.48 

194.45 

50 

198.42 

202.39 

206.35 

210.39 

214.26 

218.26 

222.23 

226.20 

230.16 

234.14 

60 

238.10 

242.07 

246.03 

250.00 

253.94 

258.94 

261.91 

265.88 

269.85 

273.82 

70 

277.78 

281.75 

285.72 

289.68 

293.62 

297.62 

301.59!  305.56 

309.53 

313.50 

80 

317.46 

321.43 

325.40 

329.36 

33S.29 

337.30 

341.271  345.24 

349.20 

353.18 

90 

357.15 

361.12 

365.09 

369.05 

372.98 

376.99 

380.96  384.93 

388.90 

392.87 

100 

396.83 

400.80 

404.77 

408.73 

412.67 

416.67 

420.64 

424.61 

428.58 

432.55 

738 

Natural  Trigonometrical  Functions 

6 

j 
ft 

K 
S 

Sine. 

VER8. 

Cos. 

Cose- 
cant. 

Tang. 

Co- 
tang. 

Se- 
cant. 

Vers. 

Sin. 

Co- 
sine. 

9 

6 

K 
ft 

~~0 

0 

.00000 

1.0000 

Infin. 

.00000 

Inlin. 

1.0000 

.00000 

1.0000 

10 

.00291 

.99709 

343.77 

.00291 

343.77 

1.0000 

.00000 

.99999 

50 

90 

20 

.00582 

.99418 

171.89 

.00582 

171.88 

1.0000 

.00002 

.99998 

40 

30 

.00873 

.99127 

114.59 

.00873 

1 14.59 

1.0000 

.00004 

.99996 

30 

40 

.01103 

.98836 

85.946 

.01164 

85.940 

1.0001 

.00007 

.99993 

20 

50 

.01454 

.98546 

68.757 

.01454 

68.750 

1.0001 

.00010 

.99989 

10 

1 

0 

.01745 

.98255 

57.299 

.01745 

57.290 

1.0001 

.00015 

.99985 

89 

10 

.02036 

.97964 

49.114 

.02036 

49.104 

1.0002 

.00021 

.99979 

50 

20 

.02327 

.97673 

42.976 

.02327 

42.964 

1.0003 

.00027 

.99973 

40 

30 

.02618 

.97382 

38.201 

.02618 

38.188 

1.0003 

.00034 

.99966 

30 

40 

.02908 

.97091 

34.382 

.02910 

34.368 

1.0004 

.00042 

.99958 

20 

50 

.03199 

.96801 

31.257 

.03201 

31.241 

1.0005 

.00051 

.99949 

10 

2 

0 

.03490 

.96510 

28.654 

.03492 

28.636 

1.0006 

.00061 

.99939 

88 

10 

.03781 

.96219 

26.450 

.03783 

26.432 

1.0007 

.00071 

.99928 

50 

20 

.04071 

.95929 

24.562 

.04075 

24.542 

1.0008 

.00083 

.99917 

40 

30 

.04362 

.95638 

22.925 

.04366 

22.904 

1.0009 

.00095 

.99905 

30 

40 

.04652 

.95347 

21.494 

.04657 

21.470 

1.0011 

.00108 

.99892 

20 

50 

.04943 

.95057 

20.230 

.04949 

20.205 

1.0012 

.00122 

.99878 

10 

3 

0 

.05234 

.94766 

19.107 

.05241 

19.081 

1.0014 

.00137 

.99863 

87 

10 

.05524 

.94476 

18.103 

.05532 

18.075 

1.0015 

.00153 

.99847 

50 

20 

.05814 

.94185 

17.198 

.05824 

17.169 

1.0017 

.00169 

.99831 

40 

30 

.06105 

.93895 

16.380 

.06116 

16.350 

1.0019 

.00186 

.99813 

30 

40 

.06395 

.93605 

15.637 

.06408 

15.605 

1.0020 

.00205 

.99795 

20 

50 

.06685 

.93314 

14.958 

.06700 

14.924 

1.0022 

.00224 

.99776 

10 

4 

0 

.06976 

.93024 

14.335 

.06993 

14.301 

1.0024 

.00243 

.99756 

86 

10 

.07266 

.92734 

13.763 

.07285 

13.727 

1.0026 

.00264 

.99736 

50 

20 

.07556 

.92444 

13.235 

.07577 

13.197 

1.0029 

.00286 

.99714 

40 

30 

.07846 

.92154 

12.745 

.07870 

12.706 

1.0031 

.00308 

.99692 

30 

40 

.08136 

.91864 

12.291 

.08163 

12.250 

1.0033 

.00331 

.99668 

20 

50 

.08426 

.91574 

11.868 

.08456 

11.826 

1.0036 

.00356 

.99644 

10 

5 

0 

.08715 

.91284 

11.474 

.08749 

11.430 

1.0038 

.00380 

.99619 

85 

10 

.09005 

.90995 

11.104 

.09042 

11.059 

1.0041 

.00406 

.99594 

50 

20 

.09295 

.90705 

10.758 

.09335 

10.712 

1.0043 

.00433 

.99567 

40 

30 

.09584 

.90415 

10.433 

.09629 

10.385 

1.0046 

.00460 

.99540 

30 

40 

.09874 

.90126 

10.127 

.09922 

10.078 

10049 

.00489 

.99511 

20 

50 

.10163 

.89836 

9.8391 

.10216 

9.7882 

1.0052 

.00518 

.99482 

10 

6 

0 

.10453 

.89547 

9.5668 

.10510 

9.5144 

1.0055 

.00548 

.99452 

84 

10 

.10742 

.89258 

9.3092 

.10805 

9.2553 

1.0058 

.00579 

.99421 

50 

20 

.11031 

.88969 

9.0651 

.11099 

9.0098 

1.0061 

.00110 

.99390 

40 

30 

.11320 

.88680 

8.8337 

.11393 

8.7769 

1.0065 

.00643 

.99357 

30 

40 

.11609 

.88391 

8.6138 

.11688 

8.5555 

1.0068 

.00676 

.99324 

20 

50 

.11898 

.88102 

8.4046 

.11983 

8.3449 

1.0071 

.00710 

.99290 

10 

7 

0 

.12187 

.87813 

8.2055 

.12278 

8.1443 

1.0075 

.00745 

.99255 

83 

10 

.12476 

.87524 

8.0156 

.12574 

7.9530 

1.0079 

.00781 

.99219 

50 

20 

.12764 

.87236 

7.8344 

.12869 

7.7703 

1.0082 

.00818 

.99182 

40 

30 

.13053 

.86947 

7.6613 

.13165 

7.5957 

1.0086 

.00855 

.99144 

30 

40 

.13341 

.86659 

7.4957 

.13461 

7.4287 

1.0090 

.00894 

.99106 

20 

50 

.13629 

.86371 

7.3372 

.13757 

7.2687 

1.0094 

.00933 

.99067 

10 

8 

0 

.13917 

.86083 

7.1853 

.14054 

7.1154 

1.0098 

.00973 

.99027 

82 

10 

.14205 

.85795 

7.0396 

.14351 

6  9682 

1.0102 

.01014 

.98986 

50 

20 

.14493 

.85507 

6.8998 

.14648 

6.8269 

1.0107 

.01056 

.98944 

40 

30 

.14781 

.85219 

6.7655 

.14945 

6.6911 

1.0111 

.01098 

.98901 

30 

40 

.15068 

.84931 

6.6363 

.15243 

6.5605 

1.0115 

.01142 

.98858 

20 

50 

.15356 

.84644 

6.5121 

.15540 

6.4348 

1.0120 

.01186 

.98814 

10 

9 

0 

.15643 

.84356 

6.3924 

.15838 

6.3137 

1.0125 

.01231 

.98769 

81 

Co- 

Vers. 

Se- 

Co- 

Tan- 

Cose- 

Vers 

Sine. 

Sine. 

Sin. 

cant 

tang. 

gent. 

cant. 

Cos. 

Natural  Trigonometrical  Functions. 


739 


6 

w 
Q 

g 

s 

Sine. 

Vers. 
Cos. 

Cose- 
cant. 

Tang. 

Co- 

TANG. 

Se- 
cant. 

1.0125 

Vers. 
Sin. 

Co- 
sine. 

'a 

6 

~9~ 

0 

.15643 

.84356 

6.3924 

.15838 

6.3137 

.01231 

.98769 

81 

10 

.15931 

.84069 

6.2772 

.16137 

6.1970 

1.0129 

.01277 

.98723 

50 

20 

.16218 

.83782 

6.1661 

.16435 

6.0844 

1.0134 

.01324 

.98676 

40 

30 

.16505 

.83495 

6.0588 

.16734 

5.9758 

1.0139 

.01371 

.98628 

30 

40 

.16791 

.83208 

5.9554 

.17033 

5.8708 

1.0144 

.01420 

.98580 

20 

50 

.17078 

.82922 

5.8554 

.17333 

5.7694 

1.0149 

.01469 

.98531 

10 

10 

0 

.17365 

.82635 

5.7588 

.17633 

5.6713 

1.0154 

.01519 

.98481 

80 

10 

.17651 

.82349 

5.6653 

.17933 

5.5764 

1.0159 

.01570 

.98430 

50 

20 

.17937 

.82062 

5.5749 

.18233 

5.4845 

1.0165 

.01622 

.98378 

40 

30 

.18223 

.81776 

5.4874 

.18534 

5.3955 

1.0170 

.01674 

.98325 

30 

40 

.18509 

.81490 

5.4026 

.18835 

5.3093 

1.0176 

.01728 

.98272 

20 

50 

.18795 

.81205 

5.3205 

.19136 

5.2257 

1.0181 

.01782 

.98218 

10 

11 

0 

.19081 

.80919 

5.2408 

.19438 

5.1445 

1.0187 

.01837 

.98163 

79 

10 

.19366 

.80634 

5.1636 

.19740 

5.0658 

1.0193 

.01893 

.98107 

50 

20 

.19652 

.80348 

5.0886 

.20042 

4.9894 

1.0199 

.01950 

.98050 

40 

30 

.19937 

.80063 

5.0158 

.20345 

4.9151 

1.0205 

.02007 

.97992 

30 

40 

.20222 

.79778 

4.9452 

.20648 

4.8430 

1.0211 

.02066 

.97934 

20 

50 

.20506 

.79493 

4.8765 

.20952 

4.7728 

1.0217 

.02125 

.97875 

10 

12 

0 

.20791 

.79209 

4.8097 

.21256 

4.7046 

1.0223 

.02185 

.97815 

78 

10 

.21076 

.78924 

4.7448 

.21560 

4.6382 

1.0230 

.02246 

.97754 

50 

20 

.21360 

.78640 

4.6817 

.21864 

4.5736 

1.0236 

.02308 

.97692 

40 

30 

.21644 

.78356 

4.6202 

.22169 

4.5107 

1.0243 

.02370 

.97630 

30 

40 

.21928 

.78072 

4.5604 

.22475 

4.4494 

1.0249 

.02434 

.97566 

20 

50 

.22211 

.77788 

4.5021 

.22781 

4.3897 

1.0256 

.02498 

.97502 

10 

13 

0 

.22495 

.77505 

4.4454 

.23087 

4.3315 

1.0263 

.02563 

.97437 

77 

10 

.22778 

.77221 

4.3901 

.23393 

4.2747 

1.0270 

.02629 

.97371 

50 

20 

.23061 

.76938 

4.3362 

.23700 

4.2193 

1.0277 

.02695 

.97304 

40 

30 

.23344 

.76655 

4.2836 

.24008 

4.1653 

1.0284 

.02763 

.97237 

30 

40 

.23627 

.76373 

4.2324 

.24316 

4.1127 

1.0291 

.02831 

.97169 

20 

50 

.23910 

.76090 

4.1824 

.24624 

4.0611 

1.0299 

.02900 

.97099 

10 

14 

0 

.24192 

.75808 

4.1336 

.24933 

4.0108 

1.0306 

.02970 

.97029 

76 

10 

.24474 

.75526 

4.0859 

.25242 

3.9616 

1.0314 

.03041 

.96959 

50 

20 

.24756 

.75244 

4.0394 

.25552 

3.9136 

1.0321 

.03113 

.96887 

40 

30 

.25038 

.74962 

3.9939 

.25862 

3.8667 

1.0329 

.03185 

.96815 

30 

40 

.25319 

.74680 

3.9495 

.26172 

3.8208 

1.0337 

.03258 

.96741 

20 

50 

.25601 

.74399 

3.9061 

.26483 

3.7759 

1.0345 

.03332 

.96667 

10 

15 

0 

.25882 

.74118 

3.8637 

.26795 

3.7320 

1.0353 

.03407 

.96592 

75 

10 

.26163 

.73837 

3.8222 

.27107 

3.6891 

1.0361 

.03483 

.96517 

50 

20 

.26443 

.73556 

3.7816 

.27419 

3.6470 

1.0369 

.03560 

.96440 

40 

30 

.26724 

.73276 

3.7420 

.27732 

3.6059 

1.0377 

.03637 

.96363 

30 

40 

.27004 

.72996 

3.7031 

.28046 

3.5656 

1.0386 

.03715 

.96285 

20 

50 

.27281 

.72716 

3.6651 

*. 28360 

3.5261 

1.0394 

.03794 

.96206 

10 

16 

0 

.27564 

.72436 

3.6279 

.28674 

3.4874 

1.0403 

.03874 

.96126 

74 

10 

,27843 

.72157 

3.5915 

.28990 

3.4495 

1.0412 

.03954 

.96045 

50 

20 

.28122 

.71877 

3.5559 

.29305 

3.4124 

1.0420 

.04036 

.95964 

40 

30 

.28401 

.71608 

3.5209 

.29621 

3.3759 

1.0429 

.04118 

.95882 

30 

40 

.28680 

.71320 

3.4867 

.29938 

3.3402 

1.0438 

.04201 

.95799 

20 

50 

.28959 

.71041 

3.4532 

.30255 

3.3052 

1.0448 

.04285 

.95715 

10 

17 

0 

.29237 

.70763 

3.4203 

.30573 

3.2708 

1.0457 

.04369 

.95630 

73 

10 

.29515 

.70485 

3.3881 

.30891 

3.2371 

1.0466 

.04455 

.95545 

50 

20 

.29793 

.70207 

3.3565 

.31210 

3.2041 

1.0476 

.04541 

.95459 

40 

30 

.30070 

.69929 

3.3255 

.31530 

3.1716 

1.0485 

.04628 

.95372 

30 

40 

.30348 

.69652 

3.2951 

.31850 

3.1397 

1.0495 

.04716 

.95284 

20 

50 

.30625 

.69375 

3.2653 

.32171 

3.1084 

1.0505 

.04805 

.95195 

10 

18 

0 

.30902 

.69098 

3.2361 

.32492 

3.0777 

1.0515 

.04894 

.95106 

72 

Co- 

Vers. 

SE- 

Co- 

Tan- 

Cose- 

Vers. 

Sine. 

sine. 

Sin.  cant. 

TANG. 

gent. 

cant. 

Cos. 

740 


Natural  Trigonometrical  Functions. 


6 
$ 

kj 
0 

Sine. 
.30902 

Vers. 
Cos. 

"(KKMW 

Cose- 
cant 

Tang 

Co- 

TANG 

Se- 
cant 

V  i  i:s 

Sin. 

Co- 
sine. 

.05106 

v. 

0 

W 

ft 

18 

3.2361 

.32492 

3.0777 

1.0515 

.04894 

72 

10 

.31178 

.68822 

3.2074 

.32814 

3.0475 

1.0525 

.04985 

.95015 

M 

20 

.31454 

.68545 

3.1792 

.33136 

3.0178 

1.0535 

.05076 

.94924 

40 

30 

.31730 

.68269 

3.1515 

.33459 

2.9887 

1.0545 

.05168 

.94832 

80 

40 

.32006 

.67994 

3.1244 

.33783 

2.9600 

1.0555 

.05260 

.94740 

20 

50 

.32282 

.67718 

3.0977 

.34108 

2.9319 

1.0566 

.05354 

.94646 

to 

19 

0 

.32557 

.67443 

3.0715 

.34433 

2.9042 

1.0576 

.05448 

.94552 

71 

10 

.32832 

.67168 

3.0458 

.34758 

2.8770 

1.0587 

.05543 

.94457 

50 

20 

.33106 

.66894 

3.0206 

.35085 

2.8502 

1.0598 

.05639 

.94361 

to 

30 

.33381 

.66619 

2.9957 

.35412 

2.8239 

1.0608 

.05736 

.94264 

80 

40 

.33655 

.66345 

2.9713 

.35739 

2.7980 

1.0619 

.05833 

.94167 

20 

50 

.33928 

.66071 

2.9474 

.36068 

2.7725 

1.0630 

.05932 

.94068 

10 

20 

0 

.34202 

.65798 

2.9238 

.36397 

2.7475 

1.0642 

.06031 

.93969 

70 

10 

.34475 

.65525 

2.9006 

.36727 

2.7228 

1.0653 

.06131 

.93869 

50 

20 

.34748 

.65252 

2.8778 

.37057 

2.6985 

1.0664 

.06231 

.93769 

40 

30 

.35021 

.64979 

2.8554 

.37388 

2.6746 

1.0676 

.06333 

.93667 

30 

40 

.35293 

.64707 

2.8334 

.37720 

2.6511 

1.0688 

.06435 

.93565 

20 

50 

.35565 

.64435 

2.8117 

.38053 

2.6279 

1.0699 

.06538 

.93462 

10 

21 

0 

.35837 

.64163 

2.7904 

.38386 

2.6051 

1.0711 

.06642 

.93358 

69 

10 

.36108 

.63892 

2.7694 

.38720 

2.5826 

1.0723 

.06747 

.93253 

60 

20 

.36379 

.63621 

2.7488 

.39055 

2.5605 

1.0736 

.06852 

.93148 

40 

30 

.36650 

.63350 

2.7285 

.39391 

2.5386 

1.0748 

.06958 

.93042 

80 

40 

.36921 

.63079 

2.7085 

.39727 

2.5171 

1.0760 

.07065 

.92935 

20 

50 

.37191 

.62809 

2.6888 

.40065 

2.4960 

1.0773 

.07173 

.92827 

10 

22 

0 

.37461 

.62539 

2.6695 

.40403 

2.4751 

1.0785 

.07282 

.92718 

68 

10 

.37730 

.62270 

2.6504 

.40741 

2.4545 

1.0798 

.07391 

.92609 

50 

20 

.37999 

.62000 

2.6316 

.41081 

2.4342 

1.0811 

.07501 

.92499 

40 

30 

.38268 

.61732 

2.6131 

.41421 

2.4142 

1.0824 

.07612 

.92388 

80 

40 

.38537 

.61463 

2.5949 

.41762 

2.3945 

1.0837 

.07724 

.92276 

20 

50 

•38805 

.61195 

2.5770 

.42105 

2.3750 

1.0850 

.07836 

.92164 

10 

23 

0 

.39073 

.60927 

2.5593 

.42447 

2.3558 

1.0864 

.07949 

.92050 

67 

10 

.39341 

.60659 

2.5419 

.42791 

2.3369 

1.0877 

.08063 

.91936 

50 

20 

.39608 

.60392 

2.5247 

.43136 

2.3183 

1.0891 

.08178 

.91822 

40 

30 

.39875 

.60125 

2.5078 

.43481 

2.2998 

1.0904 

.08294 

.91706 

30 

40 

.40141 

.59858 

2.4912 

.43827 

2.2817 

1.0918 

.08410 

.91590 

20 

50 

.40408 

.59592 

2.4748 

.44175 

2.2637 

1.0932 

.08527 

.91472 

10 

24 

0 

.40674 

.59326 

2.4586 

.44523 

2.2460 

1.0946 

.08645 

.91354 

66 

10 

.40939 

.59061 

2.4426 

.44872 

2.2286 

1.0961 

.08764 

.91236 

50 

20 

.41204 

.58795 

2.4269 

.45222 

2.2113 

1.0975 

.08884 

.91116 

40 

30 

.41469 

.58531 

2.4114 

.45573 

2.1943 

1.0989 

.09004 

.90996 

80 

40 

.41734 

.58266 

2.3961 

.45924 

2.1775 

1.1004 

.09125 

.90875 

20 

50 

.41998 

.58002 

2.3811 

.46277 

2.1609 

1.1019 

.09247 

.90753 

10 

25 

0 

.42262 

.57738 

2.3662 

.46631 

2.1445 

1.1034 

.09369 

.90631 

65 

10 

.42525 

.57475 

2.3515 

.46985 

2.1283 

1.1049 

.09492 

.90507 

BO 

20 

.42788 

.57212 

2.3371 

.47341 

2.1123 

1.1064 

.09617 

.90383 

40 

30 

.43051 

.56949 

2.3228 

.47697 

2.0965 

1.1079 

.09741 

.90258 

30 

40 

.43313 

.56686 

2.3087 

.48055 

2.0809 

1.1095 

.09867 

.90133 

20 

50 

.43575 

•56424 

2.2949 

.48414 

2.0655 

1.1110 

.09993 

.90006 

10 

26 

0 

.43837 

.56163 

2.2812 

.48773 

2.0503 

1.1126 

.10121 

.89879 

64 

10 

.44098 

.55902 

2.2676 

.49134 

2.0352 

1.1142 

.10248 

.89751 

50 

20 

.44359 

.55641 

2.2543 

.49495 

2.0204 

1.1158 

.10377 

.89623 

40 

30 

.44620 

.55380 

2.2411 

.49858 

2.0057 

1.1174 

.10506 

.89493 

80 

40 

.44880 

.55120 

2.2282 

.50222 

1.9912 

1.1190 

.10637 

.89363 

20 

50 

.45140 

.54860 

2.2153 

.50587 

1.9768 

1.1207 

.10768 

.89232 

10 

27 

.45399 

.54601 

2.2027 

.50952 

1.9626 

1.1223 

.10899 

.89101 

63 

Co- 

Vers. 

Se- 

Co- 

Tan. 

Cose- 

Vers. 

Sine. 

sine. 

Sin. 

cant. 

TANG. 

GENT. 

cant. 

Cos. 

Natural  Trigonometrical  Functions 

741 

6 

pa 

fc 

£ 

Sine. 

Vers. 
Cos. 

Cose- 
cant. 

Tang. 

Co. 

TANG. 

Se- 
cant. 

Vers. 

Sin. 

Co- 
sine. 

g 

S 

6 

27 

0 

.45399 

.54601 

2.2027 

.50952 

1.9626 

1.1223 

.10899 

.89101 

63 

10 

.45658 

.54:542 

2.1902 

.51319 

1.9486 

1.1240 

.11032 

.88968 

50 

20 

.45917 

.54083 

2.1778 

.51687 

1.9347 

1.1257 

.11165 

.88835 

40 

30 

.46175 

.53825 

2.1657 

.52057 

1.9210 

1.1274 

.11299 

.88701 

30 

40 

.46433 

.53567 

2.1536 

.52427 

1.9074 

1.1291 

.11434 

.88566 

20 

50 

.46690 

.53310 

2.1418 

.52798 

1.8940 

1.1308 

.11569 

.88431 

10 

28 

0 

.46947 

.53053 

2.1300 

.53171 

1.8807 

1.1326 

.11705 

.88295 

62 

10 

.47204 

.52796 

2.1185 

.53545 

1.8676 

1.1343 

.11842 

.88158 

50 

20 

.47460 

.52540 

2.1070 

.53919 

1.8546 

1.1361 

.11980 

.88020 

40 

30 

.47716 

.52284 

2.0957 

.54295 

1.8418 

1.1379 

.12118 

.87882 

30 

40 

.47971 

.52029 

2.0846 

.54673 

1.8291 

1.1397 

.12257 

.87742 

20 

50 

.48226 

.51774 

2.0735 

.55051 

1.8165 

1.1415 

.12397 

.87603 

10 

29 

0 

.48481 

.51519 

2.0627 

.55431 

1.8040 

1.1433 

.12538 

.87462 

61 

10 

.48735 

.51265 

2.0519 

.55812 

1.7917 

1.1452 

.12679 

.87320 

50 

20 

.48989 

.51011 

2.0413 

.56194 

1.7795 

1.1471 

.12821 

.87178 

40 

30 

.49242 

.50758 

2.0308 

.56577 

1.7675 

1.1489 

.12964 

.87035 

30 

40 

.49495 

.50505 

2.0204 

.56962 

1.7555 

1.1508 

.13108 

.86892 

20 

50 

.49748 

.50252 

2.0101 

.57348 

1.7437 

1.1528 

.13252 

.86748 

10 

30 

0 

.50000 

.50000 

2.0000 

.57735 

1.7320 

1.1547 

.13397 

.86602 

60 

10 

.50252 

.49748 

1.9900 

.58123 

1.7205 

1.1566 

.13543 

.86457 

50 

20 

.50503 

.49497 

1.9801 

.58513 

1.7090 

1.1586 

.13690 

.86310 

40 

30 

.50754 

.49246 

1.9703 

.58904 

1.6977 

1.1606 

.13837 

.86163 

30 

40 

.51004 

.48996 

1.9606 

.59297 

1.6864 

1.1626 

.13985 

.86015 

20 

50 

.51254 

.48746 

1.9510 

.59691 

1.6753 

1.1646 

.14134 

.85866 

10 

31 

0 

.51504 

.48496 

1.9416 

.60086 

1.6643 

1.1666 

.14283 

.85717 

59 

10 

.51753 

.48247 

1.9322 

.60483 

1.6534 

1.1687 

.14433 

.85566 

50 

20 

.52002 

.47998 

1.9230 

.60881 

1.6425 

1.1707 

.14584 

.85416 

40 

30 

.52250 

.47750 

1.9139 

.61280 

1.6318 

1.1728 

.14736 

.85264 

30 

40 

.52498 

.47502 

1.9048 

.61681 

1.6212 

1.1749 

.14888 

.85112 

20 

50 

•52745 

.47255, 

1.8959 

.62083 

1.6107 

J. 1770 

.15041 

.84959 

10 

32 

0 

.52992 

.47008 

1.8871 

.62487 

1.6003 

1.1792 

.15195 

.84805 

58 

10 

.53238 

.46762 

1.8783 

.62892 

1.5900 

1.1813 

.15350 

.84650 

50 

20 

.53484 

.46516 

1.8697 

.63299 

1.5798 

1.1835 

.15505 

.84495 

40 

30 

.53730 

.46270 

1.8611 

.63707 

1.5697 

1.1857 

.15661 

.84339 

30 

40 

.53975 

.46025 

1.8527 

.64117 

1.5596 

1.1879 

.15817 

.84182 

20 

50 

.54220 

.45780 

1.8443 

.64528 

1.5497 

1.1901 

.15975 

.84025 

10 

33 

0 

.54464 

.45536 

1.8361 

.64941 

1.5399 

1.1924 

.16133 

.83867 

57 

10 

.54708 

.45292 

1.8279 

.65355 

1.5301 

1.1946 

.16292 

.83708 

50 

20 

.54951 

.45049 

1.8198 

.65771 

1.5204 

1.1969 

.16451 

.83549 

40 

30 

.55194 

.44806 

1.8118 

.66188 

1.5108 

1.1992 

.16611 

.83388 

30 

40 

.55436 

.44564 

1.8039 

.66608 

1.5013 

1.2015 

.16772 

.83228 

20 

50 

.55678 

•44322 

1.7960 

.67028 

1.4919 

1.2039 

.16934 

.83066 

10 

34 

0 

.55919 

.44081 

1.7883 

.67451 

1.4826 

1.2062 

.17096 

.82904 

56 

10 

.56160 

.43840 

1.7806 

.67875 

1.4733 

1.2086 

.17259 

.82741 

50 

20 

.56401 

.43599 

1.7730 

.68301 

1.4641 

1.2110 

.17423 

.82577 

40 

30 

.56641 

.43359 

1.7655 

.68728 

1.4550 

1.2134 

.17587 

.82413 

30 

40 

.56880 

.43120 

1.7581 

.69157 

1.4460 

1.2158 

.17752 

.82247 

20 

50 

.57119 

.42881 

1.7507 

.69588 

1.4370 

1.2183 

.17918 

.82082 

10 

35 

0 

.57358 

.42642 

1.7434 

.70021 

1.4281 

1.2208 

.18085 

.81915 

55 

10 

.57596 

.42404 

1.7362 

.70455 

1.4193 

1.2233 

.18252 

.81748 

50 

20 

.57833 

.42167 

1.7291 

.70891 

1.4106 

1.2258 

.18420 

.81580 

40 

30 

.58070 

.41930 

1.7220 

.71329 

1.4019 

1.2283 

.18588 

.81411 

30 

40 

.58307 

.41693 

1.7151 

.71769 

1.3933 

1.2309 

.18758 

.81242 

20 

50 

.58543 

.41457 

1.7081 

.72211 

1.3848 

1.2335 

.18928 

.81072 

10 

36 

0 

.58778 

.41221 

1.7013 

.72654 

1.3764 

1.2361 

.19098 

.80902 

54 

Co- 

Vers. 

Se- 

CO- 

Tan- 

Cose- 

Vers. 

Sine. 

sine. 

Sin. 

cant 

TANG. 

gent. 

cant. 

Cos. 

742 

Natural  Trigonom 

etrical  Functions. 

o" 

w 

ft 

i 

0 

Sine. 

Vers. 
Cos. 

Cose- 
cant. 

Tang. 

Co- 
tang. 

Se- 
cant. 

Vers. 
Sin. 

Co- 
sine. 

9 

6 
w 

5 

~36 

.58778 

.41221 

1.7013 

.72654 

1.3764 

1.2361 

.19098 

.sosKrj 

54 

10 

.59014 

.40986 

1.6945 

.73100 

1.3680 

1.2387 

.19270 

.80730 

50 

20 

.59248 

.40752 

1.6878 

.73547 

1.3597 

1.2413 

.19442 

.80658 

40 

30 

.59482 
.59716 

.40518 

1.6812 

.73996 

1.3514 

1.2440 

.19614 

.80386 

30 

40 

.40284 

1.6746 

.74447 

1.3432 

1.2467 

.19788 

.80212 

20 

50 

.59949 

.40051 

1.6681 

.74900 

1.3351 

1.2494 

.19962 

.80038 

10 

37 

0 

.60181 

.39818 

1.6616 

.75355 

1.3270 

1.2521 

.20136 

.79863 

53 

10 

.60413 

.39586 

1.6552 

.75812 

1.3190 

1.2549 

.20312 

.79688 

50 

20 

.60645 

.39355 

1.6489 

.76271 

1.3111 

1.2577 

.20488 

.79512 

40 

30 

.60876 

.39124 

1.6427 

.76733 

1.3032 

1.2605 

.20665 

.79335 

SO 

40 

.61107 

.38893 

1.6365 

.77196 

1.2954 

1.2633 

.20842 

.79158 

20 

50 

.61337 

.38663 

1.6303 

.77661 

1.2876 

1.2661 

.21020 

.78980 

10 

38 

0 

.61566 

.38434 

1.6243 

.78128 

1.2799 

1.2690 

.21199 

.78801 

52 

10 

.61795 

.38205 

1.6182 

.78598 

1.2723 

1.2719 

.21378 

.78622 

50 

20 

.62023 

.37976 

1.6123 

.79070 

1.2647 

1.2748 

.21558 

.78441 

40 

30 

.62251 

.37748 

1.6064 

.79543 

1.2572 

1.2778 

.21739 

.78261 

30 

40 

.62479 

.37521 

1.6005 

.80020 

1.2497 

1.2807 

.21921 

.78079 

20 

50 

.62706 

.37294 

1.5947 

.80498 

1.2423 

1.2837 

.22103 

.77897 

10 

39 

0 

.62932 

.37068 

1.5890 

.80978 

1.2349 

1.2867 

.22285 

.77715 

51 

10 

.63158 

.36842 

1.5833 

.81461 

1.2276 

1.2898 

.22469 

.77531 

50 

20 

.63383 

.36617 

1.5777 

.81946 

1.2203 

1.2929 

.22653 

.77347 

40 

30 

.63608 

.36392 

1.5721 

.82434 

1.2131 

1.2960 

.22837 

.77162 

30 

40 

.63832 

.36168 , 

1.5666 

.82923 

1.2059 

1.2991 

.23023 

.76977 

20 

50 

.64056 

.35944 

1.5611 

.83415 

1.1988 

1.3022 

.23209 

.76791 

10 

40 

0 

.64279 

.35721 

1.5557 

.83910 

1.1917 

1.3054 

.23395 

.76604 

50 

10 

.64501 

.35499 

1.5503 

.84407 

1.1847 

1.3086 

.23583 

.76417 

50 

20 

.64723 

.35277 

1.5450 

.84906 

1.1778 

1.3118 

.23771 

.76229 

40 

30 

.64945 

.35055 

1.5398 

.85408 

1.1708 

1.3151 

.23959 

.76041 

30 

40 

.65166 

.34834 

1.5345 

.85912 

1.1640 

1.3184 

.24149 

.75851 

20 

50 

.65386 

.34614 

1.5294 

.86419 

1.1571 

1.3217 

.24338 

.75661 

10 

41 

0 

.65606 

.34394 

1.5242 

.86929 

1.1504 

1.3250 

.24529 

.75471 

49 

10 

.65825 

.34175 

1.5192 

.87441 

1.1436 

1.3284 

.24720 

.75280 

50 

20 

.66044 

.33956 

1.5141 

.87955 

1.1369 

1.3318 

.24912 

.75088 

40 

30 

.66262 

.33738 

1.5092 

.88472 

1.1303 

1.3352 

.25104 

.74895 

30 

40 

.66479 

.33520 

1.5042 

.88992 

1.1237 

1.3386 

.25297 

.74702 

20 

50 

.66697 

.33303 

1.4993 

.89515 

1.1171 

1.3421 

.25491 

.74509 

10 

42 

0 

.66913 

.33087 

1.4945 

.90040 

1.1106 

1.3456 

.25685 

.74314 

48 

10 

.67129 

.32871 

1.4897 

.90568 

1.1041 

1.3492 

.25880 

.74119 

50 

20 

.67344 

.32656 

1.4849 

.91099 

1.0977 

'  1.3527 

.26076 

.73924 

40 

30 

.67559 

.32441 

1.4802 

.91633 

1.0913 

1.3563 

.26272 

.73728 

30 

40 

.67773 

.32227 

1.4755 

.92170 

1.0849 

1.3600 

.26469 

.73531 

20 

50 

.67987 

.32013 

1.4709 

.92709 

1.0786 

1.3636 

.26666 

.73333 

10 

43 

0 

.68200 

.31800 

1.4663 

.93251 

1.0724 

1.3673 

.26865 

.73135 

47 

10 

.68412 

.31588 

1.4617 

.93797 

1.0661 

1.3710 

.27063 

.72937 

50 

20 

.68624 

.31376 

1.4572 

.94345 

1.0599 

1.3748 

.27263 

.72737 

40 

30 

.68835 

.31164 

1.4527 

.94896 

1.0538 

1.3786 

.27462 

.72537 

30 

40 

.69046 

.30954 

1.4483 

.95451 

1.0476 

1.3824 

.27663 

.72337 

20 

50 

.69256 

.30744 

1.4439 

.96008 

1.0416 

1.3863 

.27864 

.72136 

10 

44 

0 

.69466 

.30534 

1.4395 

.96569 

1.0355 

1.3902 

.28066 

.71934 

46 

10 

.69675 

.30325 

1.4352 

.97133 

1.0295 

1.3941 

.28268 

.71732 

50 

20 

.69883 

.30117 

1.4310 

.97699 

1.0235 

1.3980 

.28471 

.71529 

40 

30 

.70091 

.29909 

1.4267 

.98270 

1.0176 

1.4020 

.28675 

.71325 

30 

40 

.70298 

.29702 

1.4225 

.98843 

1.0117 

1.4060 

.28879 

.71121 

20 

50 

.70505 

.29495 

1.4183 

.99420 

1.0058 

1.4101 

.29084 

.70916 

10 

45 

0 

.70711 

.29289 

1.4142 

1.0000 

1.0000 

1.4142 

.29289 

.70711 

45 

Co- 

Vers. 

Se- 

Co- 

Tan- 

Cose- 

Vers. 

Sine. 

sine. 

Sin. 

cant. 

TANG. 

gent. 

cant. 

Cos. 

CIRCUMFERENCE    AND    AREA    OF   CIRCLES. 


The  Circle. 


Notation. 


d  =  diameter  of  the  circle. 

r  =  radius  of  the  circle. 

p  =  periphery  or  circumference. 

a  =  area  of  a  circle  or  part  thereof. 

b  =  length  of  a  circle-arc. 


c  =  chord  of  a  segment,  length  of. 

h  =  height  of  a  segment. 

s  =  side  of  a  regular  polygon. 

v  =  centre  angle. 

w  =  polygon  angle. 


All  measures  must  be  expressed  in  terms  of  the  same  unit. 


Formulas  for  the  Circle. 


Periphery  or  Circumfer- 
ence. 

P  =  TTd        =  3.14d. 

Diameter  and  Radius. 
it       .     3.14 

yirea  o/  Me  ft'rcte. 

a  =  —  =  0.7854d2. 
4 

p  =  2tjt      =  6.28r. 

2ir            6.28 ' 

a  =  »rr2    =  3.14r2. 

p  =  li^a  =  3.54»/aT 

d  =  2-%fc  =  1.128^ 

4tt        12.56 

2a            4a 

r  =    <J±  =  0.5641/aT 

pr         pd 

2     "~     4   • 

$.141  592  653  589  793  238  462  643  383  279  502  884  197  169  399 


2tt  = 

6.283  185 

X*  =  0.785  398 

—  =  0.318  310 

IT 

360  _ 

IT 

114.5915 

3jt  = 

9.424  778 

yzn  =  1.047  197 

—  =  0.636  619 
it 

IT-  = 

9.869  650 

4tt  = 

12.566  370 

%■*  =  1.570  796 

—  =  0.954  929 

IT 

5tt  = 

15.707  963 

Y8TT  =  0.392  699 

y/rr  = 

1.772  453 

6tt  = 

18.849  556 

%n  =  0.523  599 

—  =  1.273  239 

7T 

# 

0.564  189 

7*r  = 
8tt- 

21.991 148 
25.132  741 

frw  =  0.261  799 
%tt  =  2.094  394 

—  =  1.909  859 

IT 

—  =  2.546  478 

w 

^ 

1.253  314 

9tt  = 

28.274  334 

5J07r  =  0.008  726 
Log.  7T  =  0.4« 

7 

—  =  3.819  718 
n 

VI 149  872  69413 
43 

vi- 

0.797  884 

744 

Circumference  and  Area  op  Circles. 

Circum. 

Area. 

Circum. 

Area. 

Circum. 

Area. 

Diam- 

s~*\ 

/* — *\ 

Diam- 

/"->, 

^Sfc^ 

Diam- 

/—>v 

>^^S 

eter. 

o 

IP 

eter. 

o 

(J) 

eter. 

o 

(J 

1 

3.1416 

0.7854 

51 

160.22 

2042.8 

101 

317.30 

8011.9 

2 

6.2832 

3.1416 

52 

163.36 

2123.7 

102 

320.44 

8171.3 

S 

9.4248 

7.0686 

53 

166.50 

2206.2 

103 

323.58 

8332.3 

4 

12.566 

12.5664 

54 

169.65 

2290.2 

104 

326.73 

8494.9 

5 

15.708 

19.6350 

55 

172.79 

2375.8 

105 

329.87 

8659.0 

6 

18.850 

28.2743 

56 

175.93 

2463.0 

106 

333.01 

8824.7 

7 

21.991 

38.4845 

57 

179.07 

2551.8 

107 

336.15 

8992.0 

8 

25.133 

50.2655 

58 

182.21 

2642.1 

108 

339.29 

9160.9 

9 

28.274 

63.6173 

59 

185.35 

2734.0 

109 

342.43 

9331.3 

10 

31.416 

78.54 

60 

188.50 

2827.4 

110 

345.58 

9503.3 

11 

34.558 

95.03 

61 

191.64 

2922.5 

111 

348.72 

9676.9 

12 

37.699 

113.10 

62 

194.78 

3019.1 

112 

351.86 

9852.0 

13 

40.841 

132.73 

63 

197.92 

3117.2 

113 

355.00 

10028.8 

14 

43.982 

153.94 

64 

201.06 

3217.0 

114 

358.14 

10207.0 

15 

47.124 

176.71 

65 

204.20 

3318.3 

115 

361.28 

10386.9 

16 

50.265 

201.06 

66 

207.35 

3421.2 

116 

364.42 

10568.3 

17 

53.407 

226.98 

67 

210.49 

3525.7 

117 

367.57 

10751.3 

18 

56.549 

254.47 

68 

213.63 

3631.7 

118 

370.71 

10935.9 

19 

59.690 

283.53 

69 

216.77 

3739.3 

119 

373.85 

11122.0 

20 

62.832 

314.16 

70 

219.91 

3818.5 

120 

376.99 

11310 

21 

65.973 

346.36 

71 

223.05 

3959.2 

121 

380.13 

11499 

22 

69.115 

380.13 

72 

226.19 

4071.5 

122 

383.27 

11690 

23 

72.257 

415.48 

73 

229.34 

4185.4 

123 

386.42 

11882 

24 

75.398 

452.39 

74 

232.48 

4300.8 

124 

389.56 

12076 

25 

78.540 

490.87 

75 

235.62 

4417.9 

125 

392.70 

12272 

26 

81.681 

530.93 

76 

238.76 

4536.5 

126 

395.84 

12469 

27 

84.823 

572.56 

77 

241.90 

4656.6 

127 

398.98 

12668 

28 

87.965 

615.75 

78 

245.04 

4778.4 

128 

402.12 

12868 

29 

91.106 

660.52 

79 

248.19 

4901.7 

129 

405.27 

13070 

30 

94.248 

706.86 

80 

251.33 

5026.6 

130 

408.41 

13273 

31 

97.389 

754.77 

81 

254.47 

5153.0 

131 

411.55 

13478 

32 

100.53 

804.25 

82 

257.61 

5281.0 

132 

414.69 

13685 

33 

103.67 

855.30 

83 

260.75 

5410.6 

133 

417.83 

13893 

34 

106.81 

907.92 

84 

263.89 

6541.8 

134 

420.97 

14103 

35 

109.96 

962.11 

85 

267.04 

5674.5 

135 

424.12 

14314 

36 

113.10 

1017.88 

86 

270.18 

5808.8 

136 

427.26 

14527 

37 

116.24 

1075.21 

87 

273.32 

5944.7 

137 

430.40 

14741 

38 

119.38 

1134.11 

88 

276.46 

6082.1 

138 

433.54 

14957 

39 

122.52 

1194.59 

89 

279.60 

6221.1 

139 

436.68 

15175 

40 

125.66 

1256.63 

90 

282.74 

6361.7 

140 

439.82 

15394 

41 

128.81 

1320.25 

91 

285.88 

6503.9 

141 

442.96 

15615 

42 

131.95 

1385.44 

92 

289.03 

6647.6 

142 

446.11 

15837 

43 

135.09 

1452.20 

93 

292.17 

6792.9 

143 

449.25 

16061 

44 

138.23 

1520.52 

94 

295.31 

6939.8 

144 

452.39 

16286 

45 

141.37 

1590.43 

95 

298.45 

7088.2 

145 

455.53 

16513 

46 

144.51 

1661.90 

96 

301.59 

7238.2 

146 

458.67 

16742 

47 

147.65 

1734.94 

97 

304.73 

7389.8 

147 

461.81 

16972 

48 

150.80 

1809.55 

98 

307.88 

7543.0 

148 

464.96 

17203 

49 

153.94 

1885.74 

99 

311.02 

7697.7 

149 

468.10 

17437 

50 

157.08 

1963.50 

100 

314.16 

7854.0 

150 

471.24 

17671 

Circumference 

and  Area  of  Circles. 

745 

Circum. 

Area. 

Circum. 

Area. 

Circum. 

Area. 

Diam- 

•— \ 

if*m^ 

Diam- 

>~\ 

/^Hl\ 

Diam- 

/^\ 

^m^ 

eter. 

o 

fP 

eter. 

O 

fp 

eter. 

o 

IP 

151 

474.38 

17908 

201 

631.46 

31731 

251 

788.54 

49481 

152 

477.52 

18146 

202 

634.60 

32047 

252 

791.68 

49876 

153 

480.66 

18385 

203 

637.74 

32365 

253 

794.82 

50273 

154 

483.81 

18627 

204 

640.89 

32685 

254 

797.96 

50671 

155 

486.95 

18869 

205 

644.03 

33006 

255 

801.11 

51071 

156 

490.09 

19113 

206 

647.17 

33329 

256 

804.25 

51472 

157 

493.23 

19359 

207 

650.31 

33654 

257 

807.39 

51875 

158 

496.37 

19607 

208 

653.45 

33979 

258 

810.53 

52279 

159 

499.51 

19856 

209 

656.59 

34307 

259 

813.67 

52685 

160 

502.65 

20106 

210 

659.73 

34636 

260 

816.81 

53093 

161 

505.80 

20358 

211 

662.88 

34967 

261 

819.96 

53502 

162 

508.94 

20612 

212 

666.02 

35299 

262 

823.10 

53913 

163 

512.08 

20867 

213 

669.16 

35633 

263 

826.24 

54325 

164 

515.22 

21124 

214 

672.30 

35968 

264 

829.38 

54739 

165 

518.36 

21382 

215 

675.44 

36305 

265 

832.52 

55155 

166 

521.50 

21642 

216 

678.58 

36644 

266 

835.66 

55572 

167 

524.65 

21904 

217 

681.73 

36984 

267 

838.81 

55990 

168 

527.79 

22167 

218 

684.87 

37325 

268 

841.95 

56410 

169 

530.93 

22432 

219 

688.01 

37668 

269 

845.09 

56832 

170 

534.07 

22698 

220 

691.15 

38013 

270 

848.23 

57256 

171 

537.21 

22966 

221 

694.29 

38360 

271 

851.37 

57680 

172 

540.35 

23235 

222 

697.43 

38708 

272 

854.51 

58107 

173 

543.50 

23506 

223 

700.58 

39057 

273 

857.66 

58535 

174 

546.64 

23779 

224 

703.72 

39408 

274 

860.80 

58965 

175 

549.78 

24053 

225 

706.86 

39761 

275 

863.94 

59396 

176 

552.92 

24328 

226 

710.00 

40115 

276 

867.08 

59828 

177 

556.06 

24606 

227 

713.14 

40471 

277 

870.22 

60263 

178 

559.20 

24885 

228 

716.28 

40828 

278 

873.36 

60699 

179 

562.35 

25165 

229 

719.42 

41187 

279 

876.50 

61136 

180 

565.49 

25447 

230 

722.57 

41548 

280 

879.65 

61575 

181 

568.63 

25730 

231 

725.71 

41910 

281 

882.79 

62016 

182 

571.77 

26016 

232 

728.85 

42273 

282 

885.93 

62458 

183 

574.91 

26302 

233 

731.99 

42638 

283 

889.07 

62902 

184 

578.05 

26590 

234 

735.13 

43005 

284 

892.21 

63347 

185 

581.19 

26880 

235 

738.27 

43374 

285 

895.35 

63794 

186 

584.34 

27172 

236 

741.42 

43744 

286 

898.50 

64242 

187 

587.48 

27465 

237 

744.56 

44115 

287 

901.64 

64692 

188 

590.62 

27759 

238 

747.70 

44488 

288 

904.78 

65144 

189 

593.76 

28055 

239 

750.84 

44863 

289 

907.92 

65597 

190 

596.90 

28353 

240 

753.98 

45239 

290 

911.06 

66052 

191 

600.04 

28652 

241 

757.12 

45617 

291 

914.20 

66508 

192 

603.19 

28953 

242 

760.27 

45996 

292 

917.35 

66966 

193 

606.33 

29255 

243 

763.41 

46377 

293 

920.49 

67426 

194 

609.47 

29559 

244 

766.55 

46759 

294 

923.63 

67887 

195 

612.61 

29865 

245 

769.69 

47144 

295 

926.77 

68349 

196 

615.75 

30172 

246 

772.83 

47529 

296 

929.91 

68813 

197 

618.89 

30481 

247 

775.97 

47916 

297 

933.05 

69279 

198 

622.04 

30791 

248 

779.12 

48305 

298 

936.19 

69747 

199 

625.18 

31103 

249 

782.26 

48695 

299. 

939.34 

70215 

200 

628.32 

31416 

250 

785.40 

49087 

300 

942.48 

70686 

746 


Circumference  and   Area  op  Circles. 


Circum 

Area. 

Circum 

Area. 

Circum. 

Area. 

Diam- 

S^\ 

s— V 

Diam- 

/*->. 

>«ss^ 

Diam- 

y^V 

/""""N 

eter. 

o 

tp 

eter. 

o 

w 

eter. 
401 

o 

o 

801 

945.62 

71158 

351 

1102.70 

96  762 

1259.78 

126  293 

302 

948.76 

71631 

352 

1105.84 

97  314 

402 

1262.92 

126  923 

303 

951.90 

72107 

353 

1108.98 

97  868 

403 

1266.06 

127  556 

304 

955.04 

72583 

354 

1112.12 

98  423 

404 

1269.20 

128190 

305 

958.19 

73062 

355 

1115.27 

98  980 

405 

1272.35 

128  825 

306 

961.33 

73542 

356 

1118.41 

99  538 

406 

1275.49 

129  462 

307 

964.47 

74023 

357 

1121.55 

100  098 

407 

1278.63 

130100 

308 

967.61 

74506 

358 

1124.69 

100  660 

408 

1281.77 

130  741 

309 

970.75 

74991 

359 

1127.83 

101223 

409 

1284.91 

131382 

310 

973.89 

75477 

360 

1130.97 

101788 

410 

1288.05 

132  025 

311 

977.04 

75964 

361 

1134.11 

102  354 

411 

1291.19 

132  670 

312 

980.18 

76454 

362 

1137.26 

102  922 

412 

1294.34 

133  317 

313 

983.32 

76945 

363 

1140.40 

103  491 

413 

1297.48 

133  965 

314 

986.46 

77437 

364 

1143.54 

104  062 

414 

1300.62 

134  614 

315 

989.60 

77931 

365 

1146.68 

104  635 

415 

1303.76 

135  265 

316 

992.74 

78427 

366 

1149.82 

105  209 

416 

1306.90 

135  918 

317 

995.88 

78924 

367 

1152.96 

105  785 

417 

1310.04 

136  572 

318 

999.03 

79423 

368 

1156.11 

106  362 

418 

1313.19 

137  228 

319 

1002.17 

79923 

369 

1159.25 

106  941 

419 

1316.33 

137  885 

320 

1005.31 

80425 

370 

1162.39 

107  521 

420 

1319.47 

138  544 

321 

1008.45 

80928 

371 

1165.53 

108  103 

421 

1322.61 

139  205 

322 

1011.59 

81433 

372 

1168.67 

108  687 

422 

1325.75 

139  867 

323 

1014.73 

81940 

373 

1171.81 

109  272 

423 

1328.89 

140  531 

324 

1017.88 

82448 

374 

1174.96 

109  858 

424 

1332.04 

141196 

325 

1021.02 

82958 

375 

1178.10* 

110  447 

425 

1335.18 

141863 

326 

1024.16 

83469 

376 

1181.24 

111036 

426 

1338.32 

142  531 

327 

1027.30 

83982 

377 

1184.38 

111628 

427 

1341.46 

143  201 

328 

1030.44 

84496 

378 

1187.52 

112  221 

428 

1344.60 

143  872 

329 

1033.58 

85012 

379 

1190.66 

112  815 

429 

1347.74 

144  545 

330 

1036.73 

85530 

380 

1193.81 

113  411 

430 

1350.88 

145  220 

331 

1039.87 

86049 

381 

1196.95 

114  009 

431 

1354.03 

145  896 

332 

1043.01 

86570 

382 

1200.09 

114  608 

432 

1357.17 

146  574 

333 

1046.15 

87092 

383 

1203.23 

115  209 

433 

1360.31 

147  254 

334 

1049.29 

87616 

384 

1206.37 

115  812 

434 

1363.45 

147  934 

335 

1052.43 

88141 

385 

1209.51 

116  416 

435 

1366.59 

148  617 

336 

1055.58 

88668 

386 

1212.65 

117  021 

436 

1369.73 

149  301 

337 

1058.72 

89197 

387 

1215.80 

117  628 

437 

1372.88 

149  987 

338 

1061.86 

89727 

388 

1218.94 

118  237 

438 

1376.02 

150  674 

339 

1065.00 

90259 

389 

1222.08 

118  847 

439 

1379.16 

151  363 

340 

1068.14 

90792 

390 

1225.22 

119  459 

440 

1382.30 

152  053 

341 

1071.28 

91327 

391 

1228.36 

120  072 

441 

1385.44 

152  745 

342 

1074.42 

91863 

392 

1231.50 

120  687 

442 

1388.58 

153  439 

343 

1077.57 

92401 

393 

1234.65 

121304 

443 

1391.73 

154134 

344 

1080.71 

92941 

394 

1237.79 

121922 

444 

1394.87 

154  830 

345 

1083.85 

93482 

395 

1240.93 

122  542 

445 

1398.01 

155  528 

346 

1086.99 

94025 

396 

1244.07 

123163 

446 

1401.15 

156  228 

347 

1090.13 

94569 

397 

1247.21 

123  786 

447 

1404.29 

156  930 

348 

1093.27 

95115 

398 

1250.35 

124  410 

448 

1407.43 

157  633 

349 

1096.42 

95662 

399 

1253.50 

125  036 

449 

1410.58  158  337 

350 

1099.56 

96211 

400 

1256.64 

125  664 

450 

1413.72  1 

159  043 

Circumference 

and  Area  of  Circles. 

747 

Circum. 

Area. 

Circum. 

Area. 

Circum. 

Area. 

Diam- 

/"->v 

/^^. 

Diam- 

/TS 

y^SS^ 

Diam- 

/~\ 

/^H^v 

eter. 

o 

w 

eter. 

o 

w 

eter. 

o 

IP 

451 

1416.86 

159  751 

501 

1573.94 

197  136 

551 

1731.02 

238  448 

452 

1420.00 

160  460 

502 

1577.08 

197  923 

552 

1734.16 

239  314 

453 

1423.14 

161 171 

503 

1580.22 

198  713 

553 

1737.40 

240  182 

454 

1426.28 

161  883 

504 

1583.36 

199  504 

554 

1740.44 

241  051 

455 

1429.42 

162  597 

505 

1586.50 

200  296 

555 

1743.58 

241  922 

456 

1432.57 

163  313 

506 

1589.65 

201  090 

556 

1746.73 

242  795 

457 

1435.71 

164  030 

507 

1592.79 

201886 

557 

1749.87 

243  669 

458 

1438.85 

164  748 

508 

1595.93 

202  683 

558 

1753.01 

244  545 

459 

1441.99 

165  468 

509 

1599.07 

203  482 

559 

1756.15 

245  422 

460 

1445.13 

166190 

510 

1602.21 

204  282 

560 

1759.29 

246  301 

461 

1448.27 

166  914 

511 

1605.35 

205  084 

561 

1762.43 

247  181 

462 

1451.42 

167  639 

512 

1608.50 

205  887 

562 

1765.58 

248  063 

463 

1454.56 

168  365 

513 

1611.64 

206  692 

563 

1768.72 

248  947 

464 

1457.70 

169  093 

514 

1614.78 

207  499 

564 

1771.86 

249  832 

465 

1460.84 

169  823 

515 

1617.92 

208  307 

565 

1775.00 

250  719 

466 

1463.98 

170  554 

516 

1621.06 

209  117 

566 

1778.14 

251607 

467 

1467.12 

171287 

517 

1624.20 

209  928 

567 

1781.28 

252  497 

468 

1470.27 

172  021 

518 

1627.35 

210  741 

568 

1784.42 

253  388 

469 

1473.41 

172  757 

519 

1630.49 

211  556 

569 

1787.57 

254  281 

470 

1476.55 

173  494 

520 

1633.63 

212  372 

570 

1790.71 

255176 

471 

1479.69 

174  234 

521 

1636.77 

213  189 

571 

1793.85 

256  072 

472 

1482.83 

174  974 

522 

1639.91 

214  008 

572 

1796.99 

256  970 

473 

1485.97 

175  716 

523 

1643.05 

214  829 

573 

1800.13 

257  869 

474 

1489.11 

176  460 

524 

1646.20 

215  651 

571 

1803.27 

258  770 

475 

1492.26 

177  205 

525 

1649.34 

216  475 

575 

1806.42 

259  672 

476 

1495.40 

177  952 

526 

1652.48 

217  301 

576 

1S09.56 

260  576 

477 

1498.54 

178  701 

527 

1655.62 

218128 

577 

1812.70 

261  482 

478 

1501.68 

179  451 

528 

1658.76 

218  956 

578 

1815.84 

262  389 

479 

1504.82 

180  203 

529 

1661.90 

219  787 

579 

1818.98 

263  298 

480 

1507.96 

180  956 

530 

1665.04 

220  618 

580 

1822.12 

264  208 

481 

1511.11 

181  711 

531 

1668.19 

221452 

581 

1825.27 

265120 

482 

1514.25 

182  467 

532 

1671.33 

222  287 

582 

1828.41 

266  033 

483 

1517.39 

183  225 

533 

1674.47 

223  123 

583 

1831.55 

266  948 

484 

1520.53 

183  984 

534 

1677.61 

223  961 

584 

1834.69 

267  865 

485 

1523.67 

184  745 

535 

1680.75 

224  801 

585 

1837.83 

268  783 

486 

1526.81 

185  508 

536 

1683.89 

225  642 

586 

1840.97 

269  702 

487 

1529.96 

186  272 

537 

1687.04 

226  484 

587 

1844.11 

270  624 

488 

1533.10 

187  038 

538 

1690.18 

227  329 

588 

1847.26 

271547 

489 

1536.24 

187  805 

539 

1693.32 

228175 

589 

1850.40 

272  471 

490 

1539.38 

188  574 

540 

1696.46 

229  022 

590 

1853.54 

273  397 

491 

1542.52 

189  345 

541 

1699.60 

229  871 

591 

1856.68 

274  325 

492 

1545.66 

190  117 

542 

1702.74 

230  722 

592 

1859.82 

275  254 

493 

1548.81 

190  890 

543 

1705.88 

231  574 

593 

1862.96 

276  184 

494 

1551.95 

191  665 

544 

1709.03 

232  428 

594 

1866.11 

277  117 

495 

1555.09 

192  442 

•545 

1712.17 

233  283 

595 

1869.25 

278  051 

496 

1558.23 

193  221 

546 

1715.31 

234  140 

596 

1872.39 

278  986 

497 

1561.37 

194  000 

547 

1718.45 

234  998 

597 

1875.53 

279  923 

498 

1564.51 

194  782 

548 

1721.59 

235  858 

598 

1878.67 

280  862 

499 

1567.65 

195  565 

549 

1724.73 

236  720 

599 

1881.81 

281802 

500 

1570.80 

196  350 

550 

1727.88 

237  583 

600 

1884.% 

282  743 

748 

Circumference 

and  Area  of  Circles. 

Circum. 

Area. 

Circum. 

Area. 

Circum. 

Area. 

Diam- 

/"—N 

/SH^. 

Diam- 

/^\ 

,<^^V 

Diam- 

s~*\ 

_,»— V 

eter. 

o 

w 

eter. 

o 

IP 

eter. 

o 

o 

601 

1888.10 

283  687 

651 

2045.18 

332  853 

701 

2202.26 

385  945 

602 

1891.24 

284  631 

652 

2048.32 

333  876 

702 

2205.40 

387  047 

603 

1894.38 

285  578 

653 

2051.46 

334  901 

703 

2208.54 

888  151 

604 

1897.52 

286  526 

654 

2054.60 

335  927 

704 

2211.68 

389  256 

605 

1900.66 

287  475 

655 

2057.74 

336  955 

705 

2214.82 

390  363 

606 

1903.81 

288  426 

656 

2060.88 

337  985 

706 

2217.96 

391  471 

607 

1906.95 

289  379 

657 

2064.03 

339  016 

707 

2221.11 

392  580 

608 

1910.09 

290  333 

658 

2067.17 

340  049 

708 

2224.25 

393  692 

609 

1913.23 

291289 

659 

2070.31 

341083 

709 

2227.39 

394  805 

610 

1916.37 

292  247 

660 

2073.45 

342  119 

710 

2230.53 

395  919 

611 

1919.51 

293  206 

661 

2076.59 

343  157 

711 

2233.67 

397  035 

612 

1922.65 

294166 

662 

2079.73 

344  1% 

712 

2236.81 

398  153 

613 

1925.80 

295128 

663 

2082.&S 

345  237 

713 

2239.96 

399  272 

614 

1928.94 

296  092 

664 

2086.02 

346  279 

714 

2243.10 

400  393 

615 

1932.08 

297  057 

665 

2089.16 

347  323 

715 

2246.24 

401  515 

616 

1935.22 

298  024 

666 

2092.30 

348  368 

716 

2249.38 

402  639 

617 

1938.36 

298  992 

667 

2095.44 

349  415 

717 

2252.52 

403  765 

618 

1941.50 

299  962 

668 

2098.58 

350  464 

718 

2255.66 

404  892 

619 

1944.65 

300  934 

669 

2101.73 

351  514 

719 

2258.81 

406  020 

620 

1947.79 

301907 

670 

2104.87 

352  565 

720 

2261.95 

407150 

621 

1950.93 

302  882 

671 

2108.01 

353  618 

721 

2265.09 

408  282 

622 

1954.07 

303  858 

672 

2111.15 

354  673 

722 

2268.23 

409  416 

623 

1957.21 

304  836 

673 

2114.29 

355  730 

723 

2271.37 

410  550 

624 

1960.35 

305  815 

674 

2117.43 

356  788 

724 

2274.51 

411687 

625 

1963.50 

306  796 

675 

2120.58 

357  847 

725 

2277.65 

412  825 

626 

1966.64 

307  779 

676 

2123.72 

358  908 

726 

2280.80 

413  965 

627 

1969.78 

308  763 

677 

2126.86 

359  971 

727 

2283.94 

415  106 

628 

1972.92 

309  748 

678 

2130.00 

361035 

728 

2287.08 

416  248 

629 

1976.06 

310  736 

679 

2133.14 

362  101 

729 

2290.22 

417  393 

630 

1979.20 

311725 

680 

2136.28 

363  168 

730 

2293.36 

418  539 

631 

1982.35 

312  715 

681 

2139.42 

364  237 

731 

2296.50 

419  686 

632 

1985.49 

313  707 

682 

2142.57 

365  308 

732 

2299.65 

420  835 

633 

1988.63 

314  700 

683 

2145.71 

366  380 

733 

2302.79 

421986 

634 

1991.77 

315  696 

684 

2148.85 

367  453 

734 

2305.93 

423139 

635 

1994.91 

316  692 

685 

2151.99 

368  528 

735 

2309.07 

424  292 

636 

1998.05 

317  690 

686 

2155.13 

369  605 

736 

2312.21 

425  447 

637 

2001.19 

318  690 

687 

2158.27 

370  684 

737 

2315.35 

426  604 

638 

2004.34 

319  692 

688 

2161.42 

371  764 

738 

2318.50 

427  762 

639 

2007.48 

320  695 

689 

2164.56 

372  845 

739 

2321.64 

428  922 

640 

2010.62 

321699 

690 

2167.70 

373  928 

740 

2324.78 

430  084 

641 

2013.67 

322  705 

691 

2170.84 

375  013 

741 

2327.92 

431247 

642 

2016.90 

323  713 

692 

2173.98 

376  099 

742 

2331.06 

432  412 

643 

2020.04 

324  722 

693 

2177.12 

377  187 

743 

2334.30 

433  578 

644 

2023.19 

325  733 

694 

2180.27 

378  276 

744 

2337.34 

434  746 

645 

2026.33 

326  745 

695 

2183.41 

379  367 

745 

2340.49 

435  916 

646 

2029.47 

327  759 

696 

2186.55 

380  459 

746 

2343.63 

437  087 

647 

2032.61 

328  775 

697 

2189.69 

381554 

747 

2346.77 

438  259 

648 

2035.75 

329  792 

698 

2192.83 

382  649 

748 

2349.91 

439  433 

649 

2038.89 

330  810 

699 

2195.97 

383  746 

749 

2353.05 

440  609 

650 

2042.04 

331831 

700 

2199.11 

384  845 

750 

2356.19 

441786 

Circumference 

and   Area  op  Circles. 

749 

Circum. 

Area. 

Circum. 

Area. 

Circum. 

Area. 

Diam- 

S~\ 

/*ssv 

Diam- 

/"~\ 

>*s^S 

Diam- 

/"— \ 

/^i^ 

eter. 

o 

IP 

eter. 

o 

w 

eter. 

o 

IP 

751 

2359.34 

442  965 

801 

2516.42 

503  912 

851 

2673.50 

568  786 

752 

2362.48 

444  146 

802 

2519.56 

505171 

852 

2676.61 

570  124 

753 

2365.62 

445  328 

803 

2522.70 

506  432 

853 

2679.78 

571  463 

754 

2368.76 

416  511 

804 

2525.84 

507  694 

854 

2682.92 

572  803 

755 

2371.90 

447  697 

805 

2528.98 

508  958 

855 

2686.06 

574  146 

756 

2375.04 

448  883 

806 

2532.12 

510  223 

856 

2689.20 

575  490 

757 

2378.19 

450  072 

807 

2535.27 

511490 

857 

2692.34 

576  835 

758 

2381.33 

451  262 

808 

2538.41 

512  758 

858 

2695.49 

578  182 

759 

2384.47 

452  453 

809 

2541.55 

514  028 

859 

2698.63 

579  530 

760 

2387.61 

453  646 

810 

2544.69 

515  300 

860 

2701.77 

580  880 

761 

2390.75 

454  841 

811 

2547.83 

516  573 

861 

2704.91 

582  232 

762 

2393.89 

456  037 

812 

2550.97 

517  848 

862 

2708.05 

583  585 

763 

2397.04 

457  234 

813 

2554.11 

519  124 

863 

2711.19 

584  940 

764 

2400.18 

458  434 

814 

2557.26 

520  402 

864 

2714.34 

586  297 

765 

2403.32 

459  635 

815 

2560.40 

521681 

865 

2717.48 

587  655 

766 

2406.46 

460  837 

816 

2563.54 

522  962 

866 

2720.62 

589  014 

767 

2409.60 

462  041 

817 

2566.68 

524  245 

867 

2723.76 

590  375 

768 

2412.74 

463  247 

818 

2569.82 

525  529 

868 

2726.90 

591738 

769 

2415.88 

464  454 

819 

2572.96 

526  814 

869 

2730.04 

593102 

770 

2419.03 

465  663 

820 

2576.11 

528102 

870 

2733.19 

594  468 

771 

2422.17 

466  873 

821 

2579.25 

529  391 

871 

2736.33 

595  835 

772 

2425.31 

468  085 

822 

2582.31 

530  681 

872 

2739.47 

597  204 

773 

2428.45 

469  298 

823 

2585.53 

531  973 

873 

2742.61 

598  575 

774 

2431.59 

470  513 

824 

2588.67 

533  267 

874 

2745.75 

599  947 

775 

2434.73 

471  730 

825 

2591.81 

534  562 

875 

2748.89 

601320 

776 

2437.88 

472  948 

826 

2594.96 

535  858 

876 

2752.04 

602  696 

777 

2441.02 

474168 

827 

2598.10 

537  157 

877 

2755.18 

604  073 

778 

2444.16 

475  389 

828 

2601.24 

538  456 

878 

2758.32 

605  451 

779 

2447.30 

476  612 

829 

2604.38 

539  758 

879 

2761.46 

606  831 

780 

2450.44 

477  836 

830 

2607.52 

541061 

880 

2764.60 

608  212 

781 

2453.58 

479  062 

831 

2610.66 

542  365 

881 

2767.74 

609  595 

782 

2456.73 

480  290 

832 

2613.81 

543  671 

882 

2770.88 

611  PC'/ 

783 

2459.87 

481  519 

833 

2616.95 

544  979 

883 

2774.03 

61z  366 

784 

2463.01 

482  750 

834 

2620.09 

546  288 

884 

2777.17 

613  754 

785 

2466.15 

483  982 

835 

2623.23 

547  599 

885 

2780.«1 

615  143 

786 

2469.29 

485  216 

836 

2626.37 

548  912 

886 

2783.45 

616  534 

787 

2472.43 

486  451 

837 

2629.51 

550  226 

887 

2786.59 

617  927 

788 

2475.58 

487  688 

838 

2632.65 

551541 

888 

2789.73 

619  321 

789 

2478.72 

488  927 

839 

2635.80 

552  858 

889 

2792.88 

620  717 

790 

2481.86 

490  167 

840 

2638.94 

554177 

890 

2796.02 

622  114 

791 

2485.00 

491  409 

841 

2642.08 

555  497 

891 

2799.16 

623  513 

792 

2488.14 

492  652 

842 

2645.22 

556  819 

892 

2802.30 

624  913 

793 

2491.28 

493  897 

843 

2648.36 

558142 

893 

2805.44 

626  315 

794 

2494.42 

495  143 

844 

2651.50 

559  467 

894 

2808.58 

627  718 

795 

2497.57 

4%  391 

845 

2654.65 

560  794 

895 

2811.73 

629124 

796 

2500.71 

497  641 

846 

2657.79 

562  122 

896 

2814.87 

630  530 

797 

2503.85 

498  892 

847 

2660.93 

563  452 

897 

2818.01 

631938 

798 

2506.99 

500  145 

848 

2664.07 

564  783 

898 

2821.15 

633  348 

799 

2510.13 

501399 

849 

2667.21 

566  116 

899 

2824.29 

634  760 

800 

2513.27 

502  655 

850 

2670.35 

567  450 

900   I 

2827.43 

636  173 

750 

<'li:<  IMFERENCH 

and  Area  op  Circles. 

Circum. 

Area. 

Cirrnm. 

Area. 

Ciivuffl, 

Area. 

Diam- 

/^\ 

/" — N 

Diam- 

/*"V 

/" — N 

I>i:mi- 

/■ — V 

/-— V 

eter. 

o 

IP 

eter. 

o 

w 

eter. 
967 

o 

o 

901 

2830.58 

637  587 

934 

2934.25 

685147 

3037.92 

734  417 

902 

2833.72 

639  003 

935 

2937.39 

686  615 

968 

3041.06 

735  937 

903 

2836.86 

640  421 

936 

2940.53 

688  084 

969 

3044.20 

737  458 

904 

2840.00 

641840 

937 

2943.67 

689  555 

970 

3047.34 

738  981 

905 

2843.14 

643  261 

938 

2946.81 

691028 

971 

3050.49 

740  506 

906 

2846.28 

644  683 

939  • 

2949.96 

692  502 

972 

3053.63 

742  032 

907 

2849.42 

G46107 

940 

2953.10 

693  978 

973 

3056.77 

743  559 

908 

2852.57 

647  533 

941 

2956.24 

695  455 

974 

3059.91 

745  088 

909 

2855.71 

648  960 

942 

2959.38 

696  934 

975 

3063.05 

746  619 

910 

2858.85 

650  388 

943 

2962.52 

698  415 

976 

3066.19 

748  151 

911 

2861.99 

651  818 

944 

2965.66 

699  897 

977 

3069.34 

749  685 

912 

2865.13 

653  250 

945 

2968.81 

701380 

978 

3072.48 

751221 

913 

2868.27 

654  684 

946 

2971.95 

702  865 

979 

3075.62 

752  758 

914 

2871.42 

656118 

947 

2975.09 

704  352 

980 

3078.76 

754  2% 

915 

2874.56 

657  555 

948 

2978.23 

705  840 

981 

3081.90 

755  837 

916 

2877.70 

658  993 

949 

2981.37 

707  330 

982 

3085.04 

757  378 

917 

2880.84 

660  433 

950 

2984.51 

708  822 

983 

3088.19 

758  922 

918 

2883.98 

661874 

951 

2987.65 

710  315 

984 

3091.33 

760  466 

919 

2887.12 

663  317 

952 

2990.80 

711  809 

985 

3094.47 

762  013 

920 

2890.27 

664  761 

953 

2993.94 

713  307 

986 

3097.61 

763  561 

921 

2893.41 

666  207 

954 

2997.08 

714  803 

987 

3100.75 

765111 

922 

2896.55 

667  654 

955 

3000.22 

716  303 

988 

3103.89 

766  662 

923 

2899.69 

669  103 

956 

3003.36 

717  804 

989 

3107.04 

768  215 

924 

2902.83 

670  554 

957 

3006.50 

719  306 

990 

3110.18 

769  769 

925 

2905.97 

672  006 

958 

3009.65 

720  810 

991 

3113.32 

771325 

926 

2909.11 

673  460 

959 

3012.79 

722  316 

992 

3116.46 

772  882 

927 

2912.26 

674  915 

960 

3015.93 

723  823 

993 

3119.60 

774  441 

928 

2915.40 

676  372 

961 

3019.07 

725  332 

994 

3122.74 

776  002 

929 

2918.54 

677  831 

962 

3022.21 

726  842 

995 

3125.88 

777  564 

930 

2921.68 

679  291 

963 

3025.35 

728  354 

996 

3129.03 

779128 

931 

2924.82 

680  752 

964 

3028.50 

729  867 

997 

3132.17 

780  693 

932 

2927.96 

682  216 

965 

3031.64 

731382 

998 

3135.31 

782  260 

933 

2931.11 

683  680 

966 

3034.78 

732  899 

999 

31138.45 

783  828 

Note.— When  it  is  desired  to  find  the  circumference  corresponding  to 
any  diameter  not  in  the  table,  point  off  as  many  places  in  the  circumfer- 
ence as  have  been  pointed  off  in  the  diameter,  and  point  off  twice  as  many 
places  in  this  area  as  have  been  pointed  off  in  the  diameter.    Thus : 


Xameters. 

Circumferences. 

Areas 

9.16 

28.777 

65.8 

91.6 

287.77 

6  589.9 

916. 

2877.7 

658  993. 

9160. 

28777. 

65  899  321. 

When  it  is  desired  to  find  the  circumference  or  area  for  any  diameter 
consisting  of  a  whole  number  and  a  decimal,  it  may  be  done  by  taking  the 
difference  between  the  tabular  figures  for  the  diameters  between  which 
the  given  diameter  lies  and  multiplying  this  difference  by  the  decimal  and 
adding  the  result  to  the  tabular  value  corresponding  to  the  next  lower 
diameter. 


POWERS    AND    ROOTS. 


Number. 

Squares. 

Cubes. 

V  Roots. 

f  Boots. 

Reciprocals. 

1 

1 

1 

1.000  0000 

1.000  0000 

1.000  000  000 

2 

4 

8 

1.414  2136 

1.259  9210 

.500  000  000 

3 

9 

27 

1.732  0508 

1.442  2496 

.333  333  333 

4 

16 

64 

2.000  0000 

1.587  4011 

.250  000  000 

5 

25 

125 

2.236  0680 

1.709  9759 

.200  000  000 

6 

36 

216 

2.449  4897 

1.817  1206 

.166  666  667 

7 

49 

343 

2.645  7513 

1.912  9312 

.142  857  143 

8 

64 

512 

2.828  4271 

2.000  0000 

.125  000  000 

9 

81 

729 

3.000  0000 

2.080  0837 

.111  111  111 

10 

100 

1000 

3.162  2777 

2.154  4347 

.100  000  000 

11 

121 

1331 

3.316  6248 

2.223  9801 

.090  909  091 

12 

144 

1728 

3.464  1016 

2.289  4286 

.083333  333 

13 

169 

2197 

3.605  5513 

2.351  3347 

.076  923  077 

14 

196 

2  744 

3.741  6574 

2.410  1422 

.071  428  571 

15 

225 

3  375 

3.872  9833 

2.466  2121 

.066  666  667 

16 

256 

4  096 

4.000  0000 

2.519  8421 

.062  500  000 

17 

289 

4  913 

4.123  1056 

2.571  2816 

.058  823  529 

18 

324 

5  832 

4.242  6407 

2.620  7414 

.055  555  556 

19 

361 

6  859 

4.358  8989 

2.668  4016 

.052  631  579 

20 

400 

8000 

4.472  1360 

2.714  4177 

.050  000  000 

21 

441 

9  261 

4.582  5757 

2.758  9243 

.047  619  048 

22 

484 

10  648 

4.690  4158 

2.802  0393 

.045  454  545 

23 

529 

12167 

4.795  8315 

2.843  8670 

.043  478  261 

24 

576 

13  824 

4.898  9795 

2.884  4991 

.041  666  667 

25 

625 

15  625 

5.000  0000 

2.924  0177 

.040  000  000 

26 

676 

17  576 

5.099  0195 

2.962  4960 

.038  461  538 

27 

729 

19  683 

5.196  1524 

3.000  0000 

.037  037  037 

28 

784 

21952 

5.291  5026 

3.036  5889 

.035  714  286 

29 

841 

24  389 

5.385  1648 

3.072  3168 

.034  482  759 

30 

900 

27  000 

5.477  2256 

3.107  2325 

.033  333  333 

31 

961 

29  791 

5.567  7644 

3.141  3806 

.032  258  065 

32 

1024 

32  768 

5.656  8542 

3.174  8021 

.031  250  000 

33 

1089 

35  937 

5.744  5626 

3.207  5343 

.030  303  030 

34 

1156 

39  304 

5.830  9519 

3.239  6118 

.029  411  765 

35 

1225 

42  875 

5.916  0798 

3.271  0663 

.028  571  429 

36 

1296 

46  656 

6.000  0000 

3.301  9272 

.027  777  778 

37 

1369 

50  653 

6.082  7625 

3.332  2218 

.027  027  027 

38 

1444 

54  872 

6.164  4140 

3.361  9754 

.026  315  789 

39 

1521 

59  319 

6.244  9980 

3.391  2114 

.025  641  026 

40 

1600 

64  000 

6.324  5553 

3.419  9519 

.025  000  000 

41 

1681 

68  921 

6.403  1242 

3.448  2172 

.024  390  244 

42 

1764 

74  088 

6.480  7407 

3.476  0266 

.023  809  524 

43 

1849 

79  507 

6.557  4385 

3.503  3981 

.023  255  814 

44 

1936 

85184 

6.633  2496 

3.530  3483 

.022  727  273 

45 

2  025 

91125 

6.708  2039 

3.556  8933 

.022  222  222 

46 

2  116 

97  336 

6.782  3300 

3.583  0479 

.021  739  130 

47 

2  209 

103  823 

6.855  6546 

3.608  8261 

.021  276  600 

48 

2  304 

110  592 

6.928  2032 

3.634  2411 

.020  833  333 

49 

2  401 

117  649 

7.000  0000 

3.659  3057 

.020  408  163 

50 

2500 

125  000 

7.071  0678 

3.684  0314 

.020  000  000 

51 

2  601 

132  651 

7.141  4284 

3.708  4298 

.019  607  843 

52 

2  704 

140  608 

7.211  1026 

3.732  5111 

.019  230  769 

752 

Powers 

and  Roots 

Number. 

Squares. 

Cubes. 

l' Roots. 

f  Boots. 

Reciprocals. 

53 

2809 

148  877 

7.2801099 

3.756  2858 

.018  867  925 

54 

2  916 

157  464 

7.348  4692 

3.779  7631 

.018  518  519 

55 

3025 

166  375 

7.416  1985 

3.802  9525 

.018  181  818 

56 

3136 

175  616 

7.483  3148 

3.825  8624 

.017  857  143 

57 

3  249 

185  193 

7.549  8344 

3.848  5011 

.017  543  860 

58 

3364 

195  112 

7.615  7731 

3.870  8766 

.017  241  379 

59 

3  481 

205  379 

7.681 1457 

3.892  9965 

.016  949  153 

60 

3600 

216  000 

7.745  9667 

3.914  8676 

.016  666  667 

61 

3  721 

226  981 

7.810  2497 

3.930  4972 

.016  393  443 

62 

3  844 

238  328 

7.874  0079 

3.957  8915 

.016  129  032 

63 

3  969 

250  047 

7.937  2539 

3.979  0571 

.015  873  016 

64 

4096 

262144 

8.000  0000 

4.000  0000 

.015  625  000 

65 

4225 

274  625 

8.062  2577 

4.020  7256 

.015  384  615 

66 

4356 

287  496 

8.124  0384 

4.041  2401 

.015  151  515 

67 

4  489 

300  763 

8.185  3528 

4.061  5480 

.014  925  373 

68 

4  624 

314  432 

8.246  2113 

4.081  6551 

.014  705  882 

69 

4  761 

328  509 

8.306  6239 

4.101  5661 

.014  492  754 

70 

4900 

343  000 

8.366  6003 

4.121  2853 

.014  285  714 

71 

5  041 

357  911 

8.426  1498 

4.140  8178 

.014  084  517 

72 

5184 

373  248 

8.485  2814 

4.160  1676 

.013  888  889 

73 

5  329 

389  017 

8.544  0037 

4.179  3390 

.013  698  630 

74 

5  476 

405  224 

8.602  3253 

4.198  3364 

.013  513  514 

75 

5  625 

421  875 

8.660  2540 

4.217  1633 

.013  333  333 

76 

5  776 

438  976 

8.717  7979 

4.235  8236 

.013  157  895 

77 

5929 

456  533 

8.774  9644 

4.254  3210 

.012  987  013 

78 

6  084 

474  552 

8.831  7609 

4.272  6586 

.012  820  513 

79 

6  241 

493  039 

8.8881944 

4.290  8404 

.012  658  228 

80 

6  400 

512  000 

8.944  2719 

4.308  8695 

.012  500  000 

81 

6  561 

531441 

9.000  0000 

4.326  7487 

.012  345  679 

82 

6  724 

551368 

9.055  3851 

4.344  4815 

.012  195  122 

83 

6  889 

571  787 

9.110  4336 

4.362  0707 

.012  048  193 

84 

7  056 

592  704 

9.165  1514 

4.379  5191 

.011  904  762 

85 

7225 

614125 

9.219  5445 

4.396  8296 

.011  764  706 

86 

7  396 

636  056 

9.273  6185 

4.414  0049 

.011  627  907 

87 

7  569 

658  503 

9.327  3791 

4.431  0476 

.011  494  253 

88 

7  744 

681472 

9.380  8315 

4.447  9692 

.011  363  636 

89 

7  921 

704  969 

9.433  9811 

4.464  7451 

.011  235  955 

90 

8100 

729  000 

9.486  8330 

4.481  4047 

.011  111  111 

91 

8  281 

753  571 

9.539  3920 

4.497  9414 

.010  989  011 

92 

8  464 

778  688 

9.591  6630 

4.514  3574 

.010  869  565 

93 

8  649 

804  357 

9.643  6508 

4.530  6549 

.010  752  688 

94 

8836 

830  584 

9.695  3597 

4.546  8359 

.010  638  298 

95 

9  025 

857  375 

9.746  7943 

4.562  9026 

.010  526  316 

96 

9  216 

884  736 

9.797  9590 

4.578  8570 

.010  416  667 

97 

9  409 

912  673 

9.848  8578 

4.594  7009 

.010  309  278 

98 

9604 

941192 

9.899  4949 

4.610  4363 

.010  204  082 

99 

9  801 

970  299 

9.949  8744 

4.626  0650 

.010  101  010 

100 

10  000 

1000  000 

10.000  0000 

4.6415888 

.010  000  000 

101 

10  201 

1  030  301 

10.049  8756 

4.657  0095 

.009  900  990 

102 

10  404 

1061208 

10.099  5049 

4.672  3287 

.009  803  922 

103 

10  609 

1  092  727 

10.148  8916 

4.687  5482 

.009  708  738 

104 

10  816 

1  124  864 

10.198  0390 

4.702  6694 

.009  615  385 

Powers 

and  Roots 

753 

Number. 

Squares. 

Cubes. 

V  Roots. 

f  Roots. 

Reciprocals. 

105 

11025 

1 157  625 

10.246  9508 

4.717  6940 

.009  523  810 

106 

11236 

1 191  016 

10.295  6301 

4.732  6235 

.009  433  962 

107 

11449 

1225  043 

10.344  0804 

4.747  4594 

.009  345  794 

108 

11664 

1259  712 

10.392  3048 

4.762  2032 

.009  259  259 

109 

11881 

1295  029 

10.440  3065 

4.776  8562 

.009  174  312 

110 

12100 

1331000 

10.488  0885 

4.791  4199 

.009  090  909 

111 

12  321 

1  367  631 

10.535  6538 

4.805  8995 

.009  009  009 

112 

12  544 

1404  928 

10.583  0052 

4.820  2845 

.008  928  571 

113 

12  769 

1  442  897 

10.630  1458 

4.834  5881 

.008  849  558 

114 

12  996 

1481544 

10.677  0783 

4.848  8076 

.008  771  930 

115 

13  225 

1  520  875 

10.723  8053 

4.862  9442 

.008  695  652 

116 

13  456 

1560  896 

10.770  3296 

4.876  9990 

.008  620  690 

117 

13  689 

1  601  613 

10.816  6538 

4.890  9732 

.008  547  009 

118 

13  924 

1  643  032 

10.862  7805 

4.904  8681 

.008  474  576 

119 

14  161 

1  685  159 

10.908  7121 

4.918  6847 

.008  403  361 

120 

14  400 

1728  000 

10.954  4512 

4.932  4242 

.008  333  333 

121 

14  641 

1  771  561 

11.000  0000 

4.946  0874 

.008  264  463 

122 

14  884 

1  815  848 

11.045  3610 

4.959  6757 

.008  196  721 

123 

15129 

1  860  867 

11.090  5365 

4.973  1898 

.008  130  081 

124 

15  376 

1  906  624 

11.135  5287 

4.986  6310 

.008  064  516 

125 

15  625 

1  953  125 

11.180  3399 

5.000  0000 

.008  000  000 

126 

15  876 

2  000  376 

11.224  9722 

5.013  2979 

.007  936  508 

127 

16129 

2  048  383 

11.269  4277 

5.026  5257 

.007  874  016 

128 

16  384 

2  097  152 

11.313  7085 

5.039  6842 

.007  812  500 

129 

16  641 

2  146  689 

11.357  8167 

5.052  7743 

.007  751  938 

130 

16  900 

2197  000 

11.401  7543 

5.065  7970 

.007  692  308 

131 

17161 

2  248  091 

11.445  5231 

5.078  7531 

.007  633  588 

132 

17  424 

2  299  968 

11.489  1253 

5.091  6434 

.007  575  758 

133 

17  689 

2  352  637 

11.532  5626 

5.104  4687 

.007  518  797 

134 

17  956 

2  406  104 

11.575  8369 

5.117  2299 

.007  462  687 

135 

18  225 

2  460  375 

11.618  9500 

5.129  9278 

.007  407  407 

136 

18  496 

2  515  456 

11.661  9038 

5.142  5632 

.007  352  941 

137 

18  769 

2  571  353 

11.704  6999 

5.155  1367 

.007  299  270 

138 

19  044 

2  628  072 

11.747  3401 

5.167  6493 

.007  246  377 

139 

19  321 

2  685  619 

11.789  8261 

5.180  1015 

.007  194  245 

140 

19  600 

2  744  000 

11.832  1596 

5.192  4941 

.007142  857 

141 

19  881 

2  803  221 

11.874  3421 

5.204  8279 

.007  092  199 

142 

20164 

2  863  288 

11.916  3753 

5.217  1034 

.007  042  254 

143 

20  449 

2  924  207 

11.958  2607 

5.229  3215 

.006  993  007 

144 

20  736 

2  985  984 

12.000  0000 

5.241  4828 

.006  944  444 

145 

21025 

3  048  625 

12.041  5946 

5.253  5879 

.006  896  552 

146 

21316 

3  112  136 

12.083  0460 

5.265  6374 

.006  849  315 

147 

21609 

3  176  523 

12.124  3557 

5.277  6321 

.006  802  721 

148 

21904 

3  241  792 

12.165  5251 

5.289  5725 

.006  756  757 

149 

22  201 

3  307  949 

12.206  5556 

5.301  4592 

.006  711  409 

150 

22  500 

3  375  000 

12.247  4487 

5.313  2928 

.006  666  667 

151 

22  801 

3  442  951 

12.288  2057 

5.325  0740 

.006  622  517 

152 

23104 

3  511  008 

12.328  8280 

5.336  8033 

.006  578  947 

153 

23  409 

3  581  577 

12.369  3169 

5.348  4812 

.006  535  948 

154 

23  716 

3  652  264 

12.409  6736 

5.360  1084 

.006  493  506 

155 

24  025 

3  723  875 

12.449  8996 

5.371  6854 

.006  451  613 

156 

24  336 

3  796  416 

12.489  9960 

5.383  2126 

.006  410  256 

754 

Powers 

and  Roots 

Number. 

Squares. 

Cubes. 

V  Roots. 

fBoota. 

Reciprocals. 

157 

24  649 

3  869  893 

12.529  9641 

5.394  6907 

.006  369  427 

158 

24  964 

3  944  312 

12.569  8051 

5.406  1202 

.006  329  114 

159 

25  281 

4  019  679 

12.609  5202 

5.417  5015 

.006  289  308 

160 

25  600 

4096  000 

12.649  1106 

5.428  8352 

.006  250  000 

161 

25  921 

4  173  281 

12.688  5775 

5.440  1218 

.006  211  180 

162 

26  244 

4  251528 

12.727  9221 

5.451  3618 

.006  172  840 

163 

26  569 

4  330  747 

12.767  1453 

5.462  5556 

.006  134  969 

164 

26  896 

4  410  944 

12.806  2485 

5.473  7037 

.006  097  561 

165 

27  225 

4  492  125 

12.845  2326 

5.484  8066 

.006  060  606 

166 

27  556 

4  574  296 

12.884  0987 

5.495  8647 

.006  024  096 

167 

27  889 

4  657  463 

12.922  8480 

5.506  8784 

.005  988  024 

168 

28  224 

4  741  632 

12.961  4814 

5.517  8484 

.005  952  381 

169 

28  561 

4  826  809 

13.000  0000 

5.528  7748 

.005  917  160 

170 

28  900 

4  913  000 

13.038  4048 

5.539  6583 

.005  882  353 

171 

29  241 

5  000  211 

13.076  6968 

5.550  4991 

.005  847  953 

172 

29  584 

5  088  448 

13.114  8770 

5.561  2978 

.005  813  953 

173 

29  929 

5  177  717 

13.152  9464 

5.572  0546 

.005  780  347 

174 

30  276 

5  268  024 

13.190  9060 

5.582  7702 

.005  717  126 

175 

30  625 

5  359  375 

13.228  7566 

5.593  4447 

.005  714  286 

176 

30  976 

5  451  776 

13.266  4992 

5.604  0787 

.005  6S1  818 

177 

31329 

5  545  233 

13.304  1347 

5.614  6724 

.005  649  718 

178 

31684 

5  639  752 

13.341  6641 

5.625  2263 

.005  617  978 

179 

32  041 

5  735  339 

13.379  0882 

5.635  7408 

.005  586  592 

180 

32  400 

5  832  000 

13.416  4079 

5.646  2162 

.005  555  556 

181 

32  761 

5  929  741 

13.453  6240 

5.656  6528 

.005  524  862 

182 

33124 

6  028  568 

13.490  7376 

5.667  0511 

.005  494  505 

183 

33  489 

6  128  487 

13.527  7493 

5.677  4114 

.005  464  481 

184 

33  856 

6229  504 

13.564  6600 

5.687  7340 

.005  434  783 

185 

34  225 

6  331  625 

13.601  4705 

5.698  0192 

.005  405  405 

186 

34  596 

6  434  856 

13.638  1817 

5.708  2675 

.005  376  344 

187 

34  969 

6  539  203 

13.674  7943 

5.718  4791 

.005  347  594 

188 

35  344 

6  644  672 

13.711  3092 

5.728  6543 

.005  319149 

189 

35  721 

6  751  269 

13.747  7271 

5.738  7936 

.005  291  005 

190 

36100 

6  859  000 

13.784  0488 

5.748  8971 

.005  263  158 

191 

36  481 

6  967  871 

13.820  2750 

5.758  9652 

.005  235  602 

192 

36  864 

7  077  888 

13.856  4065 

5.768  9982 

.005  208  333 

193 

37  249 

7  189  517 

13.892  4400 

5.778  9966 

.005  181  347 

194 

37  636 

7  301  384 

13.928  3883 

5.788  9604 

.005  154  639 

195 

38  025 

7  414  875 

13:964  2400 

5.798  8900 

.005  128  205 

196 

38  416 

7  529  536 

14.000  0000 

5.808  7857 

.005  102  041 

197 

38  809 

7  645  373 

14.035  6688 

5.818  6479 

.005  076  142 

198 

39  204 

7  762  392 

14.071  2473 

5.828  4867 

.005  050  505 

199 

39  601 

7  880  599 

14.106  7360 

5.838  2725 

.005  025  126 

200 

40  000 

8000  000 

14.142  1356 

5.848  0355 

.005  000  000 

201 

40  401 

8120  601 

14.177  4469 

5.857  7660 

.004  975  124 

202 

40  804 

8  242  408 

14.212  6704 

5.867  4673 

.004  950  495 

203 

41209 

8  365  427 

14.247  8068 

5.877  1307 

.004  926  108 

204 

41  616 

8  489  664 

14.282  8569 

5.886  7653 

.004  901  961 

205 

42  025 

8  615  125 

14.317  8211 

5.896  3685 

.004  878  049 

206 

42  436 

8  741  816 

14.352  7001 

5.905  9406 

.004  854  369 

207 

42  849 

8  869  743 

14.387  4946 

5.915  4817 

.004  830  918 

208 

43  264 

8  998  912 

14.422  2051 

5.924  9921 

.004  807  692 

Powers 

and  Roots 

755 

Number. 

Squares. 

CubeB. 

V  Roots. 

f  Roots. 

Reciprocals. 

209 

43  681 

9  129  329 

14.456  8323 

5.934  4721 

.004  784  689 

210 

44100 

9  261000 

14.491  3767 

5.943  9220 

.004  761  905 

211 

44  521 

9  393  931 

14.525  8390 

5.953  3418 

.004  739  336 

212 

44  944 

9  528128 

14.560  2198 

5.962  7320 

.004  716  981 

213 

45  369 

9  663  597 

14.594  5195 

5.972  0926 

.004  694  836 

214 

45  796 

9  800  341 

14.628  7388 

5.981  4240 

.004  672  897 

215 

46  225 

9  938  375 

14.662  8783 

5.990  7264 

.004  651 163 

21G 

46  656 

10  077  696 

14.696  9385 

6.000  0000 

.004  629  630 

217 

47  089 

10  218  313 

14.730  9199 

6.009  2450 

.004  608  295 

218 

47  524 

10  360  232 

14.764  8231 

6.018  4617 

.004  587  156 

219 

47  961 

10  503  459 

14.798  6486 

6.027  6502 

.004  566  210 

220 

48  400 

10  648  000 

14.832  3970 

6.036  8107 

.004  545  455 

221 

48  841 

10  793  861 

14.866  0687 

6.045  9435 

.004  524  887 

222 

49  284 

10  941  048 

14.899  6644 

6.055  0489 

.004  504  505 

223 

49  729 

11  089  567 

14.933  1845 

6.064  1270 

.004  484  305 

224 

50176 

11  239  424 

14.966  6295 

6.073  1779 

.004  464  286 

225 

50  625 

11  390  625 

15.000  0000 

6.082  4020 

.004  444  444 

226 

51076 

11  543  176 

15.033  2964 

6.099  1994 

.004  424  779 

227 

51529 

11  697  083 

15.066  5192 

6.100  1702 

.004  405  286 

228 

51984 

11  852  352 

15.099  6689 

6-109  1147 

.004  385  965 

229 

52  441 

12  008  989 

15.132  7460 

6.118  0332 

.004  366  812 

230 

52  900 

12 167  000 

15.165  7509 

6.126  9257 

.004  347  826 

231 

53  361 

12  326  391 

15.198  6842 

6.135  7924 

.004  329  004 

232 

53  824 

12  487  168 

15.231  5462 

6.144  6337 

.004  310  345 

233 

54  289 

12  649  337 

15.264  3375 

6.153  4495 

.004  291  845 

234 

54  756 

12  812  904 

15.297  0585 

6.162  2401 

.004  273  504 

235 

55  225 

12  977  875 

15.329  7097 

6.171  0058 

.004  255  319 

236 

55  6% 

13  144  256 

15.362  2915 

6.179  7466 

.004  237  288 

237 

56169 

13  312  053 

15.394  8043 

6.188  4628 

.004  219  409 

238 

56  644 

13  481  272 

15.427  2486 

6.197  1544 

.004  201  681 

239 

57  121 

13  651  919 

15.459  6248 

6.205  8218 

.004  184  100 

240 

57  600 

13  824  000 

15.491  9334 

6.214  4650 

.004  166  667 

241 

58  081 

13  997  521 

15.524  1747 

6.223  0843 

.004  149  378 

242 

58  564 

14  172  488 

15.556  3492 

6.231  6797 

.004  132  231 

243 

59  049 

14  348  907 

15.588  4573 

6.240  2515 

.004  115  226 

244 

59  536 

14  526  784 

15.620  4994 

6.248  7998 

.004  098  361 

245 

60  025 

14  706  125 

15.652  4758 

6.257  3248 

.004  081  633 

246 

60  516 

14  886  936 

15.684  3871 

6.265  8266 

.004  065  041 

247 

61009 

15  069  223 

15.716  2336 

6.274  3054 

.004  048  583 

248 

61504 

15  252  992 

15.748  0157 

6.282  7613 

.004  032  258 

249 

62  001 

15  438  249 

15.779  7338 

6.291  1946 

.004  016  064 

250 

62  500 

15  625  000 

15.811  3883 

6.299  6053 

.004  000  000 

251 

63  001 

15  813  251 

15.842  9795 

6.307  9935 

.003  984  064 

252 

63  504 

16  003  008 

15.874  5079 

6.316  3596 

.003  968  254 

253 

64  009 

16  194  277 

15.905  9737 

6.324  7035 

.003  952  569 

254 

64  516 

16  387  064 

15.937  3775 

6.333  0256 

.003  937  008 

255 

65  025 

16  581  375 

15.968  7194 

6.341  3257 

.003  921  569 

256 

65  536 

16  777  216 

16.000  0000 

6.349  6042 

.003  906  250 

257 

66  049 

16  974  593 

16.031  2195 

6.357  8611 

.003  891  051 

258 

66  564 

17  173  512 

16.062  3784 

6.366  0968 

.003  875  969 

259 

67  081 

17  373  979 

16.093  4769 

6.374  3111 

.003  861  004 

260 

67  600 

17  576  000 

16.124  5155 

6.382  5043 

.003  846  154 

756 

Powers 

and  Roots 

. 

Number. 

Squares. 

Cubes. 

J7  Hoots. 

f  Hoots. 

Reciprocals. 

261 

68121 

17  779  581 

16.155  4944 

6.390  6765 

.003  831  418 

262 

68  644 

17  984  728 

16.186  4141 

6.398  8279 

.003  816  794 

263 

69169 

18  191  447 

16.217  2747 

6.406  9585 

.003  802  281 

264 

69  696 

18  399  744 

16.248  0768 

6.415  0687 

.003  787  879 

265 

70  225 

18  609  625 

16.278  8206 

6.423  1583 

.003  773  585 

266 

70  756 

18  821  096 

16.309  5064 

6.431  2276 

.003  759  398 

267 

71289 

19  034  163 

16.340  1346 

6.439  2767 

.003  745  318 

268 

71  824 

.  19  248  832 

16.370  7055 

6.447  3057 

.003  731  343 

269 

72  361 

19  465  109 

16.401  2195 

6.455  3148 

.003  717  472 

270 

72  900 

19  683  000 

16.431  6767 

6.463  3041 

.003  703  704 

271 

73  441 

19  902  511 

16.462  0776 

6.471  2736 

.003  690  037 

272 

73  984 

20  123  643 

16.492  4225 

6.479  2236 

.003  676  471 

273 

74  529 

20  346  417 

■16.522  7116 

6.487  1541 

.003  663  004 

274 

75  076 

20  570  824 

16.552  9454 

6.495  0653 

.003  649  635 

275 

75  625 

20  796  875 

16.583  1240 

6.502  9572 

.003  636  364 

276 

76176 

21  024  576 

16.613  2477 

6.510  8300 

.003  623  188 

277 

76  729 

21  253  933 

16.643  3170 

6.518  6839 

.003  610  108 

278 

77  284 

21  484  952 

16.673  3320 

6.526  5189 

.003  597  122 

279 

77  841 

21  717  639 

16.703  2931 

6.534  3351 

.003  584  229 

280 

78  400 

21  952  000 

16.733  2005 

6.542 1326 

.003  571  429 

281 

78  961 

22  188  041 

16.763  0546 

6.549  9116 

.003  558  719 

282 

79  524 

22  425  768 

16.792  8556 

6.557  6722 

.003  546  099 

283 

80  089 

22  665  187 

16.822  6038 

6.565  4144 

.003  533  569 

284 

80  656 

22  906  304 

16.8522995 

6.573  1385 

.003  521 127 

285 

81225 

23  149  125 

16.881  9430 

6.580  8443 

.003  508  772 

286 

81796 

23  393  656 

16.911  5345 

6.588  5323 

.003  496  503 

287 

82  369 

23  639  903 

16.941  0743 

6.596  2023 

.003  484  321 

288 

82  944 

23  887  872 

16.970  5627 

6.603  8545 

.003  472  222 

289 

83  521 

24  137  569 

17.000  0000 

6.611  4890 

.003  460  208 

290 

84100 

24  389  000 

17.029  3864 

6.619  1060 

.003  448  276 

291 

84  681 

24  642  171 

17.058  7221 

6.626  7054 

.003  436  426 

292 

85  264 

24  897  088 

17.088  0075 

6.634  2874 

.003  424  658 

293 

85  849 

25 153  757 

17.117  2428 

6.641  8522 

.003  412  969 

294 

86  436 

25  412  184 

17.146  4282 

6.649  3998 

.003  401  361 

295 

87  025 

25  672  375 

17.175  5640 

6.656  9302 

.003  389  831 

2% 

87  616 

25  934  836 

17.204  6505 

6.664  4437 

.003  378  378 

297 

88  209 

26  198  073 

17.233  6879 

6.671  9403 

.003  367  003 

298 

88  804 

26  463  592 

17.262  6765 

6.679  4200 

.003  355  705 

299 

89  401 

26  730  899 

17.291  6165 

6.686  8831 

.003  344  482 

300 

90  000 

27  000  000 

17.320  5081 

6.694  3295 

.003  333  333 

301 

90  601 

27  270  901 

17.349  3516 

6.701  7593 

.003  322  259 

302 

91204 

27  513  608 

17.378  1472 

6.709  1729 

.003  311  258 

303 

91809 

27  818  127 

17.406  8952 

6.716  5700 

.003  301  330 

304 

92  416 

28  094  464 

17.435  5958 

6.723  9508 

.003  289  474 

305 

93  025 

28  372  625 

17.464  2492 

6.731  3155 

.003  278  689 

306 

93  636 

28  652  616 

17.492  8557 

6.738  6641 

.003  267  974 

307 

94  249 

28  934  443 

17.521  4155 

6.745  9967 

.003  257  329 

308 

94  864 

29  218  112 

17.549  9288 

6.753  3134 

.003  246  753 

309 

95  481 

29  503  609 

17.578  3958 

6.760  6143 

.003  236  246 

310 

96100 

29  791  000 

17.606  8169 

6.767  8995 

.003  225  806 

311 

96  721 

30  080  231 

17.635  1921 

6.775  1690 

.003  215  434 

312 

97  344 

30  371  328 

17.663  5217 

6.782  4229 

.003  205  128 

Powers 

and  Roots 

757 

Number. 

Squares. 

Cubes. 

V  Roots. 

f  Roots. 

Reciprocals. 

313 

97  969 

30  664  297 

17.691  8060 

6.789  6613 

.003  194  888 

314 

98  596 

30  959  144 

17.720  0451 

6.796  8844 

.003  184  713 

315 

99  225 

31  255  875 

17.748  2393 

6.804  0921 

.003  174  603 

316 

99  856 

31  554  496 

17.776  3888 

6.811  2847 

.003  164  557 

317 

100  489 

31  855  013 

17.804  4938 

6.818  4620 

.003  154  574 

318 

101124 

32  157  432 

17.832  5545 

6.825  6242 

.003  144  654 

319 

101  761 

32  461  759 

17.860  5711 

6.832  7714 

.003134  796 

320 

102  400 

32  768  000 

17.888  5438 

6.839  9037 

.003  125  000 

321 

103  041 

83  076  161 

17.916  4729 

6.847  0213 

.003  115  265 

322 

103  684 

33  386  248 

17.944  3584 

6.854  1240 

.003  105  590 

323 

104  329 

33  698  267 

17.972  2008 

6.861  2120 

.003  095  975 

324 

104  976 

34  012  224 

18.000  0000 

6.868  2855 

.003  086  420 

325 

105  625 

34  328  125 

18.027  7564 

6.875  3433 

.003  076  923 

326 

106  276 

34  645  976 

18.055  4701 

6.882  3888 

.003  067  485 

327 

106  929 

34  965  783 

18.083  1413 

6.889  4188 

.003  048  104 

328 

107  584 

35  287  552 

18.110  7703 

6.896  4345 

.003  048  780 

329 

108  241 

35  611  289 

18.138  3571 

6.903  4359 

.003  039  514 

330 

108  900 

35  937  000 

18.165  9021 

6.910  4232 

.003  030  303 

331 

109  561 

36  264  691 

18.193  4054 

6.917  3964 

.003  021 148 

332 

110  224 

36  594  368 

18.220  8672 

6.924  3556 

.003  012  048 

333 

110  889 

36  926  037 

18.248  2876 

6.931  3088 

.003  003  003 

334 

111  556 

37  259  704 

18.275  6669 

6.938  2321 

.002  994  012 

335 

112  225 

37  595  375 

18.303  0052 

6.945  1496 

.002  985  075 

336 

112  896 

37  933  056 

18.330  3028 

6.952  0533 

.002  976  190 

337 

113  569 

38  272  753 

18.357  5598 

6.958  9434 

.002  967  359 

338 

114  244 

38  614  472 

18.384  7763 

6.965  8198 

.002  958  580 

339 

114  921 

38  958  219 

18.411  9526 

6.972  6826 

.002  949  853 

340 

115  600 

39  304  000 

18.439  0889 

6.979  5321 

.002  941 176 

341 

116  281 

39  651  821 

18.466  1853 

6.986  3681 

.002  932  551 

342 

116  964 

40  001  688 

18.493  2420 

6.993  1906 

.002  923  977 

343 

117  649 

40  353  607 

18.520  2592 

7.000  0000 

.002  915  452 

344 

118  336 

40  707  584 

18.547  2370 

7.006  7962 

.002  906  977 

345 

119  025 

41  063  625 

18.574  1756 

7.013  5791 

.002  898  551 

346 

119  716 

41  421  736 

18.601  0752 

7.020  3490 

.002  890  173 

347 

120  409 

41  781  923 

18.627  9360 

7.027  1058 

.002  881  844 

348 

121  104 

42  144  192 

18.654  7581 

7.033  8497 

.002  873  563 

349 

121  801 

42  508  549 

18.681  5417 

7.040  5860 

.002  865  330 

350 

122  500 

42  875  000 

18.708  2869 

7.047  2987 

.002  857  143 

351 

123  201 

43  243  551 

18.734  9940 

7.054  0041 

.002  849  003 

352 

123  904 

43  614  208 

18.761  6630 

7.060  6967 

.002  840  909 

353 

124  609 

43  986  977 

18.788  2942 

7.067  3767 

.002  832  861 

354 

125  316 

44  361  864 

18.814  8877 

7.074  0440 

.002  824  859 

355 

126  025 

44  738  875 

18.841  4437 

7.080  6988 

.002  816  901 

356 

126  736 

45  118  016 

18.867  9623 

7.087  3411 

.002  808  989 

357 

127  449 

45  499  293 

18.894  4436 

7.093  9709 

.002  801 120 

358 

128164 

45  882  712 

18.920  8879 

7.100  5885 

.002  793  296 

359 

128  881 

46  268  279 

18.947  2953 

7.107  1937 

.002  785  515 

360 

129  600 

46  656  000 

18.973  6660 

7.113  7866 

.002  777  778 

361 

130  321 

47  045  831 

19.000  0000 

7.120  3674 

.002  770  083 

362 

131  044 

47  437  928 

19.026  2976 

7.126  9360 

.002  762  431 

363 

131  769 

47  832  147 

19.052  5589 

7.133  4925 

.002  754  821 

364 

132  496 

48  228  544 

19.078  7840 

7.140  0370 

.002  747  253 

758 

Powers 

AND  HOOTS 

Number. 

Squares. 

Cubes. 

/EootaT 

f  Boom. 

Reciprocals. 

365 

133  225 

48  627  125 

19.104  9732 

7.146  5695 

.002  739  726 

366 

133  956 

49  027  896 

19.131 1265 

7.153  0901 

.002  732  240 

367 

134  689 

49  430  863 

19.157  2441 

7.159  5988 

.002  724  796 

368 

135  424 

49  836  032 

19.183  3261 

7.166  0957 

.002  717  391 

369 

136161 

50  243  409 

19.209  3727 

7.172  5809 

.002  710  027 

370 

136  900 

50  653  000 

19.235  3841 

7.179  0544 

.002  702  703 

371 

137  641 

51  064  811 

19.261  3603 

7.185  5162 

.002  695  418 

372 

138  384 

51  478  848 

19.287  3015 

7.191  9663 

.002  688  172 

373 

139  129 

51  895  117 

19.313  2079 

7.198  4050 

.002  680  965 

374 

139  876 

52  313  624 

19.339  0796 

7.204  8322 

.002  673  797 

375 

140  625 

52  734  375 

19.364  9167 

7.211  2479 

.002  666  667 

376 

141  376 

53  157  376 

19.390  7194 

7.217  6522 

.002  659  574 

377 

142129 

53  582  633 

19.416  4878 

7.224  0450 

.002  652  520 

378 

142  884 

54  010  152 

19.442  2221 

7.230  4268 

.002  645  503 

379 

143  641 

54  439  939 

19.467  9223 

7.236  7972 

.002  638  521 

380 

144  400 

54  872  000 

19.493  5887 

7.243  1565 

.002  631  579 

381 

145161 

55  306  341 

19.519  2213 

7.249  5045 

.002  624  672 

382 

145  924 

55  742  968 

19.544  8203 

7.255  8415 

.002  617  801 

383 

146  689 

56  181  887 

19.570  3858 

7.262  1675 

.002  610  966 

384 

.  147  456 

56  623104 

19.595  9179 

7.268  4824 

.002  604  167 

385 

148  225 

57  066  625 

19.621  4169 

7.274  7864 

.002  597  403 

386 

148  996 

57  512  456 

19.646  8827 

7.281  0794 

.002  590  674 

387 

149  769 

57  960  603 

19.672  3156 

7.287  3617 

.002  583  979 

388 

150  544 

58  411  072 

19.697  7156 

7.293  6330 

.002  577  320 

389 

151  321 

58  863  869 

19.723  0829 

7.299  8936 

.002  570  694 

390 

152100 

59  319  000 

19.748  4177 

7.306  1436 

.002  564  103 

391 

152  881 

59  776  471 

19.773  7199 

7.312  3828 

.002  557  545 

392 

153  664 

60  236  288 

19.798  9899 

7.318  6114 

.002  551  020 

393 

154  449 

60  698  457 

19.824  2276 

.  7.324  8295 

.002  544  529 

394 

155  236 

61 162  984 

19.849  4332 

7.331  0369 

.002  538  071 

395 

156  025 

61  629  875 

19.874  6069 

7.337  2339 

.002  531  646 

896 

156  816 

62  099  136 

19.899  7487 

7.343  4205 

.002  525  253 

397 

157  609 

62  570  773 

19.924  8588 

7.349  5966 

.002  518  892 

898 

158  404 

63  044  792 

19.949  9373 

7.355  7624 

.002  512  563 

399 

159  201 

63  521 199 

19.974  9844 

7.361  9178 

.002  506  266 

400 

160  000 

64  000  000 

20.000  0000 

7.368  0630 

.002  500  000 

401 

160  801 

64  481  201 

20.024  9844 

7.374  1979 

.002  493  766 

402 

161604 

64  964  808 

20.049  9377 

7.380  3227 

.002  487  562 

403 

162  409 

65  450  827 

20.074  8599 

7.386  4373 

.002  481  390 

404 

163  216 

65  939  264 

20.099  7512 

7.392  5418 

.002  475  248 

405 

164  025 

66  430  125 

20.124  6118 

7.398  6363 

.002  469  136 

406 

164  836 

66  923  416 

20.149  4417 

7.404  7206 

.002  463  054 

407 

165  649 

67  419  143 

20.174  2410 

7.410  7950 

.002  457  002 

408 

166  464 

67  917  312 

20.199  0099 

7.416  8595 

.002  450  980 

409 

167  281 

68  417  929 

20.223  7484 

7.422  9142 

.002  444  988 

410 

168100 

68  921000 

20.248  4567 

7.428  9589 

.002  439  024 

411 

168  921 

69  426  531 

20.273  1349 

7.434  9938 

.002  433  090 

412 

169  744 

69  934  528 

20.297  7831 

7.441  0189 

.002  427  184 

413 

170  569 

70  444  997 

20.322  4014 

7.447  0343 

.002  421  308 

414 

171396 

70  957  944 

20.346  9899 

7.453  0399 

.002  415  459 

415 

172  225 

71  473  375 

20.371  5488 

7.459  0359 

.002  409  639 

Powers 

and  Roots 

759 

Number. 

Squares. 

Cubes. 

^Roots. 

f  Roots. 

Reciprocals. 

417 

173  889 

72  511  713 

20.420  5779 

7.470  9991 

.002  398  082 

418 

174  724 

73  034  632 

20.445  0483 

7.476  9664 

.002  392  344 

419 

175  561 

73  560  059 

20.469  4895 

7.482  9242 

.002  386  635 

420 

176  400 

74  088  000 

20.493  9015 

7.488  8724 

.002  380  952 

421 

177  241 

71  618  461 

20.518  2845 

7.494  8113 

.002  375  297 

422 

178  084 

75  151  448 

20.542  6386 

7.500  7406 

.002  369  668 

423 

178  929 

75  686  967 

20.566  9638 

7.506  6607 

.002  364  066 

424 

179  776 

76  225  02 1 

20.591  2603 

7.512  5715 

.002  358  491 

425 

180  625 

76  765  625 

20.615  5281 

7.518  4730 

.002  352  941 

426 

181  476 

77  308  776 

20.639  7674 

7.524  3652 

.002  347  418 

.   427 

182  329 

77  854  483 

20.663  9783 

7.530  2482 

.002  341  920 

428 

183  184 

78  402  752 

20.688  1609 

7.536  1221 

.002  336  449 

429 

184  041 

78  953  589 

20.712  3152 

7.541  9867 

.002  331  002 

430 

184  900 

79  507  000 

20.736  4414 

7.547  8423 

.002  325  581 

431 

185  761 

80  062  991 

20.760  5395 

7.553  6888 

.002  320  186 

432 

186  624 

80  621  568 

20.784  6097 

7.559  5263 

.002  31^815 

433 

187  489 

81 182  737 

20.808  6520 

7.565  3548 

.002  309  469 

434 

188  356 

81  746  504 

20.832  6667 

7.571  1743 

.002  304  147 

435 

189  225 

82  312  875 

20.856  6536 

7.576  9849 

.002  298  851 

436 

190  096 

82  881  856 

20.880  6130 

7.582  7865 

.002  293  578 

437 

190  969 

83  453  453 

20.904  5450 

7.588  5793 

.002  288  330 

438 

191844 

84  027  672 

20.928  4495 

7.594  3633 

.002  283  105 

439 

192  721 

84  604  519 

20.952  3268 

7.600  1385 

.002  277  904 

440 

193  600 

85  184  000 

20.976  1770 

7.605  9049 

.002  272  727- 

441 

194  481 

85  766  121 

21.000  0000 

7.611  6626 

.002  267  574 

442 

195  364 

86  350  888 

21.023  7960 

7.617  4116 

.002  262  443 

443 

196  249 

86  938  307 

21.047  5652 

7.623  1519 

.002  257  336 

444 

197  136 

87  528  384 

21.071  3075 

7.628  8837 

.002  252  252 

445 

198  025 

88  121 125 

21.095  0231 

7.634  6067 

.002  247  191 

446 

198  916 

88  716  536 

21.118  7121 

7.640  3213 

.002  242  152 

447 

199  809 

89  314  623 

21.142  3745 

7.646  0272 

.002  237  136 

448 

200  704 

89  915  392 

21.166  0105 

7.651  7247 

.002  232  143 

449 

201  601 

90  518  849 

21.189  6201 

7.657  4138 

.002  227  171 

450 

202  500 

91 125  000 

21.213  2034 

7.663  0943 

.002  222  222 

451 

203  401 

91  733  851 

21.236  7606 

7.668  7665 

.002  217  295 

452 

204  304 

92  345  408 

21.260  2916 

7.674  4303 

.002  212  389 

453 

205  209 

92  959  677 

21.283  7967 

7.680  0857 

.002  207  506 

454 

206  116 

93  576  664 

21.307  2758 

7.685  7328 

.002  202  643 

455 

207  025 

94  196  375 

21.330  7290 

7.691  3717 

.002  197  802 

456 

207  936 

94  818  816 

21.354  1565 

7.697  0023 

.002  192  982 

457 

208  849 

95  443  993 

21.377  5583 

7.702  6246 

.002  188  184 

458 

209  764 

96  071  912 

21.400  9346 

7.708  2388 

.002  183  406 

459 

210  681 

96  702  579 

21.424  2853 

7.718  8448 

.002  178  649 

460 

211600 

97  336  000 

21.447  6106 

7.719  4426 

.002  173  913 

461 

212  521 

97  972 181 

21.470  9106 

7.725  0325 

.002  169  197 

462 

213  444 

98  611 128 

21.494  1853 

7.730  6141 

.002  164  502 

463 

214  369 

99  252  847 

21.517  4348 

7.736  1877 

.002  159  827 

464 

215  296 

99  897  344 

21.540  6592 

7.741  7532 

,002  155  172 

465 

216  225 

100  544  625 

21.563  8587 

7.747  3109 

.002150  538 

466 

217  156 

101 194  696 

21.587  0331 

7.752  8606 

.002  145  923 

467 

218  089 

101  847  563 

21.610  1828 

7.758  4023 

.002  141  328 

468 

219  024 

102  503  232 

21.633  3077 

7.763  9361 

.002  136  752 

760 

Towers 

and  Roots 

. 

Number. 

Squares. 

Cubes. 

^Boots. 

f  Roots. 

Reciprocals. 

469 

219  961 

103 161  709 

21.656  4078 

7.769  4620 

.002  132  196 

470 

220  900 

103  823  000 

21.679  4834 

7.774  9801 

.002  127  660 

471 

221841 

104  487  111 

21.702  5344 

7.780  4904 

.002  123  142 

472 

222  784 

105 154  048 

21.725  5610 

7.785  9928 

.002  118  644 

473 

223  729 

105  828  817 

21.748  5632 

7.791  4875 

.002  114  165 

474 

224  676 

106  496  424 

21.771  5411 

7.796  9745 

.002  109  705 

475 

225  625 

107  171  875 

21.794  4947 

7.802  4538 

.002  105  263 

476 

226  576 

107  850  176 

21.817  4242 

7.807  9254 

.002  100  840 

477 

227  529 

108  531333 

21.840  3297 

7.813  3892 

.002  0%  436 

478 

228  484 

109  215  352 

21.863  2111 

7.818  8456 

.002  092  050 

479 

229  441 

109  902  239 

21.886  0686 

7.824  2942 

.002  087  683 

480 

230  400 

110  592  000 

21.908  9023 

7.829  7353 

.002  083  333 

481 

231361 

111  284  641 

21.931  7122 

7.8351688 

.002  079  002 

482 

232  324 

111  980  168 

21.954  4984 

7.840  5949 

.002  074  689 

483 

233  289 

112  678  587 

21.977  2610 

7.846  0134 

.002  070  393 

484 

234  256 

113  379  904 

22.000  0000 

7.851  4244 

.002  066  116 

485 

235  225 

114  084  125 

22.022  7155 

7.856  8281 

.002  061  856 

486 

236196 

114  791  256 

22.045  4077 

7.862  2242 

.002  057  613 

487 

237  169 

115  501  303 

22.068  0765 

7.867  6130 

.002  053  388 

488. 

238144 

116  214  272 

22.090  7220 

7.872  9944 

.002  049  180 

489 

239121 

116  930169, 

22.113  3444 

7.878  3684 

.002  044  990 

490 

240100 

117  649  000 

22.135  9436 

7.883  7352 

.002  040  816 

491 

241081 

118  370  771 

22.158  5198 

7.889  0946 

.002  036  660 

492 

242  064 

119  095  488 

22.181  0730 

7.894  4468 

.002  032  520 

493 

243  049 

119  823  157 

22.203  6033 

7.899  7917 

.002  028  398 

494 

244  036 

120  553  784 

22.226  1108 

7.905  1294 

.002  024  291 

495 

245  025 

121  287  375 

22.248  5955 

7.910  4599 

.002  020  202 

496 

246  016 

122  023  936 

22.271  0575 

7.915  7832 

.002  016  129 

497 

247  009 

122  763  473 

22.293  4968 

7.921  0994 

.002  012  072 

498 

248  004 

123  505  992 

22.315  9136 

7.926  4085 

.002  008  032 

499 

249  001 

124  251  499 

22.338  3079 

7.931  7104 

.002  004  008 

500 

250  000 

125  000  000 

22.360  6798" 

7.937  0053 

.002  000  000 

501 

251001 

125  751  501 

22.383  0293 

7.942  2931 

.001  996  008 

502 

252  004 

126  506  008 

22.405  3565 

7.947  5739 

.001  992  032 

503 

253  009 

127  263  527 

22.427  6615 

7.952  8477 

.001  988  072 

504 

254  016 

128  024  064 

22.449  9443 

7.958  1144 

.001  984  127 

505 

255  025 

128  787  625 

22.472  2051 

7.963  3743 

.001  980  198 

506 

256  036 

129  554  216 

22.494  4438 

7.968  6271 

.001  976  285 

507 

257  049 

130  323  843 

22.516  6605 

7.973  8731 

.001  972  387 

508 

258  064 

131  096  512 

22.538  8553 

7.979  1122 

.001  968  504 

509 

259  081 

131872  229 

22.561  0283 

7.984  3444 

.001  964  637 

510 

260100 

132  651  000 

22.583 1796 

7.989  5697 

.001  960  784 

511 

261121 

133  432  831 

22.605  3091 

7.994  7883 

.001  956  947 

512 

262  144 

134  217  728 

22.627  4170 

8.000  0000 

.001  953  125 

513 

263169 

135  005  697 

22.649  5033 

8.005  2049 

.001  949  318 

514 

264  1% 

135  796  744 

22.671  5681 

8.010  4032 

.001  945  525 

515 

265  225 

136  590  875 

22.693  6114 

8.015  5946 

.001  941  748 

516 

266  256 

137  388  096 

22.715  6334 

8.020  7794 

.001  937  984 

517 

267  289 

138  188  413 

22.737  6341 

8.025  9574 

.001  934  236 

518 

268  324 

138  991  832 

22.759  6134 

8.031 1287 

.001930  502 

519 

269  361 

139  798  359 

22.781  5715 

8.036  2935 

.001  926  782 

520 

270  400 

140  608  000 

22.803  5085 

8.041  4515 

.001  923  077 

Powers 

and  Roots 

761 

Number. 

Squares. 

Cubes. 

^Roots. 

f  Boots. 

Reciprocals. 

521 

271  441 

141  420  761 

22.825  4244 

8.046  6030 

.001  919  386 

522 

272  484 

142  236  648 

22.847  3193 

8.051  7479 

.001  915  709 

523 

273  529 

143  055  667 

22.869  1933 

8.056  8862 

.001912  046 

524 

274  576 

143  877  824 

22.891  0463 

8.062  0180 

.001  908  397 

525 

275  625 

144  703  125 

22.912  8785 

8.067  1432 

.001  904  762 

526 

276  676 

145  531  576 

22.934  6899 

8.072  2620 

.001  901 141 

527 

277  729 

146  363  183 

22.956  4806 

8.077  3743 

.001  897  533 

528 

278  784 

147  197  952 

22.978  2506 

8.082  4800 

.001  893  939 

529 

279  841 

148  035  889 

23.000  0000 

8.087  5794 

.001  890  359 

530 

280  900 

148  877  001 

23.021  7289 

8.092  6723 

.001  886  792 

531 

281961 

149  721  291 

23.043  4372 

8.097  7589 

.001  883  239 

532 

283  024 

150  568  768 

23.065  1252 

8.102  8390 

.001  879  699 

533 

284  089 

151  419  437 

23.086  7928 

8.107  9128 

.001  876  173 

534 

285156 

152  273  304 

23.108  4400 

8.112  9803 

.001  872  659 

535 

286  225 

153  130  375 

23.130  0670 

8.118  0414  • 

.001  869  159 

536 

287  296 

153  990  656 

23.151  6738 

8.123  0962 

.001  865  672 

537 

288  369 

154  854  153 

23.173  2605 

8.128  1447 

.001  862 197 

538 

289  444 

155  720  872 

23.194  8270 

8.133  1870 

.001  858  736 

539 

290  521 

156  590  819 

23.216  3735 

8.138  2230 

.001  855  288 

540 

291600 

157  464  000 

23.237  9001 

8.143  2529 

.001  851  852 

541 

292  681 

158  340  421 

23.259  4067 

8.148  2765 

.001  848  429 

542 

293  764 

159  220  088 

23.280  8935 

8.153  2939 

.001  845  018 

543 

294  849 

160  103  007 

23.302  3604 

8.158  3051 

.001  841  621 

544 

295  936 

160  989 184 

23.323  8076 

8.163  3102 

.001  838  235 

545 

297  025 

161878  625 

23.345  2351 

8.168  3092 

.001  834  862 

546 

298  116 

162  771  336 

23.366  6429 

8.173  3020 

.001  831  502 

547 

299  209 

163  667  323 

23.388  0311 

8.178  2888 

.001828154 

548 

300  304 

164  566  592 

23.409  3998 

8.183  2695 

.001  824  818 

549 

301  401 

165  469  149 

23.430  7490 

8.188  2441 

.001  821  494 

550 

302  500 

166  375  000 

23.452  0788 

8.193  2127 

.001  818  182 

551 

303  601 

167  284  151 

23.473  3892 

8.198  1753 

.001  814  882 

552 

304  704 

168  196  608 

23.494  6802 

8.203  1319 

.001811594 

653 

305  809 

169 112  377 

23.515  9520 

8.208  0825 

.001  808  318 

554 

306  916 

170  031  464 

23.537  2046 

8.213  0271 

.001  805  054 

555 

308  025 

170  953  875 

23.558  4380 

8.217  9657 

.001  801  802 

556 

309  136 

171  879  616 

23.579  6522 

8.222  8985 

.001  798  561 

557 

310  249 

172  808  693 

23.600  8474 

8.227  8254 

.001  795  332 

558 

311  364 

173  741 112 

23.622  0236 

8.232  7463 

.001  792  115 

559 

312  481 

174  676  879 

23.643  1808 

8.237  6614 

.001  788  909 

560 

313  600 

175  616  000 

23.664  3191 

8.242  5706 

.001  785  714 

561  . 

314  721 

176  558  481 

23.685  4386 

8.247  4740 

.001  782  531 

562 

315  844 

177  504  328 

23.706  5392 

8.252  3715 

.001  779  359 

563 

316  969 

178  453  547 

23.727  6210 

8.257  2635 

.001  776  199 

564 

318  096 

179  406  144 

23.748  6842 

8.262  1492 

.001  773  050 

565 

319  225 

180  362  125 

23.769  7286 

8.267  0294 

.001  769  912 

566 

320  356 

181  321  496 

23.790  7545 

8.271  9039 

.001  766  784 

567 

321  489 

182  284  263 

23.811  7618 

8.276  7726 

.001  763  668 

568 

322  624 

183  250  432 

23.832  7506 

8.281  6255 

.001  760  563 

569 

323  761 

184  220  009 

23.853  7209 

8.286  4928 

.001  757  469 

570 

324  900 

185  193  000 

23.874  6728 

8.291  3444 

.001754  386 

571 

326  041 

186  169  411 

23.895  6063 

8.296  1903 

.001  751  313 

572 

327  184 

187  149  248 

23.916  5215 

8.301  0304 

.001748  252 

762 

Powers 

and  Roots 

. 

Number. 

Squares. 

Cubes. 

V' Roots. 

f  Boots. 

Reciprocals. 

573 

328  329 

188  132  517 

23.937  4184 

8.305  8651 

.001  745  201 

574 

329  476 

189  119  224 

23.958  2971 

8.310  6941 

.001  742  160 

575 

330  625 

190  109  375 

23.979  1576 

8.315  5175 

.001  739  130 

576 

331776 

191 102  976 

24.000  0000 

8.320  3353 

.001  736  111 

577 

332  927 

192  100  033 

24.020  8243 

8.325 1475 

.001  733  102 

578 

334  084 

193  100  552 

24.041  6306 

8.329  9542 

.001  730  104 

579 

335  241 

194  104  539 

24.062  4188 

8.334  7553 

.001  727  116 

580 

336  400 

195  112  000 

24.083  1891 

8.339  5509 

.001  724  138 

581 

337  561 

196  122  941 

24.103  9416 

8.344  3410 

.001  721 170 

582 

338  724 

197  137  368 

24.124  6762 

8.349  1256 

.001  718  213 

583 

339  889 

198  155  287 

24.145  3929 

8.353  9047 

.001  715  266 

584 

341056 

199  176  704 

24.166  0919 

8.358  6784 

.001  712  329 

585 

342  225 

200  201  625 

24.186  7732 

8.363  4466 

.001  709  402 

586 

343  396 

201  230  056 

24.207  4369 

8.368  2095 

.001  706  485 

587 

344  569 

202  262  003 

24.228  0829 

8.372  9668 

.001  703  578 

588 

345  744 

203  297  472 

24.248  7113 

8.377  7188 

.001  700  680 

589 

346  921 

204  336  469 

24.269  3222 

8.382  4653 

.001  697  793 

590 

348100 

205  379  000 

24.289  9156 

8.387  2065 

.001  694  915 

591 

349  281 

206  425  071 

24.310  4996 

8.391  9428 

.001692  047 

592 

350  464 

207  474  688 

24.331  0501 

8.396  6729 

.001  689  189 

593 

351649 

208  527  857 

24.351  5913 

8.401  3981 

.001  686  341 

594 

352  836 

209  584  584 

24.372  1152 

8.406  1180 

.001  683  502 

595 

354  025 

210  644  875 

24.392  6218 

8.410  8326 

.001  680  672 

696 

355  216 

211  708  736 

24.413  1112 

8.415  5419 

.001  677  852 

597 

356  409 

212  776  173 

24.433  5834 

8.420  2460 

.001  675  042 

598 

357  604 

213  847  192 

24.454  0385 

8.424  9448 

.001  672  241 

599 

358  801 

214  921  799 

24.474  4765 

8.429  6383 

.001  669  449 

600 

360  000 

216  000  000 

24.494  8974 

8.434  3267 

.001  666  667 

601 

361201 

217  081  801 

24.515  3013 

8.439  0098 

.001  663  894 

602 

362  404 

218  167  208 

24.535  6883 

8.443  6877 

.001  661 130 

603 

363  609 

219  256  227 

24.556  0583 

8.448  3605 

.001  658  375 

604 

364  816 

220  348  864 

24.576  4115 

8.453  0281 

.001  655  629 

605 

366  025 

221  445  125 

24.596  7478 

8.457  6906 

.001  652  893 

606 

367  236 

222  545  016 

24.617  0673 

8.462  3479 

.001  650  165 

607 

368  449 

223  648  543 

24.637  3700 

8.467  0001 

.001  647  446 

608 

369  664 

224  755  712 

24.657  6560 

8.471  6471 

.001  644  737 

609 

370  881 

225  866  529 

24.677  9254 

8.476  2892 

.001  642  036 

610 

372  100 

226  981  000 

24.698  1781 

8.480  9261 

.001  639  344 

611 

873  321 

228  099  131 

24.718  4142 

8.485  5579 

.001  636  661 

612 

374  544 

229  220  928 

24.738  6338 

8.490  1848 

.001  633  987 

613 

375  769 

230  346  397 

24.758  8368 

8.494  8065 

.001  631  321 

614 

376  996 

231  475  544 

24.779  0234 

8.499  4233 

.001  628  664 

615 

378  225 

232  608  375 

24.799  1935 

8.504  0350 

.001  626  016 

616 

379  456 

233  744  896 

24.819  3473 

8.508  6417 

.001  623  377 

617 

380  689 

234  885  113 

24.839  4847 

8.513  2435  ' 

.001  620  746 

618 

381924 

236  029  032 

24.859  6058 

8.517  8403 

.001  618  123 

619 

383161 

237  176  659 

24.879  7106 

8.522  4331 

.001  615  509 

620 

384  400 

238  328  000 

24.899  7992 

8.527  0189 

.001  612  903 

621 

385  641 

239  483  061 

24.919  8716 

8.531  6009 

.001  610  306 

622 

386  884 

240  641  848 

24  939  9278 

8.536  1780 

.001  607  717 

623 

388129 

241  804  367 

24.959  9679 

8.540  7501 

.001  605  136 

624 

389  376 

242  970  624 

24.979  9920 

8.545  3173 

.001  602  564 

Powers 

and  Roots 

763 

Number. 

Squares. 

Cubes. 

^Roots. 

f  Roots. 

Reciprocals. 

625 

390  625 

244  140  625 

25.000  0000 

8.549  8797 

.001  600  000 

626 

391  876 

245  134  376 

25.019  9920 

8.554  4372 

.001  597  444 

627 

393  129 

246  491  883 

25.039  9681 

8.558  9899 

.001  594  896 

628 

394  384 

247  673  152 

25.059  9282 

8.563  5377 

.001  592  357 

629 

395  641 

248  858  189 

25.079  8724 

8.568  0807 

.001  589  825 

630 

396  900 

250  047  000 

25.099  8008 

8.572  6189 

.001  587  302 

631 

398  161 

251  239  591 

25.119  7134 

8.577  1523 

.001  584  786 

632 

399  424 

252  435  968 

25.139  6102 

8.581 6809 

.001  582  278 

633 

400  689 

253  636  137 

25.159  4913 

8.586  2247 

.001  579  779 

634 

401  956 

254  840  104 

25.179  3566 

8.590  7238 

.001  577  287 

635 

403  225 

256  047  875 

25.199  2063 

8.595  2380 

.001  574  803 

636 

404  496 

257  259  456 

25.219  0404 

8.599  7476 

.001  572  327 

637 

405  769 

258  474  853 

25.238  8589 

8.604  2525 

.001  569  859 

638 

407  044 

259  694  072 

25.258  6619 

8.608  7526 

.001  567  398 

639 

408  321 

260  917  119 

25.278  4493 

8.613  2480 

.001  564  945 

640 

409  600 

262  144  000 

25.298  2213 

8.617  7388 

.001  562  500 

641 

410  881 

263  374  721 

25.317  9778 

8.622  2248 

.001  560  062 

642 

412  164 

264  609  288 

25.337  7189 

8.626  7063 

.001  557  632 

643 

413  449 

265  847  707 

25.357  4447 

8.631 1830 

.001  555  210 

644 

414  736 

267  089  984 

25.377  1551 

8.635  6551 

.001  552  795 

645 

416  025 

268  336  125 

25.396  8502 

8.640  1226 

.001  550  388 

646 

417  316 

269  585  136 

25.416  5302 

8.644  5855 

.001  547  988 

647 

418  609 

270  840  023 

25.436  1947 

8.649  0437 

.001  545  595 

648 

419  904 

272  097  792 

25.455  8441 

8.653  4974 

.001  543  210 

649 

421201 

273  359  449 

25.475  4784 

8.657  9465 

.001  540  832 

650 

422  500 

274  625  000 

25.495  0976 

8.662  3911 

.001  538  462 

651 

423  801 

275  894  451 

25.514  7013 

8.666  8310 

.001  536  098 

652 

425  104 

277  167  808 

25.534  2907 

8.671  2665 

.001  533  742 

653 

426  409 

278  445  077 

25.553  8647 

8.675  6974 

.001  531  394 

654 

427  716 

279  726  264 

25.573  4237 

8.680  1237 

.001  529  052 

655 

429  025 

281  Oil  375 

25.592  9678 

8.684  5456 

.001  526  718 

656 

430  336 

282  300  416 

25.612  4969 

8.688  9630 

.001  524  390 

657 

431649 

283  593  393 

25.632  0112 

8.693  3759 

.001  522  070 

658 

432  964 

284  890  312 

25.651  5107 

8.697  7843 

.001  519  757 

659 

434  281 

286  191 179 

25.670  9953 

8.702  1882 

.001  517  451 

660 

435  600 

287  496  000 

25.690  4652 

8.706  5877 

.001  515  152 

661 

436  921 

288  804  781 

25.709  9203 

8.710  9827 

.001  512  859 

662 

438  244 

290  117  528 

25.729  3607 

8.715  3734 

.001  510  574 

663 

439  569 

291  434  247 

25.748  7864 

8.719  7596 

.001  508  296 

664 

440  896 

292  754  944 

25.768  1975 

8.724 1414 

.001506  024 

665 

442  225 

294  079  625 

25.787  5939 

8.728  5187 

.001  503  759 

666 

443  556 

295  408  296 

25.806  9758 

8.732  8918 

.001  501  502 

667 

444  889 

296  740  963 

25.826  3431 

8.737  2604 

.001  499  250 

668 

446  224 

298  077  632 

25.845  6960 

8.741  6246 

.001  497  006 

669 

447  561 

299  418  309 

25.865  0343 

8.745  9846 

.001  494  768 

670 

448  900 

300  763  000 

25.884  3582 

8.750  3401 

.001  492  537 

671 

450  241 

302  111  711 

25.903  6677 

8.754  6913 

.001  490  313 

672 

451  584 

303  464  448 

25.922  9628 

8.759  0383 

.001  488  095 

673 

452  929 

304  821  217 

25.942  2435 

8.763  3809 

.001  485  884 

674 

454  276 

306  182  024 

25.961  5100 

8.767  7192 

.001  483  680 

675 

455  625 

307  546  875 

25.980  7621 

8.772  0532 

.001  481 481- 

676 

456  976 

308  915  776 

26.000  0000 

8.776  3830 

.001  479  290 

7G4 

Powers 

and  Roots 

Number. 

Squares. 

Cubes. 

V  Roots, 

f  Boots. 

Reciprocals. 

677 

458  329 

310  288  733 

26.019  2237 

8.780  7084 

.001  477  105 

678 

459  684 

311  665  752 

26.038  4331 

8.785  0296 

.001  474  926 

679 

461041 

313  046  839 

26.057  6284 

8.789  3466 

.001472  754 

680 

462  400 

314  432  000 

26.076  8096 

8.793  6593 

.001  470  588 

681 

463  761 

315  821  241 

26.095  9767 

8.797  9679 

.001  468  429 

682 

465124 

317  214  568 

26.115  1297 

8.802  2721 

.001  466  276 

683 

466  489 

318  611  987 

26.134  2687 

8.806  5722 

.001  464  129 

684 

467  856 

320  013  504 

26.153  3937 

8.810  8681 

.001  461  988 

685 

469  225 

321  419  125 

26.172  5047 

8.815  1598 

.001  459  854 

686 

470  596 

322  828  856 

26.191  6017 

8.819  4474 

.001  457  726 

687 

471969 

324  242  703 

26.210  6848 

8.823  7307 

.001  455  604 

688 

473  344 

325  660  672 

26.229  7541 

8.828  0099 

.001  453  488 

689 

474  721 

327  082  769 

26.248  8095 

8.832  2850 

.001  451  379 

690 

476100 

328  509  000 

26.267  8511 

8.836  5559 

.001  449  275 

691 

477  481 

329  939  371 

26.286  8789 

8.840  8227 

.001  447  178 

692 

478  864 

331  373  888 

26.305  8929 

8.845  0854 

.001  445  087 

693 

480  249 

332  812  557 

26.324  8932 

8.849  3440 

.001  443  001 

694 

481  636 

334  255  384 

26.343  8797 

8.853  5985 

.001  440  922 

695 

483  025 

335  702  375 

26.362  8527 

8.857  8489 

.001  438  849 

696 

484  416 

337  153  536 

26.381  8119 

8.862  0952 

.001  436  782 

697 

485  809 

338  608  873 

26.400  7576 

8.866  3375 

.001  434  720 

698 

487  204 

340  068  392 

26.419  6896 

8.870  5757 

.001  432  665 

699 

488  601 

341  532  099 

26.438  6081 

8.874  8099 

.001  430  615 

700 

490  000 

343  000  000 

26.457  5131 

8.879  0400 

.001  428  571 

701 

491  401 

344  472  101 

26.476  4046 

8.883  2661 

.001  426  534 

702 

492  804 

345  948  408 

26.495  2826 

8.887  4882 

.001  424  501 

703 

494  209 

347  428  927 

26.514  1472 

8.891  7063 

.001  422  475 

704 

495  616 

348  913  664 

26.532  9983 

8.895  9204 

.001  420  455 

705 

497  025 

350  402  625 

26.551  8361 

8.900  1304 

.001  418  440 

706 

498  436 

351  895  816 

26.570  6605 

8.904  3366 

.001  416  431 

707 

499  849 

353  393  243 

26.589  4716 

8.908  5387 

.001  414  427 

708 

501264 

354  894  912 

26.608  2694 

8.912  7369 

.001  412  429 

709 

502  681 

356  400  829 

26.627  0539 

8.916  9311 

.001  410  437 

710 

504  100 

357  911  000 

26.645  8252 

8.921 1214 

.001  408  451 

711 

505  521 

359  425  431 

26.664  5833 

8.925  3078 

.001  406  470 

712 

506  944 

360  944  128 

26.683  3281 

8.929  4902 

.001  404  494 

713 

508  369 

362  467  097 

26.702  0598 

8.933  6687 

.001  402  525 

714 

509  796 

363  994  344 

26.720  7784 

8.937  8433 

.001  400  560 

715 

511225 

365  525  875 

26.739  4839 

8.942  0140 

.001  398  601 

716 

612  656 

367  061  696 

26.758  1763 

8.946  1809 

.001  396  648 

717 

514  089 

368  601  813 

26.776  8557 

8.950  3438 

.001  394  700 

718 

515  524 

370  146  232 

26.795  5220 

8.954  5029 

.001  392  758 

719 

516  961 

371  694  959 

26.814  1754 

8.958  6581 

.001  390  821 

720 

518  400 

373  248  000 

26.832  8157 

8.962  8095 

.001  388  889 

721 

519  841 

374  805  361 

26.851  4432 

8.966  9570 

.001  386  963 

722 

521284 

376  367  048 

26.870  0577 

8.971 1007 

.001  385  042 

723 

522  729 

377  933  067 

26.888  6593 

8.975  2406 

.001  383  126 

724 

524  176 

379  503  424 

26.907  2481 

8.979  3766 

.001  381  215 

725 

525  625 

381  078  125 

26.925  8240 

8.983  5089 

.001  379  310 

726 

527  076 

382  657  176 

26.944  3872 

8.987  6373 

.001  377  410 

■  727 

528  529 

384  240  583 

26.962  9375 

8.991  7620 

.001  375  516 

728 

529  981 

385  828  352 

26.981  4751  ! 

8.995  8899 

.001  373  626 

Powers 

and  Roots. 

765 

Number. 

Squares. 

Cubes. 

}  Roots. 

f  Roots. 

Reciprocals. 

729 

531  441 

387  420  489 

27.000  0000 

9.000  0000 

.001  371  742 

730 

532  900 

389  017  000 

27.018  5122 

9.004 1134 

.001  369  863 

731 

534  361 

390  617  891 

27.037  0117 

9.008  2229 

.001  367  989 

•  732 

535  824 

392  223  168 

27.055  4985 

9.012  3288 

.001  366  120 

733 

537  289 

393  832  837 

27.073  9727 

9.016  4309 

.001  364  256 

734 

538  756 

395  446  904 

27.092  4344 

9.020  5293 

.001  362  398 

735 

540  225 

397  065  375 

27.110  8834 

9.024  6239 

.001  360  544 

736 

541696 

398  688  256 

27.129  3199 

9.028  7149 

.001  358  696 

737 

543169 

400  315  553 

27.147  7149 

9.032  8021 

.001  356  8j2 

738 

544  644 

401  947  272 

27.166  1554 

9.036  8857 

.001  355  014 

739 

546121 

403  583  419 

27.184  5544 

9.040  9655 

.001  353  180 

740 

547  600 

405  224  000 

27.202  9140 

9.045  0419 

.001  351  351 

741 

549  081 

406  869  021 

27.221  3152 

9.0491142 

.001  349  528 

742 

550  564 

408  518  488 

27.239  6769 

9.053  1831 

.001  347  709 

743 

552  049 

410  172  407 

27.258  0263 

9.057  2482 

.001  345  895 

744 

553  536 

411  830  784 

27.276  3634 

9.061  3098 

.001  344  086 

745 

555  025 

413  493  625 

27.294  6881 

9.065  3677 

.001  342  282 

746 

556  516 

415  160  936 

27.313  0006 

9.069  4220 

.001  340  483 

747 

558  009 

416  832  723 

27.331  3007 

9.073  4726 

.001  338  688 

748 

559  504 

418  508  992 

27.349  5887 

9.077  5197 

.001  336  898 

749 

561001 

420  189  749 

27.367  8644 

9.081  5631 

.001  335  113 

750 

562  500 

421  875  000 

27.386  1279 

9.085  6030 

.001  333  333 

751 

564  001 

423  564  751 

27.404  3792 

9.089  6352 

.001  331  558 

752 

565  504 

425  259  008 

27.422  6184 

9.093  6719 

.001  329  787 

753 

567  009 

426  957  777 

27.440  8455 

9.097  7010 

.001  328  021 

754 

568  516 

428  661  064 

27.459  0604 

9.101  7265 

.001  326  260 

755 

570  025 

430  368  875 

27.477  2633 

9.105  7485 

.001  324  503 

756 

571  536 

432  081  216 

27.495  4542 

9.109  7669 

.001  322  751 

757 

573  049 

433  798  093 

27.513  6330 

9.113  7818 

.001  321  004 

758 

574  564 

435  519  512 

27.531  7998 

9.117  7931 

.001  319  261 

759 

576  081 

437  245  479 

27.549  9546 

9.121  8010 

.001  317  523 

760 

577  600 

438  976  000 

27.568  0975 

9.125  8053 

.001  315  789 

761 

579  121 

440  711  081 

27.586  2284 

9.129  8061 

.001  314  060 

762 

580  644 

442  450  728 

27.604  3475 

9.133  8034 

.001  312  336 

763 

582169 

444  194  947 

27.622  4546 

9.137  7971 

.001  310  616 

764 

583  696 

445  943  744 

27.640  5499 

9.141  7874 

Ml  308  901 

765 

585  225 

447  697  125 

27.658  6334 

9.145  7742 

.001  307  190 

766 

586  756 

449  455  096 

27.676  7050 

9.149  7576 

.001  305  483 

767 

588  289 

451217  663 

27.694  7648 

9.153  7375 

.001  303  781 

768 

589  824 

452  984  832 

27.712  8129 

9.157  7139 

.001  302  083 

769 

591  361 

454  756  609 

27.730  8492 

9.161  6869 

.001  300  390 

770 

592  900 

456  533  000 

27.748  8739 

9.165  6565 

.001  298  701 

771 

594  441 

458  314  Oil 

27.766  8868 

9.169  6225 

.001  297  017 

772 

595  984 

460  099  648 

27.784  8880 

9.173  5852 

.001  295  337 

773 

597  529 

461  889  917 

27.802  8775 

9.177  5445 

.001  293  661 

774 

599  076 

463  684  824 

27.820  8555 

9.181  5003 

.001  291  990 

775 

600  625 

465  484  375 

27.838  8218 

9.185  4527 

.001  290  323 

776 

602  176 

467  288  576 

27.856  7766 

9.189  4018 

.001  288  660 

777 

603  729 

469  097  433 

27.874  7197 

9.193  3474 

.001  287  001 

778 

605  284 

470  910  952 

27.892  6514 

9.197  2897 

.001  285  347 

779 

606  841 

472  729  139 

27.910  5715 

9.201  2286 

.001  283  697 

780 

608  400 

474  552  000 

27.928  4801 

«.205  1641 

.001  282  051 

766 

Powers 

and  Roots 

Number. 

Squares. 

Cubes. 

Kfiftote 

f  RootH. 

Reciprocate, 

781 

609  961 

476  379  541 

27.946  3772 

9.209  0962 

.001  280  410 

782 

611524 

478  211  768 

27.964  2629 

9.213  0250 

.001  278  772 

783 

613  089 

480  048  687 

27.982  1372 

9.216  9505 

.001  277  139 

784 

614  656 

481  890  304 

28.000  0000 

9.220  8726 

.001  275  510 

785 

616  225 

483  736  625 

28.017  8515 

9.224  7914 

.001  273  885 

786 

617  7% 

485  587  656 

28.035  6915 

9.228  7068 

.001  272  265 

787 

619  369 

487  443  403 

28.053  5203 

9.232  6189 

.001  270  648 

788 

620  944 

489  303  872 

28.071  3377 

9.236  5277 

.001  269  036 

789 

622  521 

491 169  069 

28.089  1438 

9.240  4333 

.001  267  427 

790 

624100 

493  039  000 

28.106  9386 

9.244  3355 

.001  265  823 

791 

625  681 

494  913  671 

28.124  7222 

9.248  2344 

.001  264  223 

792 

627  264 

496  793  088 

28.142  4946 

9.252  1300 

.001  262  626 

793 

628  849 

498  677  257 

28.160  2557 

9.256  0224 

.001  261  034 

794 

630  436 

500  566  184 

28.178  0056 

9.259  9114 

.001  259  446 

795 

632  025 

502  459  875 

28.195  7444 

9.263  7973 

.001  257  862 

796 

633  616 

504  358  336 

28.213  4720 

9.267  6798 

.001  256  281 

797 

635  209 

506  261  573 

28.231 1884 

9.271 5592 

.001  254  705 

798 

636  804 

508  169  592 

28.248  8938 

9.275  4352 

.001  253  133 

799 

638  401 

510  082  399 

28.266  5881 

9.279  3081 

.001  251  564 

800 

640  000 

512  000  000 

28.284  2712 

9.283  1777 

.001250  000 

801 

641601 

513  922  401 

28.301  9434 

9.287  0444 

.001  248  439 

802 

643  204 

515  849  608 

28.319  6045 

9.290  9072 

.001  246  883 

803 

644  809 

517  781  627 

28.337  2546 

9.294  7671 

.001  245  330 

801 

646  416 

519  718  464 

28.354  8938 

9.298  6239 

.001  243  781 

805 

648  025 

521  660  125 

28.372  5219 

9.302  4775 

.001  242  236 

806 

649  636 

523  606  616 

28.390  1391 

9.306  3278 

.001  240  695 

807 

651249 

525  557  943 

28.407  7454 

9.310  1750 

.001  239  157 

808 

652  864 

527  514  112 

28.425  3408 

9.314  0190 

.001  237  624 

809 

654  481 

529  475129 

28.442  9253 

9.317  8599 

.001  236  094 

810 

656100 

531  441  000 

28.460  4989 

9.321  6975 

.001  234  568 

811 

657  721 

533  411  731 

28.478  0617 

9.325  5320 

.001  233  046 

812 

659  844 

535  387  328 

28.495  6137 

9.329  3634 

.001  231  527 

813 

660  969 

537  367  797 

28.513  1549 

9.333  1916 

.001  230  012 

814 

662  596 

539  353  144 

28.530  6852 

9.337  0167 

.001  228  501 

815 

664  225 

541343  375 

28.548  2048 

9.340  8386 

.001  226  994 

816 

665  856 

543  338  496 

28.565  7137 

9.344  6575 

.001  225  499 

817 

667  489 

545  338  513 

28.583  2119 

9.348  4731 

.001  223  990 

818 

669124 

547  343  432 

28.600  6993 

9.352  2857 

.001  222  494 

819 

670  761 

549  353  259 

28.618  1760 

9.356  0952 

.001  221  001 

820 

672  400 

551368  000 

28.635  6421 

9.359  9016 

.001  219  512 

821 

674  041 

553  387  661 

28.653  0976 

9.363  7049 

.001  218  027 

822 

675  684 

555  412  248 

28.670  5424 

9.367  5051 

.001  216  545 

823 

677  329 

557  441  767 

28.687  9716 

9.371  3022 

.001215  067 

824 

678  976 

559  476  224 

28.705  4002 

9.375  0963 

.001  213  592 

825 

680  625 

561  515  625 

28.722  8132 

9.378  8873 

.001  212  121 

826 

682  276 

563  559  976 

28.740  2157 

9.382  6752 

.001  210  654 

827 

683  929 

565  609  283 

28.757  6077 

9.386  4600 

.001  209  190 

828 

685  584 

567  663  552 

28.774  9891 

9.390  2419 

.001  207  729 

829 

687  241 

569  722  789 

28.792  3601 

9.394  0206 

.001  206  273 

830 

688  900 

571  787  000 

28.809  7206 

9.397  7964 

.001  204  819 

831 

690  561 

573  856  191 

28.827  0706 

9.401  5691 

.001  203  369 

832 

692  224 

.575  930  368 

28.844  4102 

9.405  3387 

.001  201  923 

Powers 

and  Roots 

767 

Number. 

Squares. 

Cubes. 

V  Roots. 

f  Roots. 

Reciprocals. 

833 

693  889 

578  009  537 

28.861  7394 

9.409  1054 

.001  200  480 

834 

695  556 

580  093  704 

28.879  0582 

9.412  8690 

.001 199  041 

835 

697  225 

582  182  875 

28.896  3666 

9.416  6297 

.001 197  605 

836 

698  896 

584  277  056 

28.913  6646 

9.420  3873 

.001 196  172 

837 

700  569 

586  376  253 

28.930  9523 

9.424  1420 

.001 194  743 

838 

702  244 

588  480  472 

28.948  2297 

9.427  8936 

.001 193  317 

839 

703  921 

590  589  719 

28.965  4967 

9.431  6423 

.001 191  895 

840 

705  600 

592  704  000 

28.982  7535 

9.435  3800 

.001 190  476 

841 

707  281 

594  823  321 

29.000  0000 

9.439  1307 

.001 189  061 

842 

708  964 

596  947  688 

29.017  2363 

9.442  8704 

.001 187  648 

843 

710  649 

599  077  107 

29.034  4623 

9.446  6072 

.001 186  240 

844 

712  336 

601  211  584 

29.051  6781 

9.450  3410 

.001 184  834 

845 

714  025 

603  351 125 

29.068  8837 

9.454  0719 

.001 183  432 

846 

715  716 

605  495  736 

29.086  0791 

9.457  7999 

.001 182  033 

847 

717  409 

607  645  423 

29.103  2644 

9.461  5249 

.001 180  638 

848 

719  104 

609  800  192 

29.120  4396 

9.465  2470 

.001 179  245 

849 

720  801 

611  960  049 

29.137  6046 

9.468  9661 

.001 177  856 

850 

722  500 

614  125  000 

29.154  7595 

9.472  6824 

.001 176  471 

851 

724  201 

616  295  051 

29.171  9043 

9.476  3957 

.001  175  088 

852 

725  904 

618  470  208 

29.189  0390 

9.480  1061 

.001  173  709 

853 

727  609 

620  650  477 

29.206  1637 

9.483  8136 

.001 172  333 

854 

729  316 

622  835  864 

29.223  2784 

9.487  5182 

.001 170  960 

855 

731  025 

625  026  375 

29.240  3830 

9.491  2200 

.001 169  591 

856 

732  736 

627  222  016 

29.257  4777 

9.494  9188 

.001 168  224 

857 

734  449 

629  422  793 

29.274  5623 

9.498  6147 

.001 166  861 

858 

736  164 

631  628  712 

29.291  6370 

9.502  3078 

.001 165  501 

859 

737  881 

633  839  779 

29.308  7018 

9.505  9980 

.001 164  144 

860 

739  600 

636  056  000 

29.325  7566 

9.509  6854 

.001 162  791 

861 

741  321 

638  277  381 

29.342  8015 

9.513  3699 

.001 161  440 

862 

743  044 

640  503  928 

29.359  8365 

9.517  0515 

.001 160  093 

863 

744  769 

642  735  647 

29.376  8616 

9.520  7303 

.001 158  749 

864 

746  496 

644  972  544 

29.393  8769 

9.524  4063 

.001 157  407 

865 

748  225 

647  214  625 

29.410  8823 

9.528  0794 

.001 156  069 

866 

749  956 

649  461  896 

29.427  8779 

9.531  7497 

.001 154  734 

867 

751  689 

651  714  363 

29.444  8637 

9.535  4172 

.001 153  403 

868 

753  424 

653  972  032 

29.4618397 

9.539  0818 

.001 152  074 

869 

755  161 

656  234  909 

29.478  8059 

9.542  7437 

.001 150  748 

870 

756  900 

658  503  000 

29.495  7624 

9.546  4027 

.001 149  425 

871 

758  641 

660  776  311 

29.512  7091 

9.550  0589 

.001 148  106 

872 

760  384 

663  054  848 

29.529  6461 

9.553  7123 

.001 146  789 

873 

762  129 

665  338  617 

29.546  5734 

9.557  3630 

.001 145  475 

874 

763  876 

667  627  624 

29.563  4910 

9.561  0108 

.001 144  165 

875 

765  625 

669  921  875 

29.580  3989 

9.564  6559 

.001 142  857 

876 

767  376 

672  221  376 

29.597  2972 

9.568  2782 

.001 141  553 

877 

769129 

674  526  133 

29.614  1858 

9.571  9377 

.001 140  251 

878 

770  884 

676  836  152 

29.631  0648 

9.575  5745 

.001 138  952 

879  . 

772  641 

679  151  439 

29.647  9342 

9.579  2085 

.001 137  656 

880 

774  400 

681  472  000 

29.664  7939 

9.582  8397 

.001 136  364 

881 

776  161 

683  797  841 

29.681  6442 

9.586  4682 

.001135  074 

882 

777  924 

686  128  968 

29.698  4848 

9.590  0937 

.001 133  787 

883 

779  689 

688  465  387 

29.715  3159 

9.593  7169 

.001 132  503 

884 

781  456 

690  807  104 

29.732 1375 

9.597  3373 

.001  131  222 

768 

Powers 

and  Roots 

Number. 

Squares. 

Cubes. 

t'Rooti 

f  Roots. 

Reciprocals. 

885 

783  225 

693  154  125 

29.748  9496 

9.600  9548 

.001  129  944 

886 

784  996 

695  506  456 

29.765  7521 

9.604  5696 

.001  128  668 

887 

786  769 

697  864  103 

29.782  5452 

9.608  1817 

.001 127  396 

888 

788  544 

700  227  072 

29.799  3289 

9.611  7911 

.001  126  126 

889 

790  321 

702  595  369 

29.816  1030 

9.615  3977 

.001 124  859 

890 

792100 

704  969  000 

29.832  8678 

9.619  0017 

.001 123  596 

891 

793  881 

707  347  971 

29.849  6231 

9.622  6030 

.001 122  334 

892 

795  664 

707  932  288 

29.866  3690 

9.626  2016 

.001 121  076 

893 

797  449 

712  121  957 

29.883  1056 

9.629  7975 

.001 119  821 

894 

799  236 

714  516  984 

29.899  8328 

9.633  3907 

.001 118  568 

895 

801025 

716  917  375 

29.916  5506 

9.636  9812 

.001 117  818 

896 

802  816 

719  323  136 

29.933  2591 

9.640  5690 

.001  116  071 

897 

804  609 

721734  273 

29.949  9583 

9.644  1542 

.001 114  827 

898 

806  404 

724  150  792 

29.966  6481 

9.647  7367 

.001 113  586 

899 

808  201 

726  572  699 

29.983  3287 

9.651  3166 

.001 112  347 

900 

810  000 

729  000  000 

30.000  0000 

9.654  8938 

.001  111  111 

901 

811801 

731  432  701 

30.016  6621 

9.658  4684 

.001 109  878 

902 

813  604 

733  870  808 

30.033  3148 

9.662  0403 

.001  108  647 

903 

815  409 

736  314  327 

30.049  9584 

9.665  60% 

.001  107  420 

904 

817  216 

738  763  264 

30.066  5928 

9.669  1762 

.001 106  195 

905 

819  025 

741  217  625 

30.083  2179 

9.672  7403 

.001  104  972 

906 

820  836 

743  677  416 

30.099  8339 

9.676  3017 

.001 103  753 

907 

822  649 

746  142  643 

30.116  4407 

9.679  8604 

.001 102  536 

908 

824  464 

748  613  312 

30.133  0383 

9.683  4166 

.001 101  322 

909 

826  281 

751  089  429 

30.149  6269 

9.686  9701 

.001 100  110 

910 

828100 

753  571  000 

30.166  2063 

9.690  5211 

.001  098  901 

911 

829  921 

756  058  031 

30.182  7765 

9.694  0694 

.001  097  695 

912 

831744 

758  550  828 

30.199  3377 

9.697  6151 

.001  096  491 

913 

833  569 

761  048  497 

30.215  8899 

9.701 1583 

.001  095  290 

914 

835  396 

763  551  944 

30.232  4329 

9.704  6989 

.001  094  092 

915 

837  225 

766  060  875 

30.248  9669 

9.708  2369 

.001  092  896 

916 

839  056 

768  575  296 

30.265  4919 

9.711  7723 

.001  091  703 

917 

840  889 

771  095  213 

30.282  0079 

9.715  3051 

.001  090  513 

918 

842  724 

773  620  632 

30.298  5148 

9.718  8354 

.001  089  325 

919 

844  561 

776  151  559 

30.315  0128 

9.722  3631 

.001  088  139 

920 

846  400 

778  688  000 

30.331  5018 

9.725  8883 

.001  086  957 

921 

848  241 

781229  961 

30.347  9818 

9.729  4109 

.001  085  776 

922 

850  084 

783  777  448 

30.364  4529 

9.732  9309 

.001  084  599 

923 

851929 

786  330  467 

30.380  9151 

9.736  4484 

.001  083  423 

924 

853  776 

788  889  024 

30.397  3683 

9.739  9634 

.001  082  251 

925 

855  625 

791  453  125 

30.413  8127 

9.743  4758 

.001  081  081 

926 

857  476 

794  022  776 

30.430  2481 

9.746  9857 

.001  079  914 

927 

859  329 

796  597  983 

30.446  6747 

9.750  4930 

.001  078  749 

928 

861184 

799  178  752 

30.463  0924 

9.753  9979 

.001  077  586 

929 

863  041 

801  765  089 

30.479  5013 

9.757  5002 

.001  076  426 

930 

864  900 

804  357  000 

30.495  9014 

9.761  0001 

.001  075  269 

931 

866  761 

806  954  491 

30.512  2926 

9.764  4974 

.001  074  114 

932 

868  624 

809  557  568 

30.528  6750 

9.767  9922 

.001  072  961 

933 

870  489 

812  166  237 

30.545  0487 

9.771  4845 

.001  071  811 

934 

872  356 

814  780  504 

30.561  4136 

9.774  9743 

.001070  664 

935 

874  225 

817  400  375 

30.577  7697 

9.778  4616 

.001  069  519 

936 

876  096 

820  025  856 

30.594  1171 

9.781  9466 

.001  068  376 

Powers 

and  Roots 

769 

Number. 

Squares. 

Cubes. 

V  Roots, 

f  Roots. 

Reciprocals. 

937 

877  969 

822  656  953 

30.610.4557 

9.785  4288 

.001  067  236 

938 

879  844 

825  293  672 

30.626  7857 

9.788*9087 

.001  066  098 

939 

881721 

827  936  019 

30.643  1069 

9.792  3861 

.001  064  963 

940 

883  600 

830  584  000 

30.659  4194 

9.795  8611 

.001  063  830 

941 

885  481 

833  237  621 

30.675  7233 

9.799  3336 

.001  062  699 

942 

887  364 

835  896  888 

30.692  0185 

9.802  8036 

.001  061  571 

943 

889  249 

838  561  807 

30.708  3051 

9.806  2711 

.001  060  445 

944 

891 136 

841  232  384 

30.724  5830 

9.809  7362 

.001  059  322 

945 

893  025 

843  908  625 

30.740  8523 

9.813  1989 

.001  058  201 

946 

894  916 

846  590  536 

30.757  1130 

9.816  6591 

.001  057  082 

947 

896  809 

849  278  123 

30.773  3651 

9.820  1169 

.001  055  966 

948 

898  704 

851  971  392 

30.789  6086 

9.823  5723 

.001  054  852 

949 

900  601 

854  670  349 

30.805  8436 

9.827  0252 

.001  053  741 

950 

902  500 

857  375  000 

30.822  0700 

9.830  4757 

.001  052  632 

951 

904  401 

860  085  351 

30.838  2879 

9.833  9238 

.001  051  525 

952 

906  304 

862  801  408 

30.854  4972 

9.837  3695 

.001  050  420 

953 

908  209 

865  523  177 

30.870  6981 

9.840  8127 

.001  049  318 

954 

910  116 

868  250  664 

80.886  8904 

9.844  2536 

.001  048  218 

955 

912  025 

870  983  875 

30.903  0743 

9.847  6920 

.001  047  120 

956 

913  936 

873  722  816 

30.919  2477 

9.851 1280 

.001  046  025 

957 

915  849 

876  467  493 

30.935  4166 

9.854  5617 

.001  044  932 

958 

917  764 

879  217  912 

30.951  5751 

9.857  9929 

.001  043  841 

959 

919  681 

881  974  079 

30.967  7251 

9.861  4218 

.001  042  753 

960 

921600 

884  736  000 

30.983  8668 

9.864  8483 

.001  041  667 

961 

923  521 

887  503  681 

31.000  0000 

9.868  2724 

.001  040  583 

962 

925  444 

890  277  128 

31.016  1248 

9.871  6941 

.001  039  501 

963 

927  369 

893  056  347 

31.032  2413 

9.8751135 

.001  038  422 

•964 

929  296 

895  841  344 

31.048  3494 

9.878  5305 

.001  037  344 

965 

931225 

898  632  125 

31.064  4491 

9.881  9451 

.001  036  269 

966 

933156 

901  428  696 

31.080  5405 

9.885  3574 

.001  035  197 

967 

935  089 

904  231  063 

31.096  6236 

9.888  7673 

.001  034  126 

968 

937  024 

907  039  232 

31.112  6984 

9.892  1749 

.001  033  058 

969 

938  961 

909  853  209 

31.128  7648 

9.895  5801 

.001  031  992 

•  970 

940  900 

912  673  000 

31.144  8230 

9.898  9830 

.001  030  928 

971 

942  841 

915  498  611 

31.160  8729 

9.902  3835 

.001  029  866 

972 

944  784 

918  330  048 

31.176  9145 

9.905  7817 

.001  028  807 

973 

946  729 

921 167  317 

31.192  9479 

9.909  1776 

.001  027  749 

974 

948  676 

924  010  424 

31.208  9731 

9.912  5712 

.001  026  694 

975 

950  625 

926  859  375 

31.224  9900 

9.915  9624 

.001  025  641 

976 

952  576 

929  714  176 

31.240  9987 

9.919  3513 

.001  024  590 

977 

954  529 

932  574  833 

31.256  9992 

9.922  7379 

.001  023  541 

978 

956  484 

935  441  352 

31.272  9915 

9.926  1222 

.001  022  495 

979 

958*441 

938  313  739 

31.288  9757 

9.929  5042 

.001  021  450 

980 

960  400 

941 192  000 

31.304  9517 

9.932  8839 

.001  020  408 

981 

962  361 

944  076  141 

31.320  9195 

9.936  2613 

.001  019  168 

982 

964  324 

946  966  168 

31.336  8792 

9.939  6363 

.001  018  330 

983 

966  289 

949  862  087 

31.352  8308 

9.943  0092 

.001  017  294 

984 

968  256 

952  763  904 

31.368  7743 

9.946  3797 

.001  016  260 

985 

970  225 

955  671  625 

31.384  7097 

9.949  7479 

.001  015  228 

986 

972  196 

958  585  256 

31.400  6369 

9.953  1138 

.001  014  199 

987 

974  169 

961  504  803 

31.416  5561 

9.956  4775 

.001  013  171 

988 

976  144 

964  430  272 

31.432  4673 

9.959  8389 

.001  012 146 

770 

Powers 

and  Roots 

Number. 

Squares. 

Cubes. 

I7  Roots. 

f  Roots. 

Reciprocals. 

asy 

978  121 

967  361  669 

31.448  3704 

9.963  1981 

.001  011 122 

990 

980100* 

970  299  000 

BL4M98M 

9.966  5549 

.001  010  101 

991 

982  081 

973  242  271 

31.480  1525 

9.969  9055 

.001  009  082 

992 

984  064 

976  191  488 

31.496  0315 

9.973  2619 

.001008  065 

993 

986  049 

979  146  657 

31.511  9025 

9.976  6120 

.001  007  049 

994 

988  036 

982  107  784 

31.527  7655 

9.979  9599 

.001  006  036 

995 

990  025 

985  074  875 

31.543  6206 

9.983  3055 

.001  005  025 

996 

992  016 

988  047  936 

31.559  4677 

9.986  6488 

.001  004  016 

997 

994  009 

991  026  973 

31.575  3068 

9.989  9900 

.001  003  009 

998 

996  004 

994  Oil  992 

31.591 1380 

9.993  3289 

.001002  004 

999 

998  001 

997  002  999 

31.606  9613 

9.996  6656 

.001  001  001 

1000 

1000  000 

1000  000  000 

31.622  7766 

10.000  0000 

.001000  000 

1001 

1002  001 

1  003  003  001 

31.638  5840 

10.003  3222 

.000  999  0010 

1002 

1004  004 

1  006  012  008 

31.654  3866 

10.006  6622 

.000  998  0040 

1003 

1006  009 

"1  009  027  027 

31.670  1752 

10.009  9899 

.000  997  0090 

1004 

1  008  016 

1  012  048  064 

31.685  9590 

10.013  3155 

.000  996  0159 

1005 

1  010  025 

1  015  075  125 

31.701  7349 

10.016  6389 

.000  995  0249 

1006 

1  012  036 

1  018  108  216 

31.717  5030 

10.019  9601 

.000  994  0358 

1007 

1  014  049 

1  021 147  343 

31.733  2633 

10.023  2791 

.000  993  0487 

1008 

1016  064 

1  024  192  512 

31.749  0157 

10.026  5958 

.000  992  0635 

1009 

1  018  081 

1  027  243  729 

31.764  7603 

10.029  9104 

.000  991  0803 

1010 

1020100 

1  030  301  000 

31.780  4972 

10.033  2228 

.000  990  0990 

1011 

1  022  121 

1  033  364  331 

31.796  2262 

10.036  5330 

.000  989  1197 

1012 

1  024  144 

1  036  433  728 

31.811  9474 

10.039  8410 

.000  988  1423 

1013 

1  026  169 

1  039  509  197 

31.827  6609 

10.043  1469 

.000  987  1668 

1014 

1028196 

1  042  590  744 

31.843  3666 

10.046  4506 

.000  986  1933 

1015 

1030  225 

1  045  678  375 

31.859  0646 

10.049  7521 

.000  985  2217 

1016 

1032  256 

1  048  772  096 

31.874  7549 

10.053  0514 

.000  984  2520 

1017 

1  034  289 

1  051  871  913 

31.890  4374 

10.056  3485 

.000  983  2842 

1018 

1  036  324 

1  054  977  832 

31.906  1123 

10.059  6435 

.000  982  3183 

1019 

1  038  361 

1  058  089  859 

31.921  7794 

10.062  9364 

.000  981  3543 

1020 

1040  400 

1  061  208  000 

31.937  4388 

10.066  2271 

.000  980  3922 

1021 

1  042  441 

1  064  332  261 

31.953  0906 

10.069  5156 

.000  979  4319 

1022 

1044  484 

1  067  462  648 

31.968  7347 

10.072  8020 

.000  978  4736 

1023 

1  046  529 

1  070  599  167 

31.984  3712 

10.076  0863 

.000  977  5171 

1024 

1  048  576 

1  073  741  824 

32.000  0000 

10.079  3684 

.000  976  5625 

1025 

1  050  625 

1  076  890  625 

32.015  6212 

10.082  6484 

.000  975  6098 

1026 

1  052  676 

1  080  045  576 

32.031  2348 

10.085  9262 

.000  974  6589 

1027 

1054  729 

1  083  206  683 

32.046  8407 

10.089  2019 

.000  973  7098 

1028 

1056  784 

1  086  373  952 

32.062  4391 

10.092  4755 

.000  972  7626 

1029 

1058  841 

1  089  547  389 

32.078  0298 

10.095  7469 

.000  971  8173 

1030 

1060  900 

1  092  727  000 

32.093  6131 

10.099  0163 

.000  970  8738 

1031 

1062  961 

1  095  912  791 

32.109  1887 

10.102  2835 

.000  969  9321 

1032 

1065  024 

1  099  104  768 

32.124  7568 

10.105  5487 

.000  968  9922 

1033 

1067  089 

1 102  302  937 

32.140  3173 

10.108  8117 

.000  968  0542 

1034 

1069156 

1 105  507  304 

32.155  8704 

10.112  0726 

.000  967  1180 

1035 

1071225" 

1 108  717  875 

32.171  4159 

10.115  3314 

.000  966  1836 

1036 

1  073  2% 

1  111  934  656 

32.186  9539 

10.118  5882 

.000  965  2510 

1037 

1075  369 

1 115  157  653 

32.202  4844 

10.1218428 

.000  964  3202 

1038 

1  077  444 

1 118  386  872 

32.218  0074 

10.125  0953 

.000  963  3911 

1039 

1  079  521 

1 121  622  319 

32.233  5229 

10.128  3457 

.000  962  4639 

1040 

1081600 

1 124  864  000 

32.249  0310 

10.131  5941 

.000  961  5385 

Powers  and  Roots. 


771 


Squares. 

1  083  681 
1  085  764 
1  087  849 
1  089  936 
1  092  025 
1  094  116 
1  096  209 
1  098  304 
1 100  401 
1 102  500 
1  104  601 
1  106  704 
1  108  809 
1 110  916 
1 113  025 
1  115  136 
1  117  249 
1 119  364 
1  121  481 
1  123  600 
1 125  721 
1 127  844 
1  129  969 
1  132  096 
1134  225 
1 136  356 
1  138  489 
1 140  624 
1  142  761 
1144  900 
1  147  041 
1  149  184 
1  151  329 
1 153  476 
1  155  625 
1 157  776 
1 159  929 
1  162  084 
1  164  241 
1  166  400 
1 168  561 
1 170  724 
1  172  889 
1 175  056 
1177  225 
1 179  396 
1  181  569 
1 183  744 
1  185  921 
1188100 
1  190  281 
1  192  464 


Cubes.      v' Roots,     f  Roots 


1 128  111  921 
1  131  366  088 
1 134  626  507 
1 137  893  184 
1 141 166  125 
1 144  445  336 
1 147  730  823 
1 151  022  592 
1 154  320  649 
1 157  625  000 
1 160  935  651 
1 164  252  608 
1 167  575  877 
1 170  905  464 
1 174  241  375 
1 177  583  616 
1  180  932  193 
1 184  287  112 
1 187  648  379 
1 191  016  000 
1 194  389  981 
1 197  770  328 
1  201 157  047 
1  204  550  144 
1  207  949  625 
1  211  355  496 
1  214  767  763 
1  218  186  432 
1  221  611  509 
1  225  043  000 
1  228  480  911 
1  231  925  248 
1  235  376  017 
1  238  833  224 
1  242  296  875 
1  245  766  976 
1  249  243  533 
1  252  726  552 
1  256  216  039 
1  259  712  000 
1  263  214  441 
1  266  723  368 
1  270  238  787 
1  273  760  704 
1  277  289  125 
1  280  824  056 
1  284  365  503 
1  287  913  472 
1  291  467  969 
1  295  029  000 
1  298  596  571 
1  302  170  688 


32.264.5316 
32.280  0248 
32.295  5105 
32.310  9888 
32.326  4598 
32.341  9233 
32.357  3794 
32.372  8281 
32.388  2695 
32.403  7035 
32.419  1301 
32.434  5495 
32.449  9615 
32.465  3662 
32.480  7635 
32.496  1536 
32.511  5364 
32.526  9119 
32.542  2802 
32.557  6412 
32.572  9949 
32.588  3415 
32.603  5807 
32.619  0129 
32.634  3377 
32.649  6554 
32.664  9659 
32.680  2693 
32.695  5654 
32.710  8544 
32.726  1363 
32.741  4111 
32.756  6787 
32.771  9392 
32.787  1926 
32.802  4398 
32.817  6782 
32.832  9103 
32.848  1354 
32.863  3535 
32.878  5644 
32.893  7684 
32.908  9653 
32.924  1553 
32.939  3382 
32.954  5141 
32.969  6830 
32.984  8450 
33.000  0000 
33.015  1480 
33.030  2891 
33.045  4233 


10.134  8403 
10.138  0845 
10.141  3266 
10.144  5667 
10.147  8047 
10.151  0406 
10.154  2744 
10.157  5062 
10.160  7359 
10.163  9636 
10.167  1893 
10.170  4129 
10.173  6344 
10.176  8539 
10.180  0714 
10.183  2868 
10.186  5002 
10.189  7116 
10.192  9209 
10.196  1283 
10.199  3336 
10.202  5369 
10.205  7382 
10.208  9375 
10.212  1347 
10.215  3300 
10.218  5233 
10.221  7146 
10.224  9039 
10.228  0912 
10.231  2766 
10.234  4599 
10.237  6413 
10.240  8207 
10.243  9981 
10.247  1735 
10.250  3470 
10.253  5186 
10.256  6881 
10.259  8557 
10.263  0213 
10.266  1850 
10.269  3467 
10.272  5065 
10.275  6644 
10.278  8203 
10.281  9743 
10.285  1264 
10.288  2765 
10.291  4247 
10.294  5709 
10.297  7153 


Reciprocals. 


.000  960  6148 
.000  959  6929 
.000  958  7728 
.000  957  8544 
.000  956  9378 
.000  956  0229 
.000  955  1098 
.000  954  1985 
.000  953  2888 
.000  952  3810 
.000  951  4748 
.000  950  5703 
.000  949  6676 
.000  948  7666 
.000  947  8673 
.000  946  9697 
.000  946  0738 
.000  945  1796 
.000  944  2871 
.000  943  3962 
.000  942  5071 
.000  941  6196 
.000  940  7338 
.000  939  8496 
.000  938  9671 
.000  938  0863 
.000  937  2071 
.000  936  3296 
.000  935  4537 
.000  934  5794 
.000  933  7068 
.000  932  8358 
.000  931  9664 
.000  931  0987 
.000  930  2326 
.000  929  3680 
.000  928  5051 
.000  927  6438 
.000  926  7841 
.000  925  9259 
.000  925  0694 
.000  924  2144 
.000  923  3610 
.000  922  5092 
.000  921  6590 
.000  920  8103 
.000  919  9632 
.000  919  1176 
.000  918  2736 
.000  917  4312 
.000  916  5903 
.000  915  7509 


772 

Powers 

and  Roots 

Number. 

Squares. 

Cubes. 

^Roote! 

f  Boots. 

Reciprocals. 

1093 

1 194  649 

1  305  751  357 

33.060  5505 

10.300  8577 

.000  914  9131 

1094 

1196  836 

1309  338  584 

33.075  6708 

10.303  9982 

.000  914  0768 

1095 

1199  025 

1312  932  375 

33.090  7842 

10.307  1368 

.000  913  2420 

10% 

1  201  216 

1  316  532  736 

33.105  8907 

10.310  2735 

■  .000  912  4008 

1097 

1203  409 

1  320  139  673 

33.120  9903 

10.313  4083 

.000  911  5770 

1098 

1205  604 

1  323  753  192 

83.136  0830 

10.316  5411 

.000  910  7468 

1099 

1  207  801 

1  327  373  299 

33.151 1689 

10.319  6721 

.000  909  9181 

1100 

1210  000 

1  331  000  000 

33.166  2479 

10.322  8012 

.000  909  0909 

1101 

1  212  201 

1  334  633  301 

33.181  3200 

10.325  9284 

.000  908  2652 

1102 

1  214  404 

1  338  273  208 

33.196  3853 

10.329  0537 

.000  907  4410 

1103 

1  216  609 

1  341  919  727 

33.211  4438 

10.332  1770 

.000  906  6183 

1104 

1  218  816 

1  345  572  864 

33.226  6955 

10.335  2985 

.000  905  7971 

1105 

1221025 

1  349  232  625 

33.241  5403 

10.338  4181 

.000  904  9774 

1106 

1  223  236 

1  352  899  016 

33.256  5783 

10.341  5358 

.000  904  1591 

1107 

1  225  449 

1  356  572  043 

33.271  6095 

10.344  6517 

.000  903  3424 

1108 

1227  664 

1  360  251  712 

33.286  6339 

10.347  7657 

.000  902  5271 

1109 

1  229  881 

1  363  938  029 

33.301  6516 

10.350  8778 

.000  901  7133 

1110 

1232100 

1  367  631  000 

33.316  6625 

10.353  9880 

.000  900  9009 

1111 

1  234  321 

1  371  330  631 

33.331  6666 

10.357  0964 

.000  900  0900 

1112 

1  236  541 

1  375  036  928 

33.346  6640 

10.360  2029 

.000  899  2806 

1113 

1238  769 

1  378  749  897 

33.361  6546 

10.363  3076 

.000  898  4726 

1114 

1  240  996 

1382  469  544 

33.376  6385 

10.366  4103 

.000  897  6661 

1115 

1  243  225 

1  386  195  875 

33.391  6157 

10.369  5113 

.000  896  8610 

1116 

1  245  456 

1  389  928  896 

33.406  5862 

10.372  6103 

.000  896  0753 

1117 

1247  689 

1  393  668  613 

33.421  5499 

10.375  7076 

.000  895  2551 

1118 

1  249  924 

1  397  415  032 

33.436  5070 

10.378  8030 

.000  894  4544 

1119 

1  252  161 

1  401 168  159 

33.451  4573 

10.381  8965 

.000  893  6550 

1120 

1254  400 

1  404  928  000 

33.466  4011 

10.384  9882 

.000  892  8571 

1121 

1256  641 

1  408  694  561 

33.481  3381 

10.388  0781 

.000  896  0607 

1122 

1258  884 

1  412  467  848 

33.496  2684 

10.391  1661 

.000  892  2656 

1123 

1  261  129 

1  416  247  867 

33.511  1921 

10.394  2527 

.000  890  4720 

1124 

1  263  376 

1  420  034  624 

33.526  1092 

10.397  3366 

.000  889  6797 

1125 

1265  625 

1  423  828  125 

33.541  0196 

10.400  4192 

.000  888  8889 

1126 

1  267  876 

1  427  628  376 

33.555  9234 

10.403  4999 

.000  888  0995 

1127 

1  270  129 

1  431  435  383 

33.570  8206 

10.406  5787 

.000  887  3114 

1128 

1272  384 

1  435  249  152 

33.585  7112 

10.409  6557 

.000  886  5248 

1129 

1  274  641 

1  439  069  689 

33.600  5952 

10.412  7310 

.000  885  7396 

1130 

1276  900 

1  442  897  000 

33.615  4726 

10.415  8044 

.000  884  9558 

1131 

1  279  161 

1  446  731  091 

33.630  3434 

10.418  8760 

.000  884  1733 

1132 

1  281  424 

1  450  571  968 

33.645  2077 

10.421  9158 

.000  883  3922 

1133 

1  283  689 

1  454  419  637 

33.660  0653 

10.425  0138 

.000  882  6125 

1134 

1285  956 

1  458  274  104 

33.674  9165 

10.428  0800 

.000  881  8342 

1135 

1288  225 

1  462  135  375 

33.689  7610 

10.431  1443 

.000  881  0573 

1136 

1  290  496 

1  466  003  456 

33.704  5991 

10.434  2069 

.000  880  2817 

1137 

1292  769 

1  469  878  353 

33.717  4306 

10.437  2677 

.000  879  5075 

1138 

1295  044 

1  473  760  072 

33.734  0556 

10.440  3677 

.000  878  7346 

1139 

1  297  321 

1  477  648  619 

33.749  0741 

10.443  3839 

.000  877  9631 

1140 

1299  600 

1  481  544  000 

33.763  8860 

10.446  4393 

.000  877  1930 

1141 

1  301  881 

1  485  446  221 

33.778  6915 

10.449  4929 

.000  876  4242 

1142 

1304  164 

1  489  355  288 

33.793  4905 

10.452  5448 

.000  875  6567 

1143 

1  306  449 

1  493  271  C07 

33.808  2830 

10.455  5948 

.000  874  8906 

1144 

1308  736 

1  497  193  984 

33.823  0691 

10.458  6431 

.000  874  1259 

Powers 

and  Roots 

773 

Number. 

Squares. 

Cubes. 

V  Roots. 

f  Roots. 

Reciprocals. 

1145 

1311025 

1  501 123  625 

33.837  8486 

10.461  6896 

.000  873  3624 

1146 

1  313  316 

1  505  060  136 

33.852  6218 

10.464  7343 

.000  872  6003 

1147 

1  315  609 

1  509  003  523 

33.867  3884 

10.467  7773 

.000  871  8396 

1148 

1  317  904 

1  512  953  792 

33.882  1487 

10.470  8158 

.000  871  0801 

1149 

1  320  201 

1  516  910  949 

33.896  9025 

10.473  8579 

.000  870  3220 

1150 

1  322  500 

1  520  875  000 

33.911  6499 

10.476  8955 

.000  869  5652 

1151 

1  324  801 

1  524  845  951 

33.926  3909 

10.479  9314 

.000  868  8097 

1152 

1  327  104 

1  528  823  808 

33.941 1255 

10.482  9656 

.000  868  0556 

1153 

1  329  409 

1  532  808  577 

33.955  8537 

10.485  9980 

.000  867  3027 

1154 

1  331  716 

1  536  800  264 

33.970  5755 

10.489  0286 

.000  866  5511 

1155 

1  334  025 

1  540  798  875 

33.985  2910 

10.492  0575 

.000  865  8009 

1156 

1  336  336 

1  544  804  416 

34.000  0000 

10.495  0847 

.000  865  0519 

1157 

1  338  649 

1  548  816  893 

34.014  7027 

10.498  1101 

.000  864  3042 

1158 

1  340  964 

1  552  836  312 

34.029  3990 

10.501 1337 

.000  863  5579 

1159 

1  343  281 

1  556  862  679 

34.044  0890 

10.504  1556 

.000  862  8128 

1160 

1345  600 

1  560  896  000 

34.058  7727 

10.507  1757 

.000  862  0690 

1161 

1  347  921 

1  564  936  281 

34.073  4501 

10.510  1942 

.000  861  3264 

1162 

1350  244 

1  568  983  528 

34.088  1211 

10.513  2109 

.000  860  5852 

1163 

1  352  569 

1  573  037  747 

34.012  7858 

10.516  2259 

.000  859  8452 

1164 

1  354  896 

1  577  098  944 

34.117  4442 

10.519  2391 

.000  859  1065 

1165 

1  357  225 

1  581 167  125 

34.132  0963 

10.522  2506 

.000  858  3691 

1166 

1  359  556 

1  585  242  296 

34.146  7422 

10.525  2604 

.000  857  6329 

1167 

1  361  889 

1  589  324  463 

34.161  3817 

10.528  2685 

.000  856  8980 

1168 

1  364  224 

1593  413  632 

34.176  0150 

10.531  2749 

.000  856  1644 

1169 

1  366  561 

1597  509  809 

34.190  6420 

10.534  2795 

.000  855  4320 

1170 

1368  900 

1  601  613  000 

34.205  2627 

10.537  2825 

.000  854  7009 

1171 

1  371  241 

1  605  723  211 

34.219  8773 

10.540  2837 

.000  853  9710 

1172 

1  373  584 

1  609  840  448 

34.234  4855 

10.543  2832 

.000  853  2423 

1173 

1  375  929 

1  613  964  717 

34.249  0875 

10.546  2810 

.000  852  5149 

1174 

1  378  276 

1  618  096  024 

34.263  6834 

10.549  2771 

.000  851  7888 

1175 

1  380  625 

1  622  234  375 

34.278  2730 

10.552  2715 

.000  851  0638 

1176 

1  382  976 

1  626  379  776 

34.292  8564 

10.555  2642 

.000  850  3401 

1177 

1  385  329 

1  630  532  233 

34.307  4336 

10.558  2552 

.000  849  6177 

1178 

1  387  684 

1  634  691  752 

34.322  0046 

10.561  2445 

.000  848  8964 

1179 

1  390  041 

1  638  858  339 

34.336  5694 

10.564  2322 

.000  848  1764 

1180 

1  392  400 

1  643  032  000 

34.351 1281 

10.567  2181 

.000  847  1576 

1181 

1  394  761 

1  647  212  741 

34.365  6805 

10.570  2024 

.000  846  7401 

1182 

1  397  124 

1  651  400  568 

34.380  2268 

10.573  1849 

.000  846  0237 

1183 

1  399  489 

1  655  595  487 

34.394  7670 

10.576  1658 

.000  845  3085 

1184 

1  401  856 

1  659  797  504 

34.409  3011 

10.579  1449 

.000  844  5946 

1185 

1  404  225 

1  664  006  625 

34.423  8289 

10.582  1225 

.000  843  8819 

1186 

1  406  596 

1  668  222  856 

34.438  3507 

10.585  0983 

.000  843  1703 

1187 

1  408  969 

1  672  446  203 

34.452  8663 

10.588  0725 

.000  842  4600 

1188 

1  411  344 

1  676  676  672 

34.467  3759 

10.591  0450 

.000  841  7508 

1189 

1  413  721 

1  680  914  629 

34.481  8793 

10.594  0158 

.000  841  0429 

1190 

1  416  100 

1  685  159  000 

34.496  3766 

10.596  9850 

.000  840  3361 

1191 

1  418  481 

1  689  410  871 

34.510  8678 

10.599  9525 

.000  839  6306 

1192 

1  420  864 

1  693  669  888 

34.525  3530 

10.602  9184 

.000  838  9262 

1193 

1  423  249 

1  697  936  057 

34.539  8321 

10.605  8826 

.000  838  2320 

1194 

1  425  636 

1  702  209  384 

34.554  3051 

10.608  8451 

.000  837  5209 

1195 

1  428  025 

1  706  489  875 

34.568  7720 

10.611  8060 

.000  836  8201 

1196 

1  430  416 

1  710  777  536 

34.583  2329 

10.614  7652 

.000  836  1204 

774 

Powers 

and  Roots 

Number. 

Squares. 

Cubes. 

V  Roots. 

fftoota 

Reciprocals. 

1197 

1432  809 

1  715  072  373 

34.597  6879 

10.617  7228 

.000  835  4219 

1198 

1435  204 

1  719  374  392 

34.612  1366 

10.620  6788 

.000  834  7245 

1199 

1  437  601 

1  723  683  599 

34.626  5794 

10.623  6331 

.000  834  0284 

1200 

1440  000 

1728  000  000 

34.641  0162 

10.626  5857 

.000  833  3333 

1201 

1  442  401 

1  732  323  601 

34.655  4469 

10.629  5367 

.000  832  6395 

1202 

1444  804 

1  736  654  408 

34.669  8716 

10.632  4860 

.000  831  9468 

1203 

1447  209 

1  740  992  427 

34.684  2904 

10.635  4338 

.000  831  2552 

1204 

1  449  616 

1  745  337  664 

34.698  7031 

10.638  3799 

.000  830  5648 

1205 

1  452  025 

1  749  690  125 

34.713  1099 

10.641  3244 

.000  829  8755 

1206 

1454  436 

1  754  049  816 

34.727  5107 

10.644  2672 

.000  829  1874 

1207 

1  456  849 

1  758  416  743 

34.741  9055 

10.647  2085 

.000  828  5004 

1208 

1  459  264 

1  762  790  912 

34.756  2944 

10.650  1480 

.000  827  8146 

1209 

1  461  681 

1  767  172  329 

34.770  6773 

10.653  0860 

.000  827  1299 

1210 

1464  100 

1  771  561  000 

34.785  0543 

10.656  0223 

.000  826  4463 

1211 

1  466  521 

1  775  956  931 

34.799  4253 

10.658  9570 

.000  825  7638 

1212 

1468  944 

1  780  360  128 

34.813  7904 

10.661  8902 

.000  825  0825 

1213 

1  471  369 

1  784  770  597 

34.828  1495 

10.664  8217 

.000  824  4023 

1214 

1  473  796 

1  789  188  344 

34.842  5028 

10.667  7516 

.000  823  7232 

1215 

1  476  225 

1  793  613  375 

34.856  8501 

10.670  6799 

.000  823  0453 

1216 

1  478  656 

1  798  045  696 

34.871  1915 

10.673  6066 

.000  822  3684 

.1217 

1  481  089 

1  802  485  313 

34.885  5271 

10.676  5317 

.000  821  6927 

1218 

1  483  524 

1  806  932  232 

34.899  8567 

10.679  4552 

.000  821  0181 

1219 

1485  961 

1  811  386  459 

34.914  1805 

10.682  3771 

.000  820  3445 

1220 

1488  400 

1  815  848  000 

34.928  4984 

10.685  2973 

.000  819  6721 

1221 

1  490  841 

1  820  316  861 

34.942  8104 

10.688  2160 

.000  819  0008 

1222 

1  493  284 

1  824  793  048 

34.957  1166 

10.691 1331 

.000  818  3306 

1223 

1  495  729 

1  829  276  567 

34.971  4169 

10.694  0486 

.000  817  6615 

1224 

1  498  176 

1  833  764  247 

34.985  7114 

10.696  9625 

.000  816  9935 

1225 

1500  625 

1  838  265  625 

35.000  0000 

10.699  8748 

.000  816  3265 

1226 

1  503  276 

1  842  771 176 

35.014  2828 

10.702  7855 

.000  815  6607 

1227 

1  505  529 

1  847  284  083 

35.028  5598 

10.705  6947 

000  814  9959 

1228 

1507  984 

1  851  804  352 

35.042  8309 

10.708  6023 

.000  814  3322 

1229 

1  510  441 

1  856  331  989 

35.057  0963 

10.711  5083 

.000  813  6696 

1230 

1512  900 

1  860  867  000 

35.071  3558 

10.714  4127 

.000  813  0081 

1231 

1  515  361 

1  865  409  391 

35.085  6096 

10.717  3155 

.000  812  3477 

1232 

1  517  824 

1  869  959  168 

35.099  8575 

10.720  2168 

.000  811  6883 

1233 

1520  289 

1  874  516  337 

35.114  0997 

10.723  1165 

.000  811  0300 

1234 

1522  756 

1  879  080  904 

35.128  3361 

10.726  0146 

.000  810  3728 

1235 

1  525  225 

1  883  652  875 

35.142  5668 

10.728  9112 

.000  809  7166 

1236 

1  527  696 

1  888  232  256 

35.156  7917 

10.731  8062 

.000  809  0615 

1237 

1530169 

1892  819053 

35.171  0108 

10.734  6997 

.000  808  4074 

1238 

1  532  644 

1  897  413  272 

35.185  2242 

10.737  5916 

.000  807  7544 

1239 

1535121 

1  902  014  919 

35.199  4318 

10.740  4819 

.000  807  1025 

1240 

1537  600 

1  906  624  000 

35.213  6337 

10.743  3707 

.000  806  4516 

1241 

1  540  081 

1  911  240  521 

35.227  8299 

10.746  2579 

.000  805  8018 

1242 

1542  564 

1  915  864  488 

35.242  0204 

10.749  1436 

.000  805  1530 

1243 

1  545  049 

1  920  495  907 

35.256  2051 

10.752  0277 

.000  804  5052 

1244 

1  547  536 

1  925  134  784 

35.270  3842 

10.754  9103 

.000  803  8585 

1245 

1550  025 

1  929  781 125 

35.284  5575 

10.757  7913 

.000  803  2129 

1246 

1  552  516 

1  934  434  936 

35.298  7252 

10.760  6708 

.000  802  5682 

1247 

1555  009 

1  939  096  223 

35.312  8872 

10.763  5488 

.000  801  9246 

1248 

1557  504 

1  943  764  992 

35.327  0435 

10.766  4252 

.000  801  2821 

Powers  and  Roots. 


775 


Number. 

Squares. 

Cubes. 

I7  Roots. 

f  Roots. 

Reciprocals. 

1249 

1560  001 

1  948  441  249 

35.341 1941 

10.769  3001 

.000  800  6405 

1250 

1  562  500 

1  953  125  000 

35.355  3391 

10.772  1735 

.000  800  0000 

1251 

1565  001 

1  957  816  251 

35.369  4784 

10.775  0453 

.000  799  3605 

1252 

1  567  504 

1  962  515  008 

35.383  6120 

10.777  9156 

.000  798  7220 

1253 

1  570  009 

1  967  221  277 

35.397  7400 

10.780  7843 

.000  798  0846 

1254 

1  572  516 

1  971  935  064 

35.411  8624 

10.783  6516 

.000  797  4482 

1255 

1  575  025 

1  976  656  375 

35.425  9792 

10.786  5173 

.000  796  8127 

1256 

1  577  536 

1  981  385  216 

35.440  0903 

10.789  3815 

.000  796  1783 

1257 

1  580  049 

1  986  121  593 

35.454  1958 

10.792  2441 

.000  795  5449 

1258 

1582  564 

1  990  865  512 

35.468  2957 

10.795  1053 

.000  794  9126 

1259 

1585  081 

1  995  616  979 

35.482  3900 

10.797  9649 

.000  794  2812 

1260 

1587  600 

2  000  376  000 

35.496  4787 

10.800  8230 

.000  793  6508 

1261 

1590121 

2  005  142  581 

35.510  5618 

10.803  6797 

.000  793  0214 

1262 

1  592  644 

2  009  916  728 

35.524  6393 

10.806  5348 

.000  792  3930 

1263 

1  595  169 

2  014  698  447 

35.538  7113 

10.809  3884 

.000  791  7656 

1264 

1  597  696 

2  019  487  744 

35.552  7777 

10.812  2404 

.000  791 1392 

1265 

1  600  225 

2  024  284  625 

35.566  8385 

10.815  0909 

.000  790  5138 

1266 

1  602  756 

2  029  089  096 

35.580  8937 

10.817  9400 

.000  789  8894 

1267 

1  605  289 

2  033  901 163 

35.594  9434 

10.820  7876 

.000  789  2660 

1268 

1  607  824 

2  038  720  832 

35.608  9876 

10.823  6336 

.000  788  6435 

1269 

1  610  361 

2  043  548  109 

35.623  0262 

10.826  4782 

.000  788  0221 

1270 

1612  900 

2  048  383  000 

35.637  0593 

10.829  3213 

.000  787  4016 

1271 

1  615  441 

2  053  225  511 

35.651  0869 

10.832  1629 

.000  786  7821 

1272 

1  617  984 

2  058  075  648 

35.665  1090 

10.835  0030 

.000  786  1635 

1273 

1  620  529 

2  062  933  417 

35.679  1255 

10.837  8416 

.000  785  5460 

1274 

1  623  076 

2  067  798  824 

35.693  1366 

10.840  6788 

.000  784  9294 

1275 

1  625  625 

2  072  671  875 

35.707  1421 

10.843  5144 

.000  784  3137 

1276 

1  628  176 

2  077  552  576 

35.721 1422 

10.846  3485 

.000  783  6991 

1277 

1  630  729 

2  082  440  933 

35.735  1367 

10.849  1812 

.000  783  0854 

1278 

1  633  284 

2  087  336  952 

35.749  1258 

10.852  0125 

.000  782  4726 

1279 

1  635  841 

2  092  240  639 

35.763  1095 

10.854  8422 

.000  781  8608 

1280 

1  638  400 

2  097  152  000 

35.777  0876 

10.857  6704 

.000  781  2500 

1281 

1  640  961 

2  102  071  841 

35.791  0603 

10.860  4972 

.000  780  6401 

1282 

1  643  524 

2  106  997  768 

35.805  0276 

10.863  3225 

.000  780  0312 

1283 

1  646  089 

2  111  932  187 

35.818  9894 

10.866  1454 

.000  779  4232 

1284 

1  648  656 

2  116  874  304 

35.832  9457 

10.868  9687 

.000  778  8162 

1285 

1  651  225 

2  121  824  125 

35.846  8966 

10.871  7897 

.000  778  2101 

1286 

1  653  796 

2  126  781  656 

35.860  8421 

10.874  6091 

.000  777  6050 

1287 

1  656  369 

2  131  746  903 

35.874  7822 

10.877  4271 

.000  777  0008 

1288 

1  658  944 

2  136  719  872 

35.888  7169 

10.880  2436 

.000  776  3975 

1289 

1  6G1  521 

2  141  700  569 

35.902  6461 

10.883  0587 

.000  775  7952 

1290 

1  664  100 

2  146  689  000 

35.916  5699 

10.885  8723 

.000  775  1938 

1291 

1  666  681 

2  151  685  171 

35.930  4884 

10.888  6845 

.000  774  5933 

1292 

1  669  264 

2  156  689  088 

35.944  4015 

10.891  4952 

.000  773  9938 

1293 

1  671  849 

2  161  700  757 

35.958  3092 

10.894  3044 

.000  773  3952 

1294 

1  674  436 

2  166  720  184 

35.972  2115 

10.897  1123 

.000  772  7975 

1295 

1  677  025 

2  171  747  375 

35.986  1084 

10.899  9186 

.000  772  2008 

1296 

1  679  616 

2  176  782  336 

36.000  0000 

10.902  7235 

.000  771  6049 

1297 

1  682  209 

2  181  825  073 

36.013  8862 

10.905  5269 

.000  771  0100 

1298 

1  684  804 

2  186  875  592 

36.027  7671 

10.908  3290 

.000  770  4160 

1299 

1  687  401 

2  191  933  899 

36.041  6426 

10.911  1296 

.000  769  8229 

1300 

1690  000 

2  197  000  000 

36.055  5128 

10.913  9287 

.000  769  2308 

776 


Powers  and  Roots. 


Number. 


Squares. 


Cubes. 


I7  Boots. 


f  Roots. 


1  692  601 
1695  204 
1697  809 
1  700  416 
I  703  025 
1  705  636 
1  708  249 
1  710  864 
1  713  481 
1  716  100 
1  718  721 
1  721  344 
1723  969 
1  726  596 
1729  225 
1731856 
1  734  489 
1  737  124 
1  739  761 
1  742  400 
1  745  041 
1747  684 
1  750  329 
1  752  976 
1  755  625 
1  758  276 
1760  929 
|  1763  584 
1  766  241 
1768  900 
1  771  561 
1  774  224 
1  776  889 
1  779  556 
1  782  225 
1  784  896 
1  787  569 
1  790  244 
1792  921 
1795  600 
1  798  281 
1800  964 
1803  649 
1806  336 
1809  025 
1  811  716 
1  814  409 
1  817  104 
1  819  801 
1822  500 
1825  201 
1  827  904 


2  202  073  901 
2  207  155  608 
2  212  245  127 
2  217  342  464 
2  222  447  625 
2  227  560  616 
2  232  681  443 
2  237  810  112 
2  242  946  629 
2  248  091 000 
2  253  243  231 
2  258  403  328 
2  263  571  297 
2  268  747  144 
2  273  930  875 
2  279  122  496 
2  284  322  013 
2  289  529  432 
2  294  744  759 
2299  968  000 
2  305  199  161 
2  310  438  248 
2  315  685  267 
2  320  940  224 
2  326  203  125 
2  331  473  976 
2  336  752  783 
2  342  039  552 
2  347  334  289 
2  352  637  000 
2  357  947  691 
2  363  266  368 
2  368  593  037 
2  373  927  704 
2  379  270  375 
2  384  621  056 
2  389  979  753 
2  395  346  472 
2  400  721  219 
2  406  104  000 
2  411  494  821 
2  416  893  688 
2  422  300  607 
2  427  715  584 
2  433  138  625 
2  438  569  736 
2  444  008  923 
2  449  456  192 
2  454  911  549 
2  460  375  000 
2  465  846  551 
2  471  326  208 


36.069  3776 
36.083  2371 
36.097  0913 
36.110  9402 
36.124  7837 
36.138  6220 
36.152  4550 
36.166  2826 
36.180  1050 
36.193  9221 
36.207  7340 
36.221  5406 
36.235  3419 
36.249  1379 
36.262  6287 
36.276  7143 
36.290  4246 
36.304  2697 
36.318  0396 
36.331  8042 
36.345  5637 
36.359  3179 
36.373  0670 
36.386  8108 
36.400  5494 
36.414  2829 
36.428  0112 
36.441  7343 
36.455  4523 
36.469  1650 
36.482  8727 
36.496  5752 
36.510  2725 
36.523  9647 
36.537  6518 
36.551  3388 
36.565  0106 
36.578  6823 
36.592  3489 
36.606  0104 
36.619  6668 
36.633  3181 
36.646  9144 
36.660  6056 
36.674  2416 
36.687  8726 
36.701  4986 
36.715  1195 
36.728  7353 
36.742  3461 
36.755  9519 
36.769  5526 


10.916  7265 
10.919  5228 
10.922  3177 
10.925  1111 
10.927  9031 
10.930  6937 
10.933  4829 
10.936  2706 
10.939  0569 
10.941  8418 
10.944  6253 
10.947  5074 
10.950  1880 
10.952  9673 
10.955  7451 
10.958  5215 
10.961  2965 
10.964  0701 
10.966  8423 
10.969  6131 
10.972  3825 
10.975  1505 
10.977  9171 
10.980  6823 
10.983  4462 
10.986  2086 
10.988  9696 
10.991  7293 
10.994  4876 
10.997  2445 
11.000  0000 
11.002  7541 
11.005  5069 
11.008  2583 
11.011  0082 
11.013  7569 
11.016  5041 
11.019  2500 
11.021  9945 
11.024  7377 
11.027  4795 
11.030  2199 
11.032  9590 
11.035  6967 
11.038  4330 
11.041 1680 
11.043  9017 
11.046  6339 
11.049  3649 
11.052  0945 
11.054  8227 
11.057  5497 


Powers 

and  Roots 

777 

Number. 

Squares. 

Cubes. 

V  Roots. 

f  Roots. 

Reciprocals. 

1353 

1830  609 

2  476  813  977 

36.783  1483 

11.060  2752 

.000  739  0983 

1354 

1  833  316 

2  482  309  864 

36.796  7390 

11.062  9994 

.000  738  5524 

1355 

1836  025 

2  487  813  875 

36.810  3246 

11.065  7222 

.000  738  0074 

1356 

1838  736 

2  493  326  016 

36.823  9053 

11.068  4437 

.000  737  4631 

1357 

1  841  449 

2  498  846  293 

36.837  4809 

11.071 1639 

.000  736  9197 

1358 

1  844  164 

2  504  374  712 

36.851  0515 

11.073  8828 

.000  736  3770 

1359 

1  846  881 

2  509  911  279 

36.864  6172 

11.076  6003 

.000  735  8352 

1360 

1849  600 

2  515  456  000 

36.878  1778 

11.079  3165 

.000  735  2941 

1361 

1  852  321 

2  521  008  881 

36.891  7335 

11.082  0314 

.000  734  7539 

1362 

1  855  044 

2  526  569  928 

36.905  2842 

11.084  7449 

.000  734  2144 

1363 

1  857  769 

2  532  139  147 

36.918  8299 

11.087  4571 

.000  733  6757 

1364 

1  860  496 

2  537  716  544 

36.932  3706 

11.090  1679 

.000  733  1378 

1365 

1  863  225 

2  543  302  125 

36.945  9064 

11.092  8775 

.000  732  6007 

1366 

1  865  956 

2  548  895  896 

36.959  4372 

11.095  5857 

.000  732  0644 

1367 

1  868  689 

2  554  497  863 

36.972  9631 

11.098  2926 

.000  731  5289 

1368 

1  871  424 

2  560  108  032 

36.986  4840 

11.100  9982 

.000  730  9942 

1369 

1  874  161 

2  565  726  409 

37.000  0000 

11.103  7025 

.000  730  4602 

1370 

1876  900 

2  571  353  000 

37.013  5110 

11.106  4054 

.000  729  9270 

1371 

1  879  641 

2  576  987  811 

37.027  0172 

11.109  1070 

.000  729  3946 

1372 

1  882  384 

2  582  630  848 

37.040  5184 

11.111  8073 

.000  728  8630 

1373 

1  885  129 

2  588  282  117 

37.054  0146 

11.114  5064 

.000  728  3321 

1374 

1  887  876 

2  593  941  624 

37.067  5060 

11.117  2041 

.000  727  8020 

1375 

1  890  625 

2  599  609  375 

37.089  9924 

11.119  9004 

.000  727  2727 

1376 

1  893  376 

2  605  285  376 

37.094  4740 

11.122  5955 

.000  726  7442 

1377 

1  896  129 

2  610  969  633 

37.107  9506 

11.125  2893 

.000  726  2164 

1378 

1  898  884 

2  616  662  152 

37.121  4224 

11.127  9817 

.000  725  6894 

1379 

1  901  641 

2  622  362  939 

37.134  8893 

11.130  6729 

.000  725  1632 

1380 

1904  400 

2  628  072  000 

37.148  3512 

11.133  3628 

.000  724  6377 

1381 

1  907  161 

2  633  789  341 

37.161  8084 

11.136  0514 

.000  724  1130 

1382 

1  909  924 

2  639  514  968 

37.175  2606 

11.138  7386 

.000  723  5890 

1383 

1  912  689 

2  645  248  887 

37.188  7079 

11.141  4246 

.000  723  0658 

1384 

1  915  456 

2  650  991 104 

37.202  1505 

11.144  1093 

.000  722  5434 

1385 

1  918  225 

2  656  741  625 

37.215  5881 

11.146  7926 

.000  722  0217 

1386 

1  920  996 

2  662  500  456 

37.229  0209 

11.149  4747 

.000  721  5007 

1387 

1  923  769 

2  668  267  603 

37.242  4489 

11.152 1555 

.000  720  9805 

1388 

1  926  544 

2  674  043  072 

37.255  8720 

11.154  8350 

.000  720  4611 

1389 

1  929  321 

2  679  826  869 

37.269  2903 

11.157  5133 

.000  719  9424 

1390 

1  932  100 

2  685  619  000 

37.282  7037 

11.160  1903 

.000  719  4245 

1391 

1  934  881 

2  691  419  471 

37.296  1124 

11.162  8659 

.000  718  9073 

1392 

1  937  664 

2  697  228  288 

37.309  5162 

11.165  5403 

.000  718  3908 

1393 

1  940  449 

2  703  045  457 

37.322  9152 

11.168  2134 

.000  717  8751 

1394 

1  943  236 

2  708  870  984 

37.336  3094 

11.170  8852 

.000  717  3601 

1395 

1  946  025 

2  714  704  875 

37.349  6988 

11.173  5558 

.000  716  8459 

1396 

1  948  816 

2  720  547  136 

37.363  0834 

11.176  2250 

.000  716  3324 

1397 

1  951  609 

2  726  397  773 

37.376  4632 

11.178  8930 

.000  715  8196 

1398 

1  954  404 

2  732  256  792 

37.389  8382 

11.181  5598 

.000  715  3076 

1399 

1  957  201 

2  738  124  199 

37.403  2084 

11.184  2252 

.000  714  7963 

1400 

1960  000 

2  744  000  000 

37.416  5738 

11.186  8894 

.000  714  2857 

1401 

1  962  801 

2  749  884  201 

37.429  9345 

11.189  5523 

.000  713  7759 

1402 

1  965  604 

2  755  776  808 

37.443  2904 

11.192  2139 

.000  713  2668 

1403 

1  968  409 

2  761  677  827 

37.456  6416 

11.194  8743 

.000  712  7584 

1404 

1  971  216 

2  767  587  264 

37.469  9880 

11.197  5334 

.000  712  2507 

778 

Powers 

and  Roots 

Number. 

Squares. 

Cubes. 

V' Roots. 

f  Roots. 

Reciprocals. 

1405 

1974  025 

2  773  505  123 

37.483  3296 

11.200  1913 

.000  711  7438 

1406 

1  976  836 

2  779  431  416 

37.496  6665 

11.202  8479 

.000  711  2376 

1407 

1  979  649 

2  785  366  143 

37.509  9987 

11.205  5032 

.000  710  7321 

1408 

1  982  464 

2  791  309  312 

37.523  3261 

11.208  1573 

.000  710  2273 

1409 

1985  281 

2  797  260  929 

37.536  6487 

11.210  8101 

.000  709  7232 

1410 

1988100 

2803  221000 

37.549  9667 

11.213  4617 

.000  709  2199 

1411 

1990  921 

2  809  189  531 

37.563  2799 

11.216  1120 

.000  708  7172 

1412 

1  993  744 

2  815  166  528 

37.576  5885 

11.218  7611 

.000  708  2153 

1413 

1996  569 

2  821 151  997 

37.589  8922 

11.221  40S9 

.000  707  7141 

1414 

1999  3% 

2  827  145  944 

37.603  1913 

11.224  0054 

.000  707  2136 

1415 

2002  225 

2  833  148  375 

37.616  4857 

11.226  7007 

.000  706  7138 

1416 

2  005  056 

2  839  159  2% 

37.629  7754 

11.229  3448 

.000  706  2147 

1417 

2  007  889 

2  845  178  713 

37.643  0604 

11.231  9876 

.000  705  7163 

1418 

2  010  724 

2  851  206  632 

37.656  3407 

11.234  6292 

.000  705  2186 

1419 

2  013  561 

2  857  243  059 

37.669  6164 

11.237  2696 

.000  704  7216 

1420 

2  016  400 

2863  288  000 

37.682  8874 

11.239  9087 

.000  704  2254 

1421 

2  019  241 

2  869  341  461 

37.696  1536 

11.242  5465 

.000  703  7298 

1422 

2  022  084 

2  875  403  448 

37.709  4153 

11.245  1831 

.000  703  2349 

1423 

2  024  929 

2  881  473  967 

37.722  6722 

11.247  8185 

.000  702  7407 

1424 

2  027  776 

2  887  553  024 

37.735  9245 

11.250  4527 

.000  702  2472 

1425 

2  030  625 

2  893  640  625 

37.749  1722 

11.253  0856 

.000  701  7544 

1426 

2  033  476 

2  899  736  776 

37.762  4152 

11.255  7173 

.000  701  2623 

1427 

2  036  329 

2  905  841  483 

37.775  6.535 

11.258  3478 

.000  700  7708 

1428 

2  039  184 

2  911954  752 

37.788  8873 

11.260  9770 

.000  700  2801 

1429 

2  042  041 

2  918  076  589 

37.802  1163 

11.263  6050 

.000  699  7901 

1430 

2  044  900 

2  924  207  000 

37.815  3408 

11.266  2318 

.000  699  3007 

1431 

2  047  761 

2  930  345  991 

37.828  5606 

11.268  8573 

.000  698  8120 

1432 

2  050  624 

2  936  493  568 

37.841  7759 

11.271  4816 

.000  698  3240 

1433 

2  053  489 

2  942  649  737 

37.854  9864 

11.274  1047 

.000  697  8367 

1434 

2  056  356 

2  948  814  504 

37.868  1924 

11.276  7266 

.000  697  3501 

1435 

2  059  225 

2  954  987  875 

37.881  3938 

11.279  3472 

.000  696  8641 

1436 

2  062  096 

2  961  169  856 

37.894  5906 

11.281  9666 

.000  696  3788 

1437 

2  064  969 

2  967  360  453 

37.907  7828 

11.284  5849 

.000  695  8942 

1438 

2  067  844 

2  973  559  672 

37.920  9704 

11.287  2019 

.000  695  4103 

1439 

2  070  721 

2  979  767  519 

37.934  1535 

11.289  8177 

.000  694  9270 

1440 

2  073  600 

2  985  984  000 

37.947  3319 

11.292  4323 

.000  694  4444 

1441 

2  076  481 

2  992  209  121 

37.960  5058 

11.295  0457 

.000  693  9625 

1442 

2  079  364 

2  998  442  888 

37.973  6751 

11.297  6579 

.000  693  4813 

1443 

2  082  249 

3  004  685  307 

37.986  8398 

11.300  2688 

.000  693  0007 

1444 

2  085136 

3  010  936  384 

38.000  0000 

11.302  8786 

.000  692  5208 

1445 

2  088  025 

3  017  196  125 

38.013  1556 

11.305  4871 

.000  692  0415 

1446" 

2  090  916 

3  023  464  536 

38.026  3067 

11.308  0945 

.000  691  5629 

1447 

2  093  809 

3  029  741  623 

38.039  4532 

11.310  7006 

.000  691  0850 

1448 

2  096  704 

3  036  027  392 

38.052  5952 

11.313  3056 

.000  690  6078 

1449 

2  099  601 

3  042  321  849 

38.065  7326 

11.315  9094 

.000  090  1312 

1450 

2102  500 

3  048  625  000 

38.078  8655 

11.318  5119 

.000  689  6552 

1451 

2  105  401 

3  054  936  851 

38.091  9939 

11.321 1132 

.000  689  1799 

1452 

2108  304 

3  061  257  408 

38.105  1178 

11.323  7134 

.000  688  7052 

1453 

2111209 

3  067  586  777 

38.118  2371 

11.326  3124 

.000  688  2312 

1454 

2  114  116 

3  073  924  664 

38.131  3519 

11.328  9102 

.000  687  7579 

1455 

2117  025 

3  080  271  375 

38.144  4622 

11.331  5067 

.000  687  2852 

1456 

2  119  936 

3  086  626  816 

38.157  5681 

11.334  1022 

.000  686  8132 

Powers  and  Roots. 


779 


Squares. 


Cubes. 


V  Boots. 


f  Roots. 


Reciprocals. 


2  122  849 
2  125  764 
2128  681 
2  131  600 
2  134  521 
2  137  444 
2  140  369 
2  143  296 
2  146  225 
2  149  156 
2  152  089 
2  155  024 
2  157  961 
2160  900 
2  163  841 
2  166  784 
2  169  729 
2  172  676 
2  175  625 
2178  576 
2  181  529 
2  184  484 
2  187  441 
2190  400 
2  193  361 
2  196  324 
2  199  289 
2  202  256 
2  205  225 
2  208  196 
2  211  169 
2  214  144 
2  217  121 
2  220100 
2  223  081 
2  226  064 
2  229  049 
2  232  036 
2  235  025 
2  238  016 
2  241009 
2  244  004 
2  247  001 
2  250  000 
2  253  001 
2  256  004 
2  259  009 
2  262  016 
2  265  025 
2  268  036 
2  271  049 
2  274  064 


3  092  990  993 
3  099  363  912 
3  105  745  579 
3  112  136  000 
3  118  535  181 
3  124  943  128 
3  131  359  847 
3  137  785  344 
3  144  219  625 
3  150  662  6% 
3  157  114  563 
3  163  575  232 
3  170  044  709 
3  176  523  000 
3  183  010  111 
3  189  506  048 
3  196  010  817 
3  202  524  424 
3  209  046  875 
3  215  578  176 
3  222  118  333 
3  228  667  352 
3  235  225  239 
3  241  792  000 
3  248  367  641 
3  254  952  168 
3  261  545  587 
3  268  147  904 
3  274  759  125 
3  281  379  256 
3  288  008  303 
3  294  646  272 
3  301  293  169 
3  307  949  000 
3  314  613  771 
3  321  287  488 
3  327  970  157 
3  334  661  784 
3  341  362  375 
3  348  071  936 
3  354  790  473 
3  361  517  992 
3  368  254  499 
3  375  000  000 
3  381  754  501 
3  388  518  008 
3  395  290  527 
3  402  072  064 
3  408  862  625 
3  415  662  216 
3  422  470  843 
3  429  288  512 


38.170  6693 
38.183  7662 
38.196  8585 
38.209  9463 
38.223  0297 
38.236  1085 
38.249  1829 
38.262  2529 
38.275  3184 
38.288  3794 
38.301  4360 
38.314  4881 
38.327  5358 
38.340  5790 
38.353  6178 
38.366  6522 
38.379  6821 
38.392  7076 
38.405  7287 
38.418  7454 
38.431  7577 
38.444  7656 
38.457  7691 
38.470  7681 
38.483  7627 
38.496  7530 
38.509  7390 
38.522  7206 
38.535  6977 
38.548  6705 
38.561  6389 
38.574  6030 
38.587  5627 
38.600  5181 
38.613  4691 
38.626  4158 
38.639  3582 
38.652  2962 
38.665  2299 
38.678  1593 
38.691  0843 
38.704  0050 
38.716  9214 
38.729  8335 
38.742  7412 
38.755  6447 
38.768  5439 
38.781  4389 
38.794  3294 
38.807  2158 
38.820  0978 
38.832  9757 


11.336  6964 
11.339  2894 
11.341  8813 
11.344  4719 
11.347  0614 
11.349  6497 
11.352  2368 
11.354  8227 
11.357  4075 
11.359  9911 
11.362  5735 
11.365  1547 
11.367  7347 
11.370  3136 
11.372  8914 
11.375  4679 
11.378  0433 
11.380  6175 
11.383  1906 
11.385  7625 
11.388  3332 
11.390  9028 
11.393  4712 
11.396  0384 
11.398  6045 
11.401 1695 
11.403  7332 
11.406  2959 
11.408  8574 
11.411  4177 
11.413  9769 
11.416  5349 

11.419  0918 

11.420  6476 
11.424  2022 
11.426  7556 
11.429  3079 
11.431  8591 
11.434  4092 
11.436  9581 
11.439  5059 
11.442  0525 
11.444  5980 
11.447  1424 
11.449  6857 
11.452  2278 
11.454  7688 
11.457  3087 
11.459  8476 
11.462  3850 
11.464  9215 
11.467  4568 


.000  686  3412 
.000  685  8711 
.000  685  4010 
.000  684  9315 
.000  684  4627 
.000  683  9945 
.000  683  5270 
.000  683  0601 
.000  682  5939 
.000  682 1282 
.000  681  6633 
.000  681 1989 
.000  680  7352 
.000  680  2721 
.000  679  8097 
.000  679  3478 
.000  678  8866 
.000  678  4261 
.000  677  9661 
.000  677  5068 
.000  677  0481 
.000  676  5900 
.000  676  1325 
.000  675  6757 
.000  675  2194 
.000  674  7638 
.000  674  3088 
.000  673  8544 
.000  673  4007 
.000  672  9474 
.000  672  4950 
.000  672  0430 
.000  671  5917 
.000  671 1409 
.000  670  6908 
.000  670  2413 
.000  669  7924 
.000  669  3440 
.000  668  8963 
.000  668  4492 
.000  668  0027 
.000  667  5567 
.000  667  1114 
.000  666  6667 
.000  666  2225 
.000  665  7790 
.000  655  3360 
.000  664  8936 
.000  664  4518 
.000  664  0106 
.000  663  5700 
.000  663  1300 


780 

Powers 

and  Roots 

Number. 

Squarei. 

Cubes. 

^Eootfc 

f  Roots. 

Reciprocals. 

1509 

2  277  081 

3  436  115  229 

38.845  8491 

11.469  9911 

.000  062  6905 

1510 

2  280100 

3  442  951  000 

38.858  7184 

11.47 

.000  662  2517 

1511 

2  283  121 

3  449  795  831 

38.871  5834 

11.175  0562 

.000  661  8134 

1512 

2  286144 

3  456  649  728 

38.884  4442 

11.477  5871 

.000  661  :?7.77 

1513 

2  289  169 

3  463  512  697 

38.897  3006 

11.480  1169 

.000  660  9385 

1514 

2  292196 

3  470  384  744 

38.910 1529 

11.482  6455 

.000  660  5020 

1515 

2  295  225 

3  477  265  875 

38.923  0009 

11.485  1731 

.000  660  0660 

1516 

2  298  256 

3  484  156  096 

38.935  8447 

11.487  6995 

.000  659  6306 

1517 

2  301  289 

3  491  055  413 

38.948  6841 

11.490  2249 

.000  659  1958 

1518 

2  304  324 

3  597  963  832 

38.961  5194 

11.492  7491 

.000  658  7615 

1519 

2  307  361 

3  504  881  359 

38.974  3505 

11.495  2722 

.000  658  3278 

1520 

2  310  400 

3  511  808  000 

38.987  1774 

11.497  7942 

.000  657  8947 

1521 

2  313  441 

3  518  743  761 

39.000  0000 

11.500  3151 

.000  657  4622 

1522 

2  316  484 

3  525  688  648 

39.012  8184 

11.502  8348 

.000  657  0302 

1523 

2  319  529 

3  532  642  667 

39.025  6326 

11.505  3535 

.000  656  5988 

1524 

2  322  576 

3  539  605  824 

39.038  4426 

11.507  8711 

.000  656  1680 

1525 

2  325  625 

3  546  578  125 

39.051  2483 

11.510  3876 

.000  655  7377 

1526 

2  328  676 

3  553  559  576 

39.064  0499 

11.512  9030 

.000  655  3080 

1527 

2  331729 

3  560  558  183 

39.076  8473 

11.515  4173 

.000  654  8788 

1528 

2  334  784 

3  567  549  552 

39.089  6406 

11.517  9305 

.000  654  4503 

1529 

2  337  841 

3  574  558  889 

39.102  4296 

11.520  4425 

.000  654  0222 

1530 

2  340  900 

3  581  577  000 

39.115  2144 

11.522  9535 

.000  653  5948 

1531 

2  343  961 

3  588  604  291 

39.127  9951 

11.525  4634 

.000  653  1679 

1532 

2  347  024 

3  595  640  768 

39.140  7716 

11.527  9722 

.000  652  7415 

1533 

2  350  089 

3  602  686  437 

39.153  5439 

11.530  4799 

.000  652  3157 

1534 

2  353156 

3  609  741  304 

39.166  3120 

11.532  9865 

.000  651  8905 

1535 

2356  225 

3  616  805  375 

39.179  0760 

11.535  4920 

.000  651  4658 

1536 

2  359  296 

3  623  878  656 

39.191  8359 

11.537  9965 

.000  651  0417 

1537 

2  362  369 

3  630  961 153 

39.204  5915 

11.540  4998 

.000  650  6181 

1538 

2  365  444 

3  638  052  872 

39.217  3431 

11.543  0021 

.000  6.50  1951 

1539 

2  368  521 

3  645  153  819 

39.230  0905 

11.545  5033 

.000  649  7726 

1540 

2  371600 

3  652  264  000 

39.242  8337 

11.548  0034 

.000  649  3506 

1541 

2  374  681 

3  657  983  421 

39.255  5728 

11.550  5025 

.000  648  9293 

1542 

2  377  764 

3  666  512  088 

39.268  3078 

11.553  0004 

.000  648  5084 

1543 

2  380  849 

3  673  650  007 

39.281  0387 

11.555  4972 

.000  648  0881 

1544 

2  383  936 

3  680  797  184 

39.293  7654 

11.557  9931 

.000  647  6684 

1545 

2  387  025 

3  687  953  625 

39.306  4880 

11.560  4878 

.000  647  2492 

1546 

2  390  116 

3  695  119  336 

39.319  2065 

11.562  9815 

.000  646  8305 

1547 

2  393  209 

3  702  294  323 

39.331  9208 

11.565  4740 

.000  646  4124 

1548 

2  398  304 

3  709  478  592 

39.344  6311 

11.567  9655 

.000  645  9948 

1549 

2  399  401 

3  716  672  149 

39.357  3373 

11.570  4559 

.000  645  5778 

1550 

2  402  500 

3  723  875  000 

39.370  0394 

11.572  9453 

.000  645  1613 

1551 

2  405  601 

3  731  087  151 

39.382  7373 

11.575  4336 

.000  644  7453 

1552 

2  408  704 

3  738  308  608 

39.395  4312 

11.577  9268 

.000  644  3299 

1553 

2  411  809 

3  745  539  377 

39.408  1210 

11.580  4069 

.000  643  9150 

1554 

2  414  916 

3  752  779  464 

39.420  8067 

11.582  8919 

.000  643  5006 

1555 

2  418  025 

3  760  028  875 

39.433  4883 

11.585  3759 

.000  643  0868 

1556 

2  421  136 

3  767  287  616 

39.446  1658 

11.587  8588 

.000  642  6735 

1557 

2  424  249 

3  774  555  693 

39.458  8393 

11.590  3407 

.000  642  2608 

1558 

2  427  364 

3  781  833  112 

39.471  5087 

11.592  8215 

.000  641  8485 

1559 

2  430  481 

3  789  119  879 

39.484  1740 

11.595  3013 

.000  641  4368 

1560 

2  433  600 

3  796  416  000 

39.496  8353 

11.597  7799 

.000  641  0256 

Powers 

and  Roots 

781 

Number. 

Squares. 

Cubes. 

VRoots. 

f  Roots. 

Reciprocals. 

1561 

2  436  721 

3  803  721  481 

39.509  4925 

11.600  2576 

.000  640  6150 

1562 

2  439  844 

3  811  036  328 

39.522  1457 

11.602  7342 

.000  640  2049 

1563 

2  442  969 

3  818  360  547 

39.534  7948 

11.605  2097 

.000  639  7953 

1564 

2  446  096 

3  825  641  444 

39.547  4399 

11.607  6841 

.000  639  3862 

1565 

2  449  225 

3  833  037  125 

39.560  0809 

11.610  1575 

.000  638  9776 

1566 

2  452  356 

3  840  389  496 

39.572  7179 

11.612  6299 

.000  638  56% 

1567 

2  455  489 

3  847  751  263 

39.585  3508 

11.615  1012 

.000  638  1621 

1568 

2  458  624 

3  855123  432 

39.597  9797 

11.617  5715 

.000  637  7551 

1569 

2  461  761 

3  862  503  009 

39.610  6046 

11.620  0407 

.000  637  3486 

1570 

2  464  900 

3  869  883  000 

39.623  2255 

11.622  5088 

.000  636  9427 

1571 

2  468  041 

3  877  292  411 

39.635  8424 

11.624  9759 

.000  636  5372 

1572 

2  471 184 

3  884  701  248 

39.648  4552 

11.627  4420 

.000  636  1323 

1573 

2  474  329 

3  892  119  157 

39.661  0640 

11.629  9070 

.000  635  7279 

1574 

2  477  476 

3  899  547  224 

39.673  6688 

11.632  3710 

.000  635  3240 

1575 

2  480  625 

3  906  984  375 

39.686  2696 

11.634  8339 

.000  634  92% 

s  1576 

2  483  776 

3  914  430  976 

39.698  8665 

11.637  2957 

.000  634  5178 

1577 

2  486  929 

3  921  887  033 

39.711  4593 

11.639  7566 

.000  634  1154 

1578 

2  490  084 

3  929  352  552 

39.724  0481 

11.642  2164 

.000  633  7136 

1579 

2  493  241 

3  936  827  539 

39.736  6329 

11.644  6751 

.000  633  3122 

1580 

2  496  400 

3  944  312  000 

39.749  2138 

11.647  1329 

.000  632  9114 

1581 

2  499  561 

3  951  805  941 

39.761  7907 

11.649  5895 

.000  632  5111 

1582 

2  502  724 

3  959  309  368 

39.774  3636 

11.652  0452 

.000  632  1113 

1583 

2  505  889 

3  966  822  287 

39.786  9325 

11.654  4998 

.000  631  7119 

1584 

2  509  056 

3  974  344  704 

39.799  4976 

11.656  9534 

.000  631  3131 

1585 

2  512  225 

3  981  876  625 

39.812  0585 

11.659  4059 

.000  630  9148 

1586 

2  515  396 

3  989  418  056 

39.824  6155 

11.661 8574 

.000  630  5170 

1587 

2  518  569 

3  996  969  003 

39.837  1686 

11.664  3079 

.000  630  1197 

1588 

2  521  744 

4  004  529  472 

39.849  7177 

11.666  7574 

.000  629  7229 

1589 

2  524  921 

4  012  099  469 

39.862  2628 

11.669  2058 

.000  629  3266 

1590 

2  528  100 

4  014  679  000 

39.874  8040 

11.671  6532 

.000  628  9308 

1591 

2  531  281 

4  027  268  071 

39.887  3413 

11.674  0996 

.000  628  5355 

1592 

2  534  464 

4  034  866  688 

39.899  8747 

11.676  5449 

.000  628  1407 

1593 

2  537  649 

4  042  474  857 

39.912  4041 

11.678  9892 

.000  627  7464 

1594 

2  540  836 

4  050  092  584 

39.924  9295 

11.681  4325 

.000  627  3526 

1595 

2  544  025 

4  057  719  875 

39.937  4511 

11.683  8748 

.000  626  9592 

15% 

2  547  216 

4  065  356  736 

39.949  9687 

11.686  3161 

.000  626  5664 

1597 

2  550  409 

4  073  003  173 

39.962  4824 

11.688  7563 

.000  626  1741 

1598 

2  553  604 

4  080  659  192 

39.974  9922 

11.691 1955 

.000  625  7822 

1599 

2  556  801 

4  088  324  799 

39.987  4980 

11.693  6337 

.000  625  3%9 

1600 

2  560  000 

4  096  000  000 

40.000  0000 

11.6%  0709 

.000  625  0000 

The  use  of  the  table  of  powers  and  roots  may  be  extended  far  beyond 
Its  apparent  limits  by  the  observance  of  the  following  rules : 

Remembering  that  the  extraction  of  the  square  root  of  a  number  is 
simply  the  separating  it  into  two  equal  factors,  we  have:  to  extract  the 
square  root  of  any  whole  number  and  decimal,  when  the  whole  number  is 
within  the  limits  of  the  table,  simply  find  the  square  root  of  the  whole 
number  in  the  table  and  divide  the  given  number  and  decimal  by  this 
root.  The  quotient  will  be  another  factor,  very  nearly  equal  to  the  required 
root.  Add  the  divisor  and  the  quotient  together  and  divide  by  two,  and 
the  result  will  be  the  true  root  to  a  very  close  degree  of  approximation. 
These  tables,  together  with  those  of  Metric  System  and  Logarithms  have 
been  taken  by  permission  from  Suplee's  "  Reference  Book." 


7v_> 


Logarithms. 


LOGARITHMS. 

There  are  four  fundamental  rules  for  operations  with  powers : 

am  t  an  =  am  +  ". 

That  is,  the  product  of  any  two  powers  of  a  number  is  equal  to  the  num- 
ber raised  to  a  power  whose  exponent  is  the  mm  of  the  exponents  of  the 
two  factors. 

o"» 

=  a»  -  *. 

a» 

Or,  the  quotient  of  two  powers  is  equal  to  the  number  raised  to  a  power 
whose  exponent  is  the  difference  of  the  exponents  of  divisor  and  dividend. 

(on)«  =  aWB. 

Or,  any  power  may  be  raised  to  a  higher  power  by  multiplying  the  two 
exponents. 

V  am  =a». 

Or,  any  root  of  any  power  may  be  extracted  by  dividing  the  exponent  by 
the  index  of  the  root. 

If  we  take  any  number,  such  as  2,  and  use  it  as  the  base  of  a  geometri- 
cal series,  we  will  see  that  the  exponents  form  an  arithmetical  series. 
Thus,  the  exponent  of  1  =  0,  of  2  =  1,  of  4  =  2,  of  8  =  3,  etc. ;  or,  proceed- 
ing, we  may  arrange  the  following  little  table : 


Powers. 

Exponents. 

Powers. 

Exponents. 

Powers. 

Exponents. 

1 

0 

1024 

10 

1048576 

20 

2 

1 

2048 

11 

2097152 

21 

4 

2 

4096 

12 

4194304 

22 

8 

3 

8192 

13 

8388608 

23 

16 

4 

16384 

14 

16777216 

24 

32 

5 

32768 

15 

64 

6 

65536 

16 

128 

7 

131072 

17 

256 

8 

262144 

18 

512 

9 

524288 

19 

Suppose  now  we  wish  to  multiply  128  by  512,  we  see  that  128  =  27  and 
512  =  29;  hence,  128  x  512  =  2*'-»  =  216,  and  in  the  table,  opposite  the 
exponent  16,  we  find  the  power  65536,  which  is  the  product  of  the  two 
factors,  obtained  by  the  simple  addition  of  the  exponents. 


Again, 


128       T 


To  raise  a  number  to  a  power,  such  as  16  to  the  fifth  power,  we  have 
16  =  2*  and  (2*)&  =  Z»  =  1048576. 

Again,  the  seventh  root  of  2097152  is  formed  as  follows : 

2097152  -  22i  and  f  ~&  -  2V  =  23  =  8. 

In  the  small  table  of  the  powers  of  2  given  above  there  are  many  gaps, 
because  only  those  powers  which  have  whole  exponents  are  given.  For  all 
the  numbers  between  16  and  32,  for  example,  the  exponents  will  be  deci- 
mals, and  will  be  greater  than  4  and  less  than  5,  etc.  In  practice,  the  base 
used  is  not  2,  but  10,  and  all  the  intermediate  exponents  have  been  com- 
puted to  many  decimals,  these  forming  a  table  of  logarithms. 


Logarithms.  783 


Table  of  Logarithms  of  Numbers. 

Pages  82  to  104  give  the  mantissas,  or  decimal  portions  of  the  logarithms, 
of  all  whole  numbers  from  1  to  10009.  The  characteristics,  or  whole  num- 
bers, which,  with  these  decimals,  form  the  complete  logarithms,  are  found 
as  follows : 

The  logarithm  of  1  =  0,  of  10  =  1,  of  100  =  2,  of  1000  =  3,  etc. ;  hence, 
the  logarithm  of  any  number  between  100  and  1000  must  lie  between  2  and 
3,  and  be  greater  than  2  and  less  than  3,  and  so  for  any  number.  There- 
fore we  have  the  rule  that  the  whole  portion  of  a  logarithm  of  any  num- 
ber is  one  less  than  there  are  figures  in  the  number.  The  decimal  portion 
for  any  number  below  10009  is  taken  directly  from  the  table.    Thus, 

log.  365  =  2.56229, 

the  decimal  portion,  56229,  being  found  directly  opposite  365  in  the  table, 
and  the  whole  portion  being  2,  or  1  less  than  the  number  of  places  in  365. 
In  like  manner  we  have 

log.  36.5    =1.56229, 

log.    3.65  =  0.56229. 

The  mantissa,  or  decimal  portion,  is  always  positive,  but  the  character- 
istic is  negative  when  the  number  is  less  than  unity.    Thus, 

log.  0.365  =1.56229, 
log.  0.0365  ="2.56229, 
log.  0.00365=5.56229, 

the  minus  being  placed  over  the  characteristic  to  show  that  it  applies  to 
that  portion  only,  and  not  to  the  mantissa. 

If  the  given  number  has  more  than  three  places,  the  mantissa  is  found 
in  the  body  of  the  table.  Thus,  the  logarithm  of  1873  =  3.27254,  the  figures 
0.27  being  found  opposite  187,  and  the  254  on  the  same  horizontal  line 
under  3. 

If  the  last  three  figures  of  the  mantissa  are  preceded  by  an  asterisk,  the 
first  two  figures  are  to  be  taken  from  the  next  line  below,  in  the  first 
column.    Thus, 

log.  3897  =  3.59073, 

in  which,  opposite  389,  we  find  58,  and  then,  passing  on  under  7,  we  find 
*073,  the  asterisk  indicating  that  we  are  to  go  one  line  below,  taking  out 
59,  not  58,  for  the  first  two  figures  of  the  mantissa,  giving  us  0.59073,  as 
above. 

The  table,  as  will  be  seen,  enables  the  logarithm  of  any  number  of  four 
places  to  be  taken  out  at  once.  If  the  number  of  which  the  logarithm  is 
required  has  more  than  four  places,  the  logarithm  can  be  found  from  the 
table,  as  follows : 

In  the  column  at  the  extreme  right  of  each  page,  under  the  heading 
P.  P.  (Proportional  Parts),  will  be  found  in  the  black  figures  the  differences 
between  any  logarithm  and  the  next  succeeding  logarithm  for  the  adjoin- 
ing portions  of  the  table.  The  smaller  figures  in  the  same  column  form 
little  multiplication  tables,  in  which  these  differences  are  multiplied  by 
0.1,  0.2,  0.3,  etc. 

The  use  of  these  proportional  parts  and  their  decimal  parts  is  best 
shown  by  actual  example.  Suppose  it  is  desired  to  find  the  logarithm  of 
18702.  Opposite  187  and  under  0  in  the  table  we  find  the  mantissa,  0.27184. 
The  proportional  part,  or  difference  at  this  point  between  one  logarithm 
and  the  next,  is  23,  or,  in  other  words,  there  is  a  difference  of  23  between 
the  last  two  figures  of  the  logarithm  of  1870  ard  1871.  For  0.1  difference 
in  the  number,  the  difference  in  the  logarithms  would  be  2.3 ;  for  0.2,  it 
would  be  4.6,  etc.,  as  shown  in  the  small  table  under  23  in  the  column 
P.  P.  For  2  points  additional,  therefore,  we  simply  add  4.6  to  the  loga- 
rithm of  1870,  and  we  have  the  logarithm  of  18702.    Thus, 

log.  1870    =0.27184 
p.  p.  for  2  =  4.6 

log.  18702  =  4.271886,  or 
4.27189 


784  Logarithms. 


Again,  let  it  be  required  to  find  the  logarithm  of  36.797. 

log.  35.79   =  1.65376      p.  p.  =  12 
p.  p.  for  7  ■•  8.4 

log.  35.797  =  1.553844 

If  the  given  number  has  six  or  more  figures  the  method  is  the  same, 
except  that  the  proportional  part  is  reduced  one-tenth  for  each  additional 
figure.    Thus,  the  logarithm  of  3725.96  is  found  as  follows : 

log.  3725      =  3.57113       p.  p.  =  11 
p.  p.  for  9    =  9.9 

p.  p.  for  6    = 0.66 

log.  3725.96  =  3.5712356,  or  3.57124 

The  operation  of  finding  the  number  corresponding  to  a  given  loga- 
rithm is  the  reverse  of  the  preceding.  Thus,  the  number  corresponding  to 
the  logarithm  2.73924  is  found  as  follows : 

In  the  table  the  next  smaller  logarithm  is 

73918,  and  its  number  =  584500 

The  given  log.  =  73924 
and  the  difference  =6 
The  nearest  difference  in  the  table  =  5.6  =  corresponding  to  7 

Subtracting      0.4      corresponding  to  5 

Hence,  the  number  is     584575 
Since  the  characteristic  =  2,  there  must  be  one  more  place 
before  the  decimal  point ;  hence, 

log.  2.73924  =  num.     584.575 


Logarithms  op  Numbers. 


785 


Num.  100  to  139.   Log.  000  to  145. 


P.  P. 


00  000  043  087  130  173 
432  475  518  561  604 
860  903  945  988  *030 

01  284  326  368  410  452 
703  745  787  828  870 

02  119  160  202  243  284 

531  572  612  653  694 
938  979  *019  *060  *100 

03  342  383  423  463  503 

743  782  822  862  902 

04  139  179  218  258  297 

532  571  610  650  689 
922  961  999  *038  *077 

05  308  346  385  423  461 

690  729  767  805  843 

06  070  108  145  183  221 
446  483  521  558  595 
819  856  893  930  967 

07  188  225  262  298  335 
555  591  628  664  700 

918  954  990  *027  *063 

08  279  314  350  386  422 
636  672  707  743  778 
991  *026  *061  *096  *132 

09  342  377  412  447  482 

691  726  760  795  830 

10  037  072  106  140  175 
380  415  449  483  517 
721  755  789  823  857 

11  059  093  126  160  193 

394  428  461  494  528 

727  760  793  826  860 

12  057  090  123  166  189 
385  418  450  483  516 
710  743  775  808  840 

13  033  066  098  130  162 
354  386  418  450  481 
672  704  735  767  799 
988  *019  *051  *082  *114 

14  301  333  364  395  426 

613  644  675  706  737 


217  260  303  346  389 
647  689  732  775  817 
*072  *115  *157  *199  *242 
494  536  578  620  662 
912  953  995  *036  *078 

325  366  407  449  490 
735  776  816  857  898 
*141  *181  *222  *262  *302 
543  583  623  663  703 
941  981  *021  *060  *100 

336  376  415  454  493" 
727  766  805  844  883 
*115  *154  *192  *231  *269 
500  538  576  614  652 
881  918  956  994  *032 

258  296  333  371  408 
633  670  707  744  781 
*004  *041  *078  *U5  *151 
372  408  445  482  518 
737  773  809  846  882 

*099  *135  *171  *207  *243 
458  493  529  565  600 
814  849  884  920  955 

*167  *202  *237  *272  *307 
517  552  587  621  656 

864  899  934  968  *003 

209  243  278  312  346 

551  585  619  653  687 

890  924  958  992  *025 

227  261  294  327  361 

561  594  628  661  694 

893  926  959  992  *024 

222  254  287  320  352 

548  581  613  646  678 

872  905  937  969  *001 

194  226  258  290  322 
513  545  577  609  640 
830  862  893  925  956 
*145  *176  *208  *239  *270 
457  489  520  551  582 

768  799  829  860  891 


4.4 
8.8 

13.2 
17.6 
•22.0 
26.4 

30.8 
35.2 
39.6 


4.3 

8.6 
12.9 
17.2 
21.5 
25.8 
30.1 
34.4 
38.7 


42     41 


4.2 
8.4 
12.6 
16.8 
21.0 
25.2 
29.4 
33.6 
37.8 

40 

4.0 

8.0 
12.0 
16.0 
20.0 
24.0 
'28.0 
32.0 
36.0 

38 


7.6 
11.4 
15.2 
19.0 

22.8 
26.6 
30.4 
34.2 


36 

1 

3.6 

2 

7.2 

3 

10.8 

4 

14.4 

6 

18.0 

6 

21.6 

7 

25.2 

8 

28.8 

y 

32.4 

4.1 

8.2 
12.3 
16.4 
20.5 
24.6 
28.7 
32.8 
36.9 

39 

3.9 
7.8 
11.7 
15.6 
19.5 
23.4 
27.3 
31.2 
35.1 

37 

3.7 

7.4 
11.1 
14.8 
18.5 
22.2 
25.9 
29.6 
33.3 

35 

3.5 
7.0 
10.5 
14.0 
17.5 
21.0 
24.5 
28.0 
31.5 


P.  P. 


ree 


Logarithms  of  Numbers. 


Num 

.  140  to 

179. 

Log 

.  146  to  255. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7   8   9 

P.  P. 

140 

14   613 

644 

675 

706 

737 

768 

799 

829  860  891 

34 

33 

141 

922 

953 

983  *014  *045 

*076  *106  *137  *168  *198 

• 

3.3 
6.6 

142 

15   229 

259 

290 

320 

351 

381 

412 

442  473  503 

1 

0.1 

6.8 

143 

534 

564 

594 

625 

655 

685 

715 

746  776  806 

B 

10.2 

9.9 

144 

836 

866 

897 

927 

957 

987  *017  *047  *077  *107 

4 

.r> 

13.6 
17.0 

13.2 
16  5 

145 

16   137 

167 

197 

227 

256 

286 

316 

346  376  406 

6 
7 
B 

20.4 
28.8 

27.2 

19.8 
23.1 

20.4 

146 

435 

465 

495 

524 

554 

584 

613 

643  673  702 

147 

732 

761 

791 

820 

850 

879 

909 

938  967  997 

9 

30.6 

29.7 

148 

17   026 

056 

085 

114 

143 

173 

202 

231  260  289 

32 

31 

149 

319 

348 

377 

406 

435 

464 

493 

522  551  580 

150 

609 

638 

667 

696 

725 

754 

782 

811  840  869 

1 
2 

3.2 
6.4 

3.1 

6.2 

151 

898 

926 

955 

984  *013 

*041  *070  *099  *127  *156 

8 

9.6 

9.3 

152 

18   184 

213 

241 

270 

298 

327 

355 

384  412  441 

4 
6 

c. 

12.8 
16.0 
19.2 

12.4 
15.5 
18.6 

153 

469 

498 

526 

554 

583 

611 

639 

667  696  724 

154 
155 

752 
19   033 

780 
061 

808 
089 

837 
117 

865 
145 

893 
173 

921 
201 

949  977  *005 
229  257  285 

7 
8 
9 

22.4 
25.6 
28.8 

21.7 
24.8 
27.9 

156 

312 

340 

368 

396 

424 

451 

479 

507  535  562 

30 

29 

157 

590 

618 

645 

673 

700 

728 

756 

783  811  838 

158 

866 

893 

921 

948 

976 

*003  *030  *058  *085  *112 

1 

3.0 

2.9 

159 

20   140 

167 

194 

222 

249 

276 

303 

330  358  385 

2 
3 

6.0 
9.0 

5.8 
8.7 

160 

412 

439 

466 

493 

520 

548 

575 

602  629  656 

4 
5 
6 

12.0 
15.0 
18.0 

11.6 
14.5 
17.4 

161 

683 

710 

737 

763 

790 

817 

844 

871  898  925 

162 

952 

978  *005  *032  *059 

*085  *112  *139  *165  *192 

7 

21.0 

20.3 

163 

21   219 

245 

272 

299 

325 

352 

378 

405  431  458 

8 
9 

24.0 
27.0 

23.2 
26.1 

164 

484 

511 

537 

564 

590 

617 

643 

669  696  722 

165 

748 

775 

801 

827 

854 

880 

906 

932  958  985 

28 

27 

166 

22   Oil 

037 

063 

089 

115 

141 

167 

194  220  246 

1 

2.8 

2.7 

167 

272 

298 

324 

350 

376 

401 

427 

453  479  505 

2 

3 
4 

5.6 
8.4 
11.2 

5.4 
8.1 
10.8 

168 

531 

557 

583 

608 

634 

660 

686 

712  737  763 

169 
170 

789 
23   045 

814 
070 

840 
096 

866 
121 

891 
147 

917 
172 

943 

198 

968  994  *019 
223  249  274 

5 

0 

7 

14.0 
16.8 
19.6 

13.5 
16.2 
18.9 

171 

300 

325 

350 

376 

401 

426 

452 

477  502  528 

9 

22.4 
25.2 

21.6 
24.3 

172 

553 

578 

603 

629 

654 

679 

704 

729  754  779 

173 

805 

830 

855 

880 

905 

930 

955 

980  *005  *030 

26 

25 

174 

24   055 

080 

105 

130 

155 

180 

204 

229  254  279 

1 

2.6 

2.5 

175 

304 

329 

353 

378 

403 

428 

452 

477  502  527 

2 
3 
4 

5.2 
7.8 
10.4 

5.0 
7.5 
10.0 

176 

551 

576 

601 

625 

650 

674 

699 

724  748  773 

177 

797 

822 

846 

871 

895 

920 

944 

969  993  *018 

5 

13.0 

12.5 

178 

25   042 

066 

091 

115 

139 

164 

188 

212  237  261 

6 
7 
8 

15.6 

18.2 
20.8 

15.0 
17.5 

20.0 

179 

285 

310 

334 

358 

382 

406 

431 

455  479  503 

180 

527 

551 

575 

600 

624 

648 

672 

696  720  744 

9 

23.4 

22.5 

N 

L   0 

1 

2 

3 

4 

5 

6 

7   8   9 

P.  P 

. 

Logarithms  of  Numbers. 


787 


Num 

180  to  219. 

Log 

255  to  342. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7   8   9 

P.  P. 

180 

25   527 

551 

575 

600 

624 

648 

672 

696  720  744 

24 

181 

768 

792 

816 

840 

864 

888 

912 

935  959  983 

1 
2 

2.4 

4.8 

182 

26   007 

031 

055 

079 

102 

126 

150 

174  198  221 

183 

245 

269 

293 

316 

340 

364 

387 

411  435  458 

3 

7.2 

184 

482 

505 

529 

553 

576 

600 

623 

647  670  694 

4 
5 

9.6 

12.0 

185 

717 

741 

764 

788 

811 

834 

858 

881  905  928 

6 

7 
8 

14.4 
16.8 
19.2 

186 

951 

975 

988  *021  *045 

*068  *091  *114  *138  *161 

187 

27   184 

207 

231 

254 

277 

300 

323 

346  370  393 

9 

21.6 

188 

416 

439 

462 

485 

508 

531 

554 

577  600  623 

23 

189 

046 

669 

692 

715 

738 

761 

784 

807  830  852 

190 

875 

898 

921 

944 

967 

989  *012  *035  *058  *081 

1 

2 

2.3 

4.6 

191 

28   103 

126 

149 

171 

194 

217 

240 

262  285  307 

3 

6.9 

192 

330 

353 

375 

398 

421 

443 

466 

488  511  533 

4 
5 

6 

9.2 
11.5 
13.8 

193 

556 

578 

601 

623 

646 

668 

691 

713  735  758 

194 
195 

780 
29   003 

803 
026 

825 

048 

847 
070 

870 
092 

892 

115 

914 

137 

937  959  981 
159  181  203 

7 
8 
9 

16.1 

18.4 
20.7 

196 

226 

248 

270 

292 

314 

336 

358 

380  403  425 

22 

197 

447 

469 

491 

513 

535 

557 

579 

601  623  645 

198 

667 

688 

710 

732 

754 

776 

798 

820  842  863 

1 

2.2 

199 

885 

907 

929 

951 

973 

994  *016  *038  *060  *081 

2 
3 

4.4 

6.6 

200 

30   103 

125 

x146 

168 

190 

211 

233 

255  276  298 

4 
5 
6 

8.8 
11.0 
13.2 

201 

320 

341 

363 

384 

406 

428 

449 

471  492  514 

202 

535 

557 

578 

600 

621 

643 

664 

685  707  728 

7 

15.4 

203 

750 

771 

792 

814 

835 

856 

878 

899  920  942 

8 
9 

17.6 
19.8 

204 

963 

984  *006  *027  *048 

*069  *091  *112  *133  *154 

205 

31   175 

197 

218 

239 

260 

281 

302 

323  345  366 

21 

206 

387 

408 

429 

450 

471 

492 

513 

534  555  576 

1 

2.1 

207 

597 

618 

639 

660 

681 

702 

723 

744  765  785 

2 
3 
4 

4.2 
6.3 
8.4 

208 

806 

827 

848 

869 

890 

911 

931 

952  973  994 

209 
210 

32   015 
222 

035 
243 

056 
263 

077 
284 

098 
305 

118 
325 

139 
346 

160  181  201 
366  387  408 

5 
6 

7 

10.5 
12.6 
14.7 

211 

428 

449 

469 

490 

510 

531 

552 

572  593  613 

8 
9 

16.8 
18.9 

212 

634 

654 

675 

695 

715 

736 

756 

777  797  818 

213 

838 

858 

879 

899 

919 

940 

960 

980  *001  *021 

19 

214 

33   041 

062 

082 

102 

122 

143 

163 

183  203  224 

1 

2.0 

1.9 

215 

244 

264 

284 

304 

325 

345 

365 

385  405  425 

2 
3 
4 

4.0 
6.0 

8.0 

3.8 
5.7 
7.6 

216 

445 

465 

486 

506 

526 

546 

566 

586  606  626 

217 

646 

666 

686 

706 

726 

746 

766 

786  806  826 

5  1 

).0 

9.5 

218 

846 

866 

885 

905 

925 

945 

965 

985  *005  *025 

6  1 

7  1 

8  1 

2.0 
4.0 
6.0 

11.4 
13.3 
15.2 

219 

34   044 

064 

084 

104 

124 

143 

163 

183  203  223 

220 

242 

262 

282 

301 

321 

341 

361 

380  400  420 

9  1 

8.0 

17.1 

N 

L   0 

1 

2 

3 

4 

5 

6 

7   8   9 

P 

.  P 

7ss 


Logarithms  of  Numbhbs. 


Num.  220  to  259.     LoK.  342  to  414. 


N 

L   0 

t 

2 

3 

4 

5   6   7   8   9 

P 

.  P. 

220 

34   242 

262 

282 

301 

321 

341  361  380  400  420 

221 

439 

459 

479 

498 

518 

537  557  577  596  616 

20 

222 

635 

655 

674 

694 

713 

733  753  772  792  811 

1 

2.0 

223 
224 

830 
35   025 

850 
044 

869 
064 

889 
083 

908 
102 

928  947  967  986  *005 
122  141  160  180  199 

2 
3 
i 

4.0 
6.0 

8.0 

225 

218 

238 

257 

276 

295 

315  334  353  372  392 

5 
6 

10.0 
12.0 
14.0 

226 

411 

430 

449 

468 

488 

507  526  545  564  583 

7 

227 

603 

622 

641 

660 

679 

698  717  736  755  774 

8 

16.0 

228 

793 

813 

832 

851 

870 

889  908  927  946  965 

9 

18.0 

229 

984  *003  *021  *040  *059 

*078  *097  *116  *135  *154 

230 

36   173 

192 

211 

229 

248 

267  286  305  324  342 

19 

231 

361 

380 

399 

418 

436 

455  474  493  511  530 

232 

549 

568 

586 

605 

624 

642  661  680  698  717 

1 

1.9 

233 

736 

754 

773 

791 

810 

829  847  866  884  903 

2 
3 

4 

3.8 
5.7 

7.6 

234 

922 

940 

959 

977 

9% 

*014  *033  *051  *070  *088 

235 

37   107 

125 

144 

162 

181 

199  218  236  254  273 

5 
6 

9.5 

11.4 

236 

291 

310 

328 

346 

365 

38  .401  420  438  457 

7 

13.3 

237 

475 

493 

511 

530 

548 

566  5   603  621  639 

8 
9 

15.2 
17.1 

238 

658 

676 

694 

712 

731 

749  767  785  803  822 

239 

840 

858 

876 

894 

912 

931  949  967  985  *003 

240 

38   021 

039 

057 

075 

093 

112  130  148  166  184 

241 

202 

220 

238 

256 

274 

292  310  328  346  364 

18 

242 

382 

399 

417 

435 

453 

471  489  507  525  543 

243 

561 

578 

596 

614 

632 

650  668  686  703  721 

1 
2 
3 

1.8 

244 

739 

757 

775 

792 

810 

828  846  863  881  899 

3.6 
5.4 

245 

917 

934 

952 

970 

987 

*005  *023  *041  *058  *076 

4 
5 

7.2 
9.0 

246 

39   094 

111 

129 

146 

164 

182  199  217  235  252 

6 

10.8 

247 

270 

287 

305 

322 

340 

358  375  393  410  428 

7 
8 
9 

12.6 
14.4 
1R2 

248 

445 

463 

480 

498 

515 

533  550  568  585  602 

249 

620 

637 

655 

672 

690 

707  724  742  759  777 

250 

794 

811 

829 

846 

863 

881  898  915  933  950 

251 

967 

985  *002  *019  *037 

*054  *071  *088  *106  *123 

252 

40   140 

157 

175 

192 

209 

226  243  261  278  295 

253 

312 

329 

346 

364 

381 

398  415  432  449  466 

17 

254 

483 

500 

518 

535 

552 

569  586  603  620  637 

1 

1.7 

255 

654 

671 

688 

705 

722 

739  756  773  790  807 

2 
3 

3.4 
5.1 

256 

824 

841 

858 

875 

892 

909  926  943  960  976 

4 

6.8 

257 

993  *010  *027  *044  *061 

*078  *095  *111  *128  *145 

5 
6 

7 

8.5 
10.2 
11.9 

258 

41   162 

179 

196 

212 

229 

246  263  280  296  313 

259 

330 

347 

363 

380 

397 

414  430  447  464  481 

8 
9 

13.6 
15.3 

260 

497 

514 

531 

547 

564 

581  597  614  631  647 

N 

L   0 

1. 

2 

3 

4 

5   6   7   8   9 

P 

.  P. 

Logarithms  of  Numbers. 


789 


Num.  260  to  299.    Log.  414  to  476. 


N 

L   0 

1 

2 

3 

4 

5   6   7   8   9 

P 

.  P. 

260 

41   497 

514 

531 

547 

564 

581  597  614  631  647 

261 

664 

681 

697 

714 

731 

747  764  780  797  814 

262 

830 

847 

863 

880 

896 

913  929  946  963  979 

263 

9%  *012  *029  *045  *062 

*078  *095  *111  *127  144 

264 

42   160 

177 

193 

210 

226 

243  259  275  292  308 

17 

265 

325 

341 

357 

374 

390 

406  423  439  455  472 

1  ii 

266 

488 

504 

521 

537 

553 

570  586  602  619  635 

2 

3.4 

267 

651 

667 

684 

700 

716 

732  749  765  781  797 

3 

5.1 

268 

813 

830 

846 

862 

878 

894  911  927  943  959 

4 
5 
6 

6.8 

8.5 
10.2 

269 

975 

991 

*008  *024  *040 

*056  *072  *088  *104  *120 

270 

43   136 

152 

169 

185 

201 

217  233  249  265  281 

7 
8 

11.9 
13.6 

271 

297 

313 

329 

345 

361 

377  393  409  425  441 

9 

15.3 

272 

457 

473 

489 

505 

521 

537  553  569  584  600 

273 

616 

632 

648 

664 

680 

696  712  727  743  759 

274 

775 

791 

807 

823 

838 

854  870  886  902  917 

275 

933 

949 

965 

981 

996 

*012  *028  *044  *059  *075 

276 

44   091 

107 

122 

138 

154 

170  185  201  217  232 

16 

277 

248 

264 

279 

295 

311 

326  342  358  373  389 

278 

404 

420 

436 

451 

467 

483  498  514  529  545 

1 

1.6 

279 

560 

576 

592 

607 

623 

638  654  669  685  700 

2 
3 

3.2 
4.8 

280 

716 

731 

747 

762 

778 

793  809  824  840  855 

4 
5 
6 

6.4 
8.0 
9.6 

281 

871 

886 

902 

917 

932 

948  963  979  994  *010 

282 

45   025 

040 

056 

071 

086 

102  117  133  148  163 

7 

11.2 

283 

179 

194 

209 

225 

240 

255  271  286  301  317 

8 
9 

12.8 
14.4 

284 

332 

347 

362 

378 

393 

408  423  439  454  469 

285 

484 

500 

515 

530 

545 

561  576  591  606  621 

286 

637 

652 

667 

682 

697 

712  728  743  758  773 

287 

788 

803 

818 

834 

849 

864  879  894  909  924 

288 

939 

954 

969 

984  *000 

*015  *030  *045  *060  *075 

289 

46   090 

105 

120 

135 

150 

165  180  195  210  225 

15 

290 

240 

255 

270 

285 

300 

315  330  345  359  374 

1 

1.5 

291 

389 

404 

419 

434 

449 

464  479  494  509  523 

2 
3 
4 

3.0 
4.5 
6.0 

292 

538 

553 

568 

583 

598 

613  627  642  657  672 

293 

687 

702 

716 

731 

746 

761  776  790  805  820 

5 

7.5 

294 

835 

850 

864 

879 

894 

909  923  938  953  967 

6 

7 

9.0 
10.5 

295 

982 

997  *012  *026  *041 

*056  *070  *085  *100  *114 

8 
9 

12.0 
13.5 

296 

47   129 

144 

159 

173 

188 

202  217  232  246  261 

297 

276 

290 

305 

319 

334 

349  363  378  392  407 

298 

422 

436 

451 

465 

480 

494  509  524  538  553 

299 

567 

582 

5% 

611 

625 

640  654  669  683  698 

300 

712 

727 

741 

756 

770 

784  799  813  828  842 

N 

L   0 

1 

2 

3 

4 

5   6   7   8   9 

P 

.  P. 

790 


Logarithms  of  Numbers. 


Num.  300  to  339.     Log.  477  to  531. 


N 

L   0 

1 

2 

3 

4 

5   6   7   8   9 

P.  P. 

300 

47   712 

727 

741 

756 

770 

784  799  813  828  842 

301 

857 

871 

885 

900 

mi 

929  943  958  972  986 

302 

48   001 

015 

029 

044 

058 

073  087  101  116  130 

303 

144 

159 

173 

187 

202 

216  230  244  259  273 

304 

287 

302 

316 

330 

344 

359  373  387  401  416 

14 

305 

430 

444 

458 

473 

487 

501  515  530  544  558 

1   '  « 

306 

572 

586 

601 

615 

629 

643  657  671  686  700 

l 
2 

i.i 
2.8 

307 

714 

728 

742 

756 

770 

785  799  813  827  841 

3 

4.2 

308 

855 

869 

883 

897 

911 

926  940  954  968  982 

4 
5 
6 

5.6 
7.0 
8.4 

309 

996  *010  *024  *038  *052 

*066  *080  *094  *108  *122 

310 

49   136 

150 

164 

178 

192 

206  220  234  248  262 

7 
8 

9.8 
11.2 

311 

276 

290 

304 

318 

332 

346  360  374  388  402 

9 

12.6 

312 

415 

429 

443 

457 

471 

485  499  513  527  541 

313 

554 

568 

582 

596 

610 

624  638  651  665  679 

314 

693 

707 

721 

734 

748 

762  776  790  803  817 

315 

831 

845 

859 

872 

886 

900  914  927  941  955 

316 

969 

982 

996  *010  *024 

*037  *051  *065  *079  *092 

13 

317 

50   106 

120 

133 

147 

161 

174  188  202  215  229 

318 

243 

256 

270 

284 

297 

311  325  338  352  365 

1 

1.3 

319 

379 

393 

406 

420 

433 

447  461  474  488  501 

2 
3 

2.6 
3.9 

320 

615 

529 

542 

556 

569 

583  596  610  623  637 

4 

5 
6 

5.2 
6.5 

7.8 

321 

651 

664 

678 

691 

705 

718  732  745  759  772 

322 

786 

799 

813 

826 

840 

853  866  880  893  907 

7 

9.1 

323 

920 

934 

947 

961 

974 

987  *001  *014  *028  *041 

8 
9 

10.4 
11.7 

324 

51   055 

068 

081 

095 

108 

121  135  148  162  175 

325 

188 

202 

215 

228 

242 

255  268  282  295  308 

326 

322 

335 

348 

362 

375 

388  402  415  428  441 

327 

455 

468 

481 

495 

508 

521  534  548  561  574 

328 

587 

601 

614 

627 

640 

654  667  680  693  706 

329 

720 

733 

746 

769 

772 

786  799  812  825  838 

12 

330 

851 

865 

878 

891 

904 

917  930  943  957  970 

1 

1.2 

331 

983 

996  *009  *022  *035 

*048  *061  *075  *088  *101 

2 
3 

4 

2.4 
3.6 
4.8 

332 

52   114 

127 

140 

153 

166 

179  192  205  218  231 

333 

244 

257 

270 

284 

297 

310  323  336  349  362 

5 

6.0 

334 

375 

388 

401 

414 

427 

440  453  466  479  492 

6 
7 

7.2 
8.4 

335 

504 

517 

530 

543 

556 

569  582  595  608  621 

8 

9 

9.6 
10.8 

336 

634 

647 

660 

673 

686 

699  711  724  737  750 

337 

763 

776 

789 

802 

815 

827  840  853  866  879 

338 

892 

905 

917 

930 

943 

956  969  982  994  *007 

339 

53   020 

033 

046 

058 

071 

084  097  110  122  135 

340 

148 

161 

173 

186 

199 

212  224  237  250  263 

N 

L   0 

1 

2 

3 

4 

5   6   7   8   9 

P 

.  P. 

Logarithms  of  Numbers. 


791 


Num. 

340  to  379. 

Log. 

531 

to  579. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P.  P. 

340 

53   148 

161 

173 

186 

199 

212 

224 

237 

250  263 

341 

275 

288 

301 

314 

326 

339 

352 

364 

377  390 

342 

403 

415 

428 

441 

453 

466 

479 

491 

504  517 

343 

529 

542 

555 

567 

580 

593 

605 

618 

631  643 

344 

656 

668 

681 

694 

706 

719 

732 

744 

757  769 

13 

345 

782 

794 

807 

820 

832 

845 

857 

870 

882  895 

1 
2 

1.3 
2.6 

346 

908 

920 

933 

945 

958 

970 

983 

995  *008  *020 

347 

54   033 

045 

058 

070 

083 

095 

108 

120 

133  145 

3 

3.9 

348 

158 

170 

183 

195 

208 

220 

233 

245 

258  270 

4 
5 
6 

5.2 
6.5 

7.8 

349 

283 

295 

307 

320 

332 

345 

357 

370 

382  394 

350 

407 

419 

432 

444 

456 

469 

481 

494 

506  518 

7 
8 

9.1 
10.4 

351 

531 

543 

555 

568 

580 

593 

605 

617 

630  642 

9 

11.7 

352 

654 

667 

679 

691 

704 

716 

728 

741 

753  765 

353 

777 

790 

802 

814 

827 

839 

851 

864 

876  888 

354 

900 

913 

925 

937 

949 

962 

974 

986 

998  *011 

355 

£5   023 

035 

047 

060 

072 

084 

096 

108 

121  133 

356 

145 

157 

169 

182 

194 

206 

218 

230 

242  255 

12 

357 

267 

279 

291 

303 

315 

328 

340 

352 

364  376 

358 

388 

400 

413 

425 

437 

449 

461 

473 

485  497 

1 

1.2 

359 

509 

522 

534 

546 

558 

570 

582 

594 

606  618 

2 
3 

2.4 
3.6 

360 

630 

642 

654 

666 

678 

691 

703 

715 

727  739 

4 
5 
6 

4.8 
6.0 
7.2  • 

361 

751 

763 

775 

787 

799 

811 

823 

835 

847  859 

362 

871 

883 

895 

907 

919 

931 

943 

955 

967  979 

7 

8.4 

363 

991  *003  *015  *027  *038 

*050  *062  *074  *086  *098 

8 
9 

9.6 
10.8 

364 

56   110 

122 

134 

146 

158 

170 

182 

194 

205  217 

365 

229 

241 

253 

265 

277 

289 

301 

312 

324  336 

366 

348 

360 

372 

384 

396 

407 

419 

431 

443  455 

367 

467 

478 

490 

502 

514 

526 

538 

549 

561  573 

368 

585 

597 

608 

620 

632 

644 

656 

667 

679  691 

369 

703 

714 

726 

738 

750 

761 

773 

785 

797  808 

11 

370 

820 

832 

844 

855 

867 

879 

891 

902 

914  926 

1 

1.1 

371 

937 

949 

961 

972 

984 

996  *008  *019  *031  *043 

2 
3 
4 

2.2 
3.3 
4.4 

372 

57   054 

066 

078 

089 

101 

113 

124 

136 

148  159 

373 

171 

183 

194 

206 

217 

229 

241 

252 

264  276 

5 

5.5 

374 

287 

299 

310 

322 

334 

345 

357 

368 

380  392 

6 

7 

6.6 

7.7 

375 

403 

415 

426 

438 

449 

461 

473 

484 

4%  507 

8 
9 

8.8 
9.9 

376 

519 

530 

542 

553 

565 

576 

588 

600 

611  623 

377 

634 

646 

657 

669 

680 

692 

703 

715 

726  738 

378 

749 

761 

772 

784 

795 

807 

818 

830 

841  852 

379 

864 

875 

887 

898 

910 

921 

933 

944 

955  967 

380 

978 

990  *001  *013  *024 

*035  *047  *058  *070  *081 

N 

L   0 

1 

2 

3 

4 

S 

6 

7 

8   9 

P 

.  P. 

792 


Logarithms  op  Numbers. 


Num 

380  to  419. 

Log 

579  to  623. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P.  P. 

380 

57   978 

990  *001  *013  *024 

*035  *047  »058  *070  *081 

381 

58   092 

104 

115 

127 

138 

149 

161 

172 

184  195 

882 

206 

218 

229 

240 

252 

263 

274 

286 

297  309 

883 

320 

331 

343 

354 

365 

377 

388 

399 

410  422 

884 

433 

444 

456 

467 

478 

490 

501 

512 

524  535 

11 

885 

546 

557 

569 

580 

591 

602 

614 

625 

636  647 

386 

659 

670 

681 

692 

704 

715 

726 

737 

749  760 

1 

2 

2.2 

887 

771 

782 

794 

805 

816 

827 

838 

850 

861  872 

3 

3.3 

388 

883 

894 

906 

917 

928 

939 

950 

961 

973  984 

4 
5 
6 

4.4 
5.5 
6.6 

389 

995  *006  *017  *028  *040 

*051  *062  *073  *084  *095 

390 

59   106 

118 

129 

140 

151 

162 

173 

184 

195  207 

7 
8 

7.7 
8.8 

891 

218 

229 

240 

251 

262 

273 

284 

295 

306  318 

9 

9.9 

392 

329 

340 

351 

362 

373 

384 

395 

406 

417  428 

893 

439 

450 

461 

472 

483 

494 

506 

517 

528  539 

894 

550 

561 

572 

583 

594 

605 

616 

627 

638  649 

895 

660 

671 

682 

693 

704 

715 

726 

737 

748  759 

396 

770 

780 

791 

802 

813 

824 

835 

846 

857  868 

10 

897 

879 

890 

901 

912 

923 

934 

945 

956 

966  977 

898 

988 

999  *010  *021  *032 

*043  *054  *065  *076  *086 

1 

1.0 

899 

60   097 

108 

119 

130 

141 

152 

163 

173 

184  195 

2 
3 

2.0 
3.0 

400 

206 

217 

228 

239 

249 

260 

271 

282 

293  304 

4 
5 
6 

4.0 
5.0 
6.0 

401 

314 

325 

336 

347 

358 

369 

379 

390 

401  412 

402 

423 

433 

444 

455 

466 

477 

487 

498 

509  520 

7 

7.0 

403 

531 

541 

552 

563 

574 

584 

595 

606 

617  627 

8 
9 

8.0 
9.0 

404 

638 

649 

660 

670 

681 

692 

703 

713 

724  735 

405 

746 

756 

767 

778 

788 

799 

810 

821 

831  842 

406 

853 

863 

874 

885 

895 

906 

917 

927 

938  949 

407 

959 

970 

981 

991  *002 

*013  *023  *034  *045  *055 

408 

61   066 

077 

087 

098 

109 

119 

130 

140 

151  162 

409 

172 

183 

194 

204 

215 

225 

236 

247 

257  268 

410 

278 

289 

300 

310 

321 

331 

342 

352 

363  374 

411 

384 

395 

405 

416 

426 

437 

448 

458 

469  479 

412 

490 

500 

511 

521 

532 

542 

553 

563 

574  584 

413 

595 

606 

616 

627 

637 

648 

658 

669 

679  690 

414 

700 

711 

721 

731 

742 

752 

763 

773 

784  794 

415 

805 

815 

826 

836 

847 

857 

868 

878 

888  899 

416 

909 

920 

930 

941 

951 

962 

972 

982 

993  *003 

417 

62   014 

024 

034 

045 

055 

066 

076 

086 

097  107 

418 

118 

128 

138 

W9 

159 

170 

180 

190 

201  211 

419 

221 

232 

242 

252 

263 

273 

284 

294 

304  315 

420 

325 

335 

346 

356 

366 

377 

387 

397 

408  418 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P. 

P. 

Logarithms  of  Numbers. 


793 


Num 

420  to  459. 

Log 

623  to  662. 

N 

L   0 

i 

2 

3 

4 

5 

6   7   8   9 

P.  P. 

420 

62   325 

335 

346 

356 

366 

377 

387  397  408  418 

421 

428 

439 

449 

459 

469 

480 

490  500  511  521 

422 

531 

542 

552 

562 

572 

583 

593  603  613  624 

423 

634 

644 

655 

665 

675 

685 

696  706  716  726 

424 

737 

747 

757 

767 

778 

788 

798  808  818  829 

425 

839 

849 

859 

870 

880 

890 

900  910  921  931 

426 

941 

951 

961 

972 

982 

992  *002  *012  *022  *033 

427 

63   043 

053 

063 

073 

083 

094 

104  114  124  134 

428 

144 

155 

165 

175 

185 

195 

205  215  225  236 

10 

429 

246 

256 

266 

276 

286 

296 

306  317  327  337 

430 

347 

357 

367 

377 

387 

397 

407  417  428  438 

1 

2 

l.U 
2.0 

431 

448 

458 

468 

478 

488 

498 

508  518  528  538 

3 

3.0 

432 

548 

558 

568 

579 

589 

599 

609  619  629  639 

4 
5 
6 

4.0 
5.0 
6.0 

433 

649 

659 

669 

679 

689 

699 

709  719  729  739 

434 

749 

759 

769 

779 

789 

799 

809  819  829  839 

7 
8 
9 

7.0 
8.0 
9.0 

435 

849 

859 

869 

879 

889 

899 

909  919  929  939 

436 

949 

959 

969 

979 

988 

998  *008  *018  *028  *038 

437 

64   048 

058 

068 

078 

088 

098 

108  118  128  137 

438 

147 

157 

167 

177 

187 

197 

207  217  227  237 

439 

246 

256 

266 

276 

286 

296 

306  316  326  335 

440 

345 

355 

365 

375 

385 

395 

404  414  424  434 

441 

444 

454 

464 

473 

483 

493 

503  513  523  532 

442 

542 

552 

562 

572 

582 

591 

601  611  621  631 

443 

640 

650 

660 

670 

680 

689 

699  709  719  729 

444 

738 

748 

758 

768 

777 

787 

797  807  816  826 

445 

836 

846 

856 

865 

875 

885 

895  904  914  924 

9 

446 

933 

943 

953 

963 

972 

982 

992  *002  *011  *021 

1 

0.9 

447 

65   031 

040 

050 

060 

070 

079 

089  099  108  118 

2 
3 

4 

1.8 
2.7 
3.6 

448 

128 

137 

147 

157 

167 

176 

186  196  205  215 

449 

225 

234 

244 

254 

263 

273 

283  292  302  312 

5 
6 

4.5 
5.4 

450 

321 

331 

341 

350 

360 

369 

379  389  398  408 

7 

6.3 

451 

418 

427 

437 

447 

456 

466 

475  485  495  504 

8 
9 

7.2 
8.1 

452 

514 

523 

533 

543 

552 

562 

571  581  591  600 

453 

610 

619 

629 

639 

648 

658 

667  677  686  696 

454 

706 

715 

725 

734 

744 

753 

763  772  782  792 

455 

801 

811 

820 

830 

839 

849 

858  868  877  887 

456 

896 

906 

916 

925 

935 

944 

954  963  973  982 

457 

992  *001  *011  *020  *030 

*039  *049  *058  *068  *077 

458 

66   087 

0% 

1% 

115 

124 

134 

143  153  162  172 

459 

181 

191 

200 

210 

219 

229 

238  247  257  266 

460 

276 

285 

295 

304 

314 

323 

332  342  351  361 

N 

L   0 

1 

2 

3 

4 

5 

6   7   8   9 

P. 

P. 

794 


Logarithms  op  Numbers. 


Nutn 

460  to  499. 

Log. 

662  to  698. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7   8   9 

P.  P. 

460 

66   276 

285 

295 

304 

314 

323 

332 

342  351  361 

461 

370 

380 

389 

398 

408 

417 

427 

436  445  455 

462 

464 

474 

483 

492 

502 

511 

521 

530  539  549 

463 

558 

567 

577 

586 

596 

605 

614 

624  633  642 

464 

652 

661 

671 

680 

689 

699 

708 

717  727  736 

465 

745 

755 

764 

773 

783 

792 

801 

811  820  829 

466 

839 

848 

857 

867 

876 

885 

894 

904  913  922 

467 

932 

941 

950 

960 

969 

978 

987 

997  *006  *015 

468 

67   025 

034 

043 

052 

062 

071 

080 

089  099  108 

10 

469 

117 

127 

136 

145 

154 

164 

173 

182  191  201 

470 

210 

219 

228 

237 

247 

256 

265 

274  284  293 

1 
2 

1.0 
2.0 

471 

302 

311 

321 

330 

339 

348 

357 

367  376  385 

3 

3.0 

472 

394 

403 

413 

422 

431 

440 

449 

459  468  477 

4 

5 
6 

4.0 
5.0 
6.0 

473 

486 

495 

504 

514 

523 

532 

641 

550  560  569 

474 
475 

578 
669 

587 
679 

5% 

688 

605 
697 

614 
706 

624 

715 

633 

724 

642  651  660 
733  742  752 

7 
8 
9 

7.0 
8.0 
9.0 

476 

761 

770 

779 

788 

797 

806 

815 

825  834  843 

477 

852 

861 

870 

879 

888 

897 

906 

916  925  934 

478 

943 

952 

961 

970 

979 

988 

997  *006  *015  *024 

479 

68   034 

043 

052 

061 

070 

079 

088 

097  106  115 

480 

124 

133 

142 

151 

160 

169 

178 

187  196  205 

481 

215 

224 

233 

242 

251 

260 

269 

278  287  296 

482 

305 

314 

323 

332 

341 

350 

359 

368  377  386 

483 

395 

404 

413 

422 

431 

440 

449 

458  467  476 

484 

485 

494 

502 

511 

520 

529 

538 

547  556  565 

485 

574 

583 

592 

601 

610 

619 

628 

637  646  655 

9 

486 

664 

673 

681 

690 

699 

708 

717 

726  735  744 

1 

0.9 

487 

753 

762 

771 

780 

789 

797 

806 

815  824  833 

2 
3 

4 

1.8 
2.7 
3.6 

488 

842 

851 

860 

869 

878 

886 

895 

904  913  922 

489 
490 

931 
69   020 

940 
028 

949 
037 

958 
046 

966 

055 

975 

064 

984 
073 

993  *002  *011 
082  090  099 

5 
6 

7 

4.5 
5.4 
6.3 

491 

108 

117 

126 

135 

144 

152 

162 

170  179  188 

8 
9 

7.2 
8.1 

492 

197 

205 

214 

223 

232 

241 

249 

258  267  276 

493 

285 

294 

302 

311 

320 

329 

338 

346  355  364 

494 

373 

381 

390 

399 

408 

417 

425 

434  443  452 

495 

461 

469 

478 

487 

496 

504 

513 

522  531  539 

496 

548 

557 

566 

574 

583 

592 

601 

609  618  627 

497 

636 

644 

653 

662 

671 

679 

688 

697  705  714 

498 

723 

732 

740 

749 

758 

767 

775 

784  793  801 

499 

810 

819 

827 

836 

845 

854 

862 

871  880  888 

500 

897 

906 

914 

923 

932 

940 

949 

958  966  975 

N 

L   0 

1 

2 

3 

4 

5 

6 

7   8   9 

P. 

P. 

Logarithms  of  Numbers. 


795 


Num. 

500  to  539. 

Log. 

698  to  732. 

IN 

L   0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P.  P. 

500 

69   897 

906 

914 

922 

932 

940 

949 

958 

966  975 

501 

984 

992  *001  *010  *018 

*027  *036  *044  *053  *062 

502 

70   070 

079 

088 

096 

105 

114 

122 

131 

140  148 

503 

157 

165 

174 

183 

191 

200 

209 

217 

226  234 

504 

243- 

252 

260 

269 

278 

286 

295 

303 

312  321 

505 

329 

338 

346 

355 

364 

372 

381 

389 

398  406 

506 

415 

424 

432 

441 

449 

458 

467 

475 

484  492 

507 

501 

509 

518 

526 

535 

544 

552 

561 

569  578 

508 

586 

595 

603 

612 

621 

629 

638 

646 

655  663 

9 

509 

672 

680 

689 

697 

706 

714 

723 

731 

740  749 

510 

757 

766 

774 

783 

791 

800 

808 

817 

825  834 

1 
2 

0.9 
1.8 

511 

842 

851 

859 

868 

876 

885 

893 

902 

910  919 

3 

2.7 

512 

927 

935 

944 

952 

961 

969 

978 

986 

995  *003 

4 
5 
6 

3.6 
4.5 
5.4 

513 

71   012 

020 

029 

037 

046 

054 

063 

071 

079  088 

514 

515 

096 

181 

105 
189 

113 
198 

122 
206 

130 
214 

139 
223 

147 
231 

155 
240 

164  172 
248  257 

7 
8 
9 

6.3 
7.2 
8.1 

516 

265 

273 

282 

290 

299 

307 

315 

324 

332  341 

517 

349 

357 

366 

374 

383 

391 

399 

408 

416  425 

518 

433 

441 

450 

458 

466 

475 

483 

492 

500  508 

519 

517 

525 

533 

542 

550 

559 

567 

575 

584  592 

520 

600 

609 

617 

625 

634 

642 

650 

659 

667  675 

521 

684 

692 

700 

709 

717 

725 

734 

742 

750  759 

522 

767 

775 

784 

792 

800 

809 

817 

825 

834  842 

523 

850 

858 

867 

875 

883 

892 

900 

908 

917  925 

524 

933 

941 

950 

958 

966 

975 

983 

991 

999  *008 

525 

72   016 

024 

032 

041 

049 

057 

066 

074 

082  090 

8 

526 

099 

107 

115 

123 

132 

140 

148 

156 

165  173 

1 

0.8 

527 

181 

189 

198 

206 

214 

222 

230 

239 

247  255 

2 
3 
4 

1.6 
2.4 
3.2 

528 

263 

272 

280 

288 

296 

304 

313 

321 

329  337 

529 
530 

346 

428 

354 
436 

362 

444 

370 
452 

378 
460 

387 
469 

395 

477 

403 

485 

411  419 
493  501 

5 
6 

7 

4.0 
4.8 
5.6 

531 

509 

518 

526 

534 

542 

550 

558 

567 

575  583 

8 
9 

6.4 
7.2 

532 

591 

599 

607 

616 

624 

632 

640 

648 

656  665 

533 

673 

681 

689 

697 

705 

713 

722 

730 

738  746 

534 

754 

762 

770 

779 

787 

795 

803 

811 

819  827 

535 

835 

843 

852 

860 

868 

876 

884 

892 

900  908 

536 

916 

925 

933 

941 

949 

957 

965 

973 

981  989 

537 

997  *006  *014  *022  *030 

*038  *046  *054 

062  *070 

538 

73   078 

086 

094 

102 

111 

119 

127 

135 

143  151 

539 

159 

167 

175 

183 

191 

199 

207 

215 

223  231 

540 

239 

247 

255 

263 

272 

280 

288 

296 

304  312 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P. 

P. 

796 


Logarithms  of  Numbers. 


Num.  540  to  579.     Log.  732  to  763. 


73  239  247  255  263  272 
820  828  336  344  352 
400  408  416  424  432 
480  488  496  504  512 
560  568  576  584  592 

640  648  656  664  672 

719  727  735  743  751 

799  807  815  823  830 

878  886  894  902  910 

957  965  973  981  989 

74  036  044  052  060  068 
115  123  131  139  147 
194  202  210  218  225 
273  280  288  296  304 
351  359  367  374  382 

429  437  445  453  461 

507  515  523  531  539 

586  593  601  609  617 

663  671  679  687  695 
741  749  757  764  772 

819  827  834  842  850 

8%  904  912  920  927 

974  981  989  997  *005 

75  051  059  066  074  082 
128  136  143  151  159 

205  213  220  228  236 

282  289  297  305  312 

358  366  374  381  389 

435  442  450  458  465 

511  519  526  534  542 

587  595  603  610  618 

664  671  679  686  694 
740  747  755  762  770 
815  823  831  838  846 
891  899  906  914  921 

967  974  982  989  997 

76  042  050  057  065  072 
118  125  133  140  148 
193  200  208  215  223 
268  275  283  290  298 

343  350  358  365  373 


280  288  296  304  312 

360  368  376  384  892 

440  448  456  464  472 

520  528  536  544  552 

600  608  616  624  632 

679  687  695  703  711 

759  767  775  783  791 

838  846  854  862  870 

918  926  933  941  949 

997  *005  *013  *020  *028 

076  084  092  099  107 

155  162  170  178  186 

233  241  249  257  265 

312  320  327  335  343 

390  398  406  414  421 

468  476  484  492  500 

547  554  562  570  578 

624  632  640  648  656 

702  710  718  726  733 

780  788  796  803  811 

858  865  873  881  889 

935  943  950  958  966 

*012  *020  *028  *035  *043 

089  097  105  113  120 

166  174  182  189  197 

243  251  259  266  274 

320  328  335  343  351 

397  404  412  420  427 

473  481  488  496  504 

549  557  565  572  580 

626  633  641  648  656 

702  709  717  724  732 

778  785  793  800  808 

853  861  868  876  884 

929  937  944  952  959 

*005  *012  *020  *027  *035 

080  087  095  103  110 

155  163  170  178  185 

230  238  245  253  260 

305  313  320  328  335 

380  388  395  403  410 


Logarithms  of  Numbers. 


797 


Num 

580  to  619. 

Log. 

763  to  792. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P.  P. 

580 

76   343 

350 

358 

365 

373 

380 

388 

395 

403  410 

8 

581 

418 

425 

433 

440 

448 

455 

462 

470 

477  485 

1 

2 

0.8 
1.5 

582 

492 

500 

507 

515 

522 

530 

537 

545 

552  559 

583 

567 

574 

582 

589 

597 

604 

612 

619 

626  634 

3 

2.4 

584 

641 

649 

656 

664 

671 

678 

686 

693 

701  708 

4 

5 

3.2 
4.0 

585 

716 

723 

730 

738 

745 

753 

760 

768 

775  782 

6 

7 
8 

4.8 
5.6 
6.4 

586 

790 

797 

805 

812 

819 

827 

834 

842 

849  856 

587 

864 

871 

879 

886 

893 

901 

908 

916 

923  930 

9 

7.2 

588 

938 

945 

953 

960 

967 

975 

982 

989 

997  *004 

589 

77   012 

019 

026 

034 

041 

048 

056 

063 

070  078 

590 

085 

093 

100 

107 

115 

122 

129 

137 

144  151 

591 

159 

166 

173 

181 

188 

195 

203 

210 

217  225 

592 

232 

240 

247 

254 

262 

269 

276 

283 

291  298 

593 

305 

313 

320 

327 

335 

342 

349 

357 

364  371 

594 

379 

386 

393 

401 

408 

415 

422 

430 

437  444 

595 

452 

459 

466 

474 

481 

488 

495 

503 

510  517 

596 

525 

532 

539 

546 

554 

561 

568 

576 

583  590 

597 

597 

605 

612 

619 

627 

634 

641 

648 

656  663 

7 

598 

670 

677 

685 

692 

699 

706 

714 

721 

728  735 

599 

743 

750 

757 

764 

772 

779 

786 

793 

801  808 

1 
2 

0.7 

1.4 

600 

815 

822 

830 

837 

844 

851 

859 

866 

873  880 

3 
4 
5 

2.1 

2.8 
3.5 

601 

887 

895 

902 

909 

916 

924 

931 

938 

945  952 

602 

960 

967 

974 

981 

988 

996  *003  *010  *017  *025 

6 

4.2 

603 

78   032 

039 

046 

053 

061 

068 

075 

082 

089  097 

7 
8 
9 

4.9 
5.6 
6.3 

604 

104 

111 

118 

125 

132 

140 

147 

154 

161  168 

605 

176 

183 

190 

197 

204 

211 

219 

226 

233  240 

606 

247 

254 

262 

269 

276 

283 

290 

297 

305  312 

607 

319 

326 

333 

340 

347 

355 

362 

369 

376  383 

608 

390 

398 

405 

412 

419 

426 

433 

440 

447  455 

609 

462 

469 

476 

483 

490 

497 

504 

512 

519  526 

610 

533 

540 

547 

554 

561 

569 

576 

583 

590  597 

611 

604 

611 

618 

625 

633 

640 

647 

654 

661  668 

612 

675 

682 

689 

696 

704 

711 

718 

725 

732  739 

613 

746 

753 

760 

767 

774 

781 

789 

796 

802  810 

614 

817 

824 

831 

838 

845 

852 

859 

866 

873  880 

615 

888 

895 

902 

909 

916 

923 

930 

937 

944  951 

616 

958 

965 

972 

979 

986 

993  *000  *007  *014  *021 

617 

79   029 

036 

043 

050 

057 

064 

071 

078 

085  092 

618 

099 

106 

113 

120 

127 

134 

141 

148 

155  162 

619 

169 

176 

183 

190 

197 

204 

211 

218 

225  232 

620 

239 

246 

253 

260 

267 

274 

281 

288 

295  302 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8   9 

P 

P. 

706 


Logarithms  of  Ntjmbbrs. 


Num.  620  to  659.    Log.  792  to  819. 


N 

L   0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

620 

79   239 

246 

253 

260 

267 

274 

281 

288 

295 

302 

621 

309 

316 

323 

330 

337 

344 

351 

358 

365 

372 

622 

379 

386 

393 

400 

407 

414 

421 

428 

435 

442 

623 

449 

456 

463 

470 

477 

484 

491 

498 

505 

511 

624 

518 

525 

532 

539 

546 

553 

560 

567 

574 

581 

625 

588 

595 

602 

609 

616 

623 

630 

637 

644 

650 

626 

657 

664 

671 

678 

685 

692 

699 

706 

713 

720 

627 

727 

734 

741 

748 

754 

761 

768 

775 

782 

789 

628 

7% 

803 

810 

817 

824 

831 

837 

844 

851 

858 

629 

865 

872 

879 

886 

893 

900 

906 

913 

920 

927 

630 

934 

941 

948 

955 

962 

969 

975 

982 

989 

996 

631 

80   003 

010 

017 

024 

030 

037 

044 

051 

058 

065 

632 

072 

079 

085 

092 

099 

106 

113 

120 

127 

134 

633 

140 

147 

154 

161 

168 

175 

182 

188 

195 

202 

634 

209 

216 

223 

229 

236 

243 

250 

257 

264 

271 

635 

277 

284 

291 

298 

305 

312 

318 

325 

332 

339 

636 

346 

353 

359 

366 

373 

380 

387 

393 

400 

407 

7 

637 

414 

421 

428 

434 

441 

448 

455 

462 

468 

475 

638 

482 

489 

496 

502 

509 

516 

523 

530 

536 

543 

1 

0.7 

639 

550 

557 

564 

570 

577 

584 

591 

598 

604 

611 

2 
3 

1.4 
2.1 

640 

618 

625 

632 

638 

645 

652 

659 

665 

672 

679 

4 
5 
6 

2.8 
3.5 
4.2 

641 

686 

693 

699 

706 

713 

720 

726 

733 

740 

747 

642 

754 

760 

767 

774 

781 

787 

794 

801 

808 

814 

7 

4.9 

643 

821 

828 

835 

841 

848 

855 

862 

868 

875 

882 

8 
9 

5.6 
6.3 

644 

889 

895 

902 

909 

916 

922 

929 

936 

943 

949 

645 

956 

963 

969 

976 

983 

990 

996  *003  *010  *017 

646 

81   023 

030 

037 

043 

050 

057 

064 

070 

077 

084 

647 

090 

097 

104 

111 

117 

124 

131 

137 

144 

151 

648 

158 

164 

171 

178 

184 

191 

198 

204 

211 

218 

649 

224 

231 

238 

245 

251 

258 

265 

271 

278 

285 

650 

291 

298 

305 

311 

318 

325 

331 

338 

345 

351 

651 

358 

365 

371 

378 

385 

391 

398 

405 

411 

418 

652 

425 

431 

438 

445 

451 

458 

465 

471 

478 

485 

653 

491 

498 

505 

511 

518 

525 

531 

538 

544 

551 

654 

558 

564 

571 

578 

584 

591 

598 

604 

611 

617 

655 

624 

631 

637 

644 

651 

657 

664 

671 

677 

684 

656 

690 

697 

704 

710 

717 

723 

730 

737 

743 

750 

657 

757 

763 

770 

776 

783 

790 

796 

803 

809 

816 

658 

823 

829 

836 

842 

849 

856 

862 

869 

875 

882 

659 

889 

895 

902 

908 

915 

921 

928 

935 

941 

948 

660 

954 

961 

968 

974 

981 

987 

994  *000  *007  *014 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

Logarithms  of  Numbers. 


799 


Sum 

.  660  to  699. 

Log 

.  819  to  845. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

660 

81   954 

961 

968 

974 

981 

987 

994  *000  *007  *014 

7 

661 

82   020 

027 

033 

040 

046 

053 

060 

066 

073 

079 

1 

I 

0.7 
1.4 

662 

086 

092 

099 

105 

112 

119 

125 

132 

138 

145 

663 

151 

158 

164 

171 

178 

184 

191 

197 

204 

210 

2.1 

664 

217 

223 

230 

236 

243 

249 

256 

263 

269 

276 

4 
5 

2.8 
3.5 

665 

282 

289 

295 

302 

308 

315 

321 

328 

334 

341 

6 
7 

8 

4.2 
4.9 
5.6 

666 

347 

354 

360 

367 

373 

380 

387 

393 

400 

406 

667 

413 

419 

426 

432 

439 

445 

452 

458 

465 

471 

9 

6.3 

668 

478 

484 

491 

497 

504 

510 

517 

523 

530 

536 

669 

543 

549 

556 

562 

569 

575 

582 

588 

595 

601 

670 

607 

614 

620 

627 

633 

640 

646 

653 

659 

666 

671 

672 

679 

685 

692 

698 

705 

711 

718 

724 

730 

672 

737 

743 

750 

756 

763 

769 

776 

782 

789 

795 

673 

802 

808 

814 

821 

827 

834 

840 

847 

853 

860 

674 

866 

872 

879 

885 

892 

898 

905 

911 

918 

924 

675 

930 

937 

943 

950 

956 

963 

969 

975 

982 

988 

676 

995  *001  *008  *014  *020 

*027  *033  *040  *046  *052 

677 

83   059 

065 

072 

078 

085 

091 

097 

104 

110 

117 

6 

678 

123 

129 

136 

142 

149 

155 

161 

168 

174 

181 

679 

187 

193 

200 

206 

213 

219 

225 

232 

238 

245 

1 
2 

0.6 
1.2 

480 

251 

257 

264 

270 

276 

283 

289 

296 

302 

308 

3 
4 
5 

1.8 
2.4 
3.0 

681 

315 

321 

327 

334 

340 

347 

353 

359 

366 

372 

682 

378 

385 

391 

398 

404 

410 

417 

423 

429 

436 

6 

3.6 

683 

442 

448 

455 

461 

467 

474 

480 

487 

493 

499 

7 
8 
9 

4.2 
4.8 
5.4 

684 

506 

512 

518 

525 

531 

537 

544 

550 

556 

563 

685 

569 

575 

582 

588 

594 

601 

607 

613 

620 

626 

686 

632 

639 

645 

651 

658 

664 

670 

677 

683 

689 

687 

696 

702 

708 

715 

721 

727 

734 

740 

746 

753 

688 

759 

765 

771 

778 

784 

790 

797 

803 

809 

816 

689 

822 

828 

835 

841 

847 

853 

860 

866 

872 

879 

690 

885 

891 

897 

904 

910 

916 

923 

929 

935 

942 

691 

948 

954 

960 

967 

973 

979 

985 

992 

998  *004 

692 

84   Oil 

017 

023 

029 

036 

042 

048 

055 

061 

067 

693 

073 

080 

086 

092 

098 

105 

111 

117 

123 

130 

694 

136 

142 

148 

155 

161 

167 

173 

180 

186 

192 

695 

198 

205 

211 

217 

223 

230 

236 

242 

248 

255 

696 

261 

267 

273 

280 

286 

292 

298 

305 

311 

317 

697 

323 

330 

336 

342 

348 

354 

361 

367 

373 

379 

698 

386 

392 

398 

404 

410 

417 

423 

429 

435 

442 

699 

448 

454 

460 

466 

473 

479 

485 

491 

497 

504 

700 

510 

516 

522 

528 

535 

541 

547 

553 

559 

566 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

MM) 


Logarithms  op  Numbers. 


Num.  700  to  739.      Log.  845  to  869. 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

700 

84   510 

516 

522 

528 

535 

541 

547 

553 

559 

566 

701 

572 

578 

584 

590 

597 

603 

609 

615 

621 

628 

702 

634 

640 

646 

652 

658 

665 

671 

677 

683 

689 

703 

696 

702 

708 

714 

720 

726 

733 

739 

745 

751 

704 

757 

763 

770 

776 

782 

788 

794 

800 

807 

813 

705 

819 

825 

831 

837 

844 

850 

856 

862 

868 

874 

706 

880 

887 

893 

899 

905 

911 

917 

924 

930 

936 

707 

942 

948 

954 

960 

967 

973 

979 

985 

991 

997 

708 

85   003 

009 

016 

022 

028 

034 

040 

046 

052 

058 

709 

065 

071 

077 

083 

089 

095 

101 

107 

114 

120 

710 

126 

132 

138 

144 

150 

156 

163 

169 

175 

181 

711 

187 

193 

199 

205 

211 

217 

224 

230 

236 

242 

712 

248 

254 

260 

266 

272 

278 

285 

291 

297 

303 

713 

309 

315 

321 

327 

333 

339 

345 

352 

358 

364 

714 

370 

376 

382 

388 

394 

400 

406 

412 

418 

425 

715 

431 

437 

443 

449 

455 

461 

467 

473 

479 

485 

716 

491 

497 

503 

509 

516 

522 

528 

534 

540 

546 

717 

552 

558 

564 

570 

576 

582 

588 

594 

600 

606 

6 

718 

612 

618 

625 

631 

637 

643 

649 

655 

661 

667 

719 

673 

679 

685 

691 

697 

703 

709 

715 

721 

727 

1 

2 

u.o 
1.2 

720 

733 

739 

745 

751 

757 

763 

769 

775 

781 

788 

3 

4 

1.8 
2.4 

721 

794 

800 

806 

812 

818 

824 

830 

836 

842 

848 

5 

3.0 

722 

854 

860 

866 

872 

878 

884 

890 

896 

902 

908 

6 
7 
8 

3.6 
4.2 
4.8 

723 

914 

920 

926 

932 

938 

944 

950 

956 

962 

968 

724 

974 

980 

986 

992 

998 

*004  *010  *016  *022  *028 

9 

5.4 

725 

86   034 

040 

046 

052 

058 

064 

070 

076 

082 

088 

726 

094 

100 

106 

112 

118 

124 

130 

136 

141 

147 

727 

153 

159 

165 

171 

177 

183 

189 

195 

201 

207 

728 

213 

219 

225 

231 

237 

243 

249 

255 

261 

267 

729 

273 

279 

285 

291 

297 

303 

308 

314 

320 

326 

730 

332 

338 

344 

350 

356 

362 

368 

374 

380 

386 

731 

392 

398 

404 

410 

415 

421 

427 

433 

439 

445 

732 

451 

457 

463 

469 

475 

481 

487 

493 

499 

504 

733 

510 

516 

522 

528 

534 

540 

546 

552 

558 

564 

734 

570 

576 

581 

587 

593 

599 

605 

611 

617 

623 

735 

629 

635 

641 

646 

652 

658 

664 

670 

676 

682 

736 

688 

694 

700 

705 

711 

717 

723 

729 

735 

741 

737 

747 

753 

759 

764 

770 

776 

782 

788 

794 

800 

738 

806 

812 

817 

823 

829 

835 

841 

847 

853 

859 

739 

864 

870 

876 

882 

888 

894 

900 

906 

911 

917 

740 

923 

929 

935 

941 

947 

953 

958 

964 

970 

976 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

Logarithms  of  Numbers. 


801 


Num.  740  to  779.     Log.  869  to  892. 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

740 

86   923 

929 

935 

941 

947 

953 

958 

964 

970 

976 

741 

982 

988 

994 

999  *005 

*011  *017  *023  *029  *035 

742 

87   040 

046 

052 

058 

064 

070 

075 

081 

087 

093 

743 

099 

105 

111 

116 

122 

128 

134 

140 

146 

151 

744 

157 

163 

169 

175 

181 

186 

192 

198 

204 

210 

745 

216 

221 

227 

233 

239 

245 

251 

256 

262 

268 

746 

274 

280 

286 

291 

297 

303 

309 

315 

320 

326 

747 

332 

338 

344 

349 

355 

361 

367 

373 

379 

384 

748 

390 

396 

402 

408 

413 

419 

425 

431 

437 

442 

749 

448 

454 

460 

466 

471 

477 

483 

489 

495 

500 

750 

506 

512 

518 

523 

529 

535 

541 

547 

552 

558 

751 

564 

570 

576 

581 

587 

593 

599 

604 

610 

616 

752 

622 

628 

633 

639 

645 

651 

656 

662 

668 

674 

753 

679 

685 

691 

697 

703 

708 

714 

720 

726 

731 

754 

737 

743 

749 

754 

760 

766 

772 

777 

783 

789 

755 

795 

800 

806 

812 

818 

823 

829 

835 

841 

846 

756 

852 

858 

864 

869 

875 

881 

887 

892 

898 

904 

757 

910 

915 

921 

927 

933 

938 

944 

950 

955 

961 

6 

758 

967 

973 

978 

984 

990 

996  *001  *007  *013  *018 

759 

88   024 

030 

036 

041 

047 

053 

058 

064 

070 

076 

1 

2 

v.o 
1.2 

760 

081 

087 

093 

098 

104 

110 

116 

121 

127 

133 

3 
4 

1.8 
2.4 

761 

138 

144 

150 

156 

161 

167 

173 

178 

184 

190 

5 

3.0 

762 

195 

201 

207 

213 

218 

224 

230 

235 

241 

247 

6 

7 
8 

3.6 
4.2 
4.8 

763 

252 

258 

264 

270 

275 

281 

287 

292 

298 

304 

764 

309 

315 

321 

326 

332 

338 

343 

349 

355 

360 

9 

5.4 

765 

366 

372 

377 

383 

389 

395 

400 

406 

412 

417 

766 

423 

429 

434 

440 

446 

451 

457 

463 

468 

474 

767 

480 

485 

491 

497 

502 

508 

513 

519 

525 

530 

768 

536 

542 

547 

553 

559 

564 

570 

576 

581 

587 

769 

593 

598 

604 

610 

615 

621 

627 

632 

638 

643 

770 

649 

655 

660 

666 

672 

677 

683 

689 

694 

700 

771 

705 

711 

717 

722 

728 

734 

739 

745 

750 

756 

772 

762 

767 

773 

779 

784 

790 

795 

801 

807 

812 

773 

818 

824 

829 

835 

840 

846 

852 

857 

863 

868 

774 

874 

880 

885 

891 

897 

902 

908 

913 

919 

925 

775 

930 

936 

941 

947 

953 

958 

964 

969 

975 

981 

776 

986 

992 

997  *003  *009 

*014  *020  *025  *031  *037 

777 

89   042 

048 

053 

059 

064 

070 

076 

081 

087 

092 

778 

098 

104 

109 

115 

120 

126 

131 

137 

143 

148 

779 

154 

159 

165 

170 

176 

182 

187 

193 

198 

204 

780 

209 

215 

221 

226 

232 

237 

243 

248 

254 

260 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

S02 


Logarithms  op  Numbers. 


Num 

.  780  to  819. 

Log 

892  to  913. 

N 

L   o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

780 

89   209 

215 

221 

226 

232 

237 

243 

248 

254 

260 

781 

265 

271 

276 

282 

287 

293 

298 

304 

310 

315 

782 

321 

326 

332 

337 

343 

348 

354 

360 

365 

371 

783 

376 

382 

387 

393 

398 

404 

409 

415 

421 

426 

784 

432 

437 

443 

448 

454 

459 

465 

470 

476 

481 

785 

487 

492 

498 

504 

509 

515 

520 

526 

531 

537 

786 

542 

548 

553 

559 

564 

570 

575 

581 

586 

592 

787 

597 

603 

609 

614 

620 

625 

631 

636 

642 

647 

788 

653 

658 

664 

669 

675 

680 

686 

691 

697 

702 

789 

708 

713 

719 

724 

730 

735 

741 

746 

752 

757 

790 

763 

768 

774 

779 

785 

790 

796 

801 

807 

812 

791 

818 

823 

829 

834 

840 

845 

851 

856 

862 

867 

792 

873 

878 

883 

889 

894 

900 

905 

911 

916 

922 

793 

927 

933 

938 

944 

949 

955 

960 

966 

971 

977 

794 

982 

988 

993 

998  *004 

*009  *015  *020  *026  *031 

795 

90   037 

042 

048 

053 

059 

064 

069 

075 

080 

0S5 

796 

091 

097 

102 

108 

113 

119 

124 

129 

135 

140 

797 

146 

151 

157 

162 

168 

173 

179 

184 

189 

195 

5 

798 

200 

206 

211 

217 

222 

227 

233 

238 

244 

249 

799 

255 

260 

266 

271 

276 

282 

287 

293 

298 

304 

1 

2 

v.o 
1.0 

800 

309 

314 

320 

325 

331 

336 

342 

347 

352 

358 

3 
4 

1.5 

2.0 

801 

363 

369 

374 

380 

385 

390 

396 

401 

407 

412 

5 

2.5 

802 

417 

423 

428 

434 

439 

445 

450 

455 

461 

466 

6 
7 
8 

3.0 
3.5 
4.0 

803 

472 

477 

482 

488 

493 

499 

504 

509 

515 

520 

804 

526 

531 

536 

542 

547 

553 

558 

563 

569 

574 

9 

4.5 

805 

580 

585 

590 

596 

601 

607 

612 

617 

623 

628 

806 

634 

639 

644 

650 

655 

660 

666 

671 

677 

682 

807 

687 

693 

698 

703 

709 

714 

720 

725 

730 

736 

808 

741 

747 

752 

757 

763 

768 

773 

779 

784 

789 

809 

795 

800 

806 

811 

816 

822 

827 

832 

838 

843 

810 

849 

854 

859 

865 

870 

875 

881 

886 

891 

897 

811 

902 

907 

913 

918 

924 

929 

934 

940 

945 

950 

812 

956 

961 

966 

972 

977 

982 

988 

993 

998  *004 

813 

91   009 

014 

020 

025 

030 

036 

041 

046 

052 

057 

814 

062 

068 

073 

078 

084 

089 

094 

100 

105 

110 

815 

116 

121 

126 

132 

137 

142 

148 

153 

158 

164 

816 

169 

174 

180 

185 

190 

196 

201 

206 

212 

217 

817 

222 

228 

233 

238 

243 

249 

254 

259 

265 

270 

818 

275 

281 

286 

291 

297 

302 

307 

312 

318 

323 

819 

328 

334 

339 

344 

350 

355 

360 

365 

371 

376 

820 

381 

387 

392 

397 

403 

408 

413 

418 

424 

429 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

Logarithms  op  Numbers. 


803 


Num.  820  to  859.  Log.  913  to  934. 


5   6 


91  381  387  392  397  403 
434  440  445  450  455 
487  492  498  503  508 
540  545  551  556  561 
593  598  603  609  614 

645  651  656  661  666 

698  703  709  714  719 

'  751  756  761  766  772 

803  808  814  819  824 

855  861  866  871  876 

908  913  918  924  929 

960  965  971  976  981 

92  012  018  023  028  033 
065  070  075  080  085 
117  122  127  132  137 

169  174  179  184  189 

221  226  231  236  241 

273  278  283  288  293 

324  330  335  340  345 

376  381  387  392  397 

428  433  438  443  449 

480  485  490  495  500 

531  536  542  547  552 

583  588  593  598  603 

634  639  645  650  655 

686  691  696  701  706 

737  742  747  752  758 

788  793  799  804  809 

840  845  850  855  860 

891  896  901  906  911 

942  947  952  957  962 

993  998  *003  *008  *013 

93  044  049  054  059  064 
095  100  105  110  115 
146  151  156  161  166 

197  202  207  212  217 

247  252  258  263  268 

298  303  308  313  318 

349  354  359  364  369 

399  404  409  414  420 

4-50  455  460  465  470 


408  413  418  424  429 

461  466  471  477  482 

514  519  524  529  535 

566  572  577  582  587 

619  624  630  635  640 

672  677  682  687  693 

724  730  735  740  745 

777  782  787  793  798 

829  834  840  845  850 

882  887  892  897  903 

934  939  944  950  955 

986  991  997  *002  *007 

038  044  049  054  059 

091  096  101  106  111 

143  148  153  158  163 

195  200  205  210  215 

247  252  257  262  267 

298  304  309  314  319 

350  355  361  366  371 

402  407  412  418  423 

454  .459  464  469  474 

505  511  516  521  526 

557  562  567  572  578 

609  614  619  624  629 

660  665  670  675  681 

711  716  722  727  732 

763  768  773  778  783 

814  819  824  829  834 

865  870  875  881  886 

916  921  927  932  937 

967  973  978  983  988 

*018  *024  *029  *034  *039 

069  075  080  085  090 

120  125  131  136  141 

171  176  181  186  192 

222  227  232  237  242 

273  278  283  288  293 

323  328  334  339  344 

374  379  384  389  394 

425  430  435  440  445 

475  480  485  490  495 


*04 


Logarithms  of  Numbers. 


Num 

860  to  899. 

Log 

934  to  954. 

N 

L   0 

1 

2 

3 

4 

S 

6 

7 

8 

9 

P.  P. 

860 

93   450 

455 

460 

465 

470 

475 

480 

485 

490 

495 

861 

500 

505 

510 

515 

520 

526 

531 

536 

541 

546 

862 

551 

556 

561 

566 

571 

576 

581 

586 

591 

596 

863 

601 

606 

611 

616 

621 

626 

631 

636 

641 

646 

864 

651 

656 

661 

666 

671 

676 

682 

687 

692 

697 

865 

702 

707 

712 

717 

722 

727 

732 

737 

742 

747 

866 

752 

757 

762 

767 

772 

777 

782 

787 

792 

797 

867 

802 

807 

812 

817 

822 

827 

832 

837 

842 

847- 

868 

852 

857 

862 

867 

872 

877 

882 

887 

892 

897 

869 

902 

907 

912 

917 

922 

927 

932 

937 

942 

947 

870 

952 

957 

962 

967 

972 

977 

982 

987 

992 

997 

871 

94   002 

007 

012 

017 

022 

027 

032 

037 

042 

047 

872 

052 

057 

062 

067 

072 

077 

082 

086 

091 

0% 

873 

101 

106 

111 

116 

121 

126 

131 

136 

141 

146 

874 

151 

156 

161 

166 

171 

176 

181 

186 

191 

196 

875 

201 

206 

211 

216 

221 

226 

231 

236 

240 

245 

876 

250 

255 

260 

265 

270 

275 

280 

285 

290 

295 

877 

300 

305 

310 

315 

320 

325 

330 

335 

340 

345 

8 

878 

349 

354 

359 

364 

369 

374 

379 

384 

389 

394 

1 
2 

0.5 
1.0 

879 

399 

404 

409 

414 

419 

424 

429 

433 

438 

443 

880 

448 

453 

458 

463 

468 

473 

478 

483 

488 

493 

3 
4 

1.5 
2.0 

881 

498 

503 

507 

512 

517 

522 

527 

532 

537 

642 

5 

2.5 

882 

547 

552 

557 

562 

567 

571 

676 

581 

586 

591 

6 

7 
8 

3.0 
3.5 
4.0 

883 

596 

601 

606 

611 

616 

621 

626 

630 

635 

640 

884 

645 

650 

655 

660 

665 

670 

675 

680 

685 

689 

9 

4.5 

885 

694 

699 

704 

709 

714 

719 

724 

729 

734 

738 

886 

743 

748 

753 

758 

763 

768 

773 

778 

783 

787 

887 

792 

797 

802 

807 

812 

817 

822 

827 

832 

836 

888 

841 

846 

851 

856 

861 

866 

871 

876 

880 

885 

889 

890 

895 

900 

905 

910 

915 

919 

924 

929 

934 

890 

939 

944 

949 

954 

959 

963 

968 

973 

978 

983 

891 

988 

993 

998  *002  *007 

*012  *017  *022  *027  *032 

892 

95   036 

041 

046 

051 

056 

061 

066 

071 

075 

080 

893 

085 

090 

095 

100 

105 

109 

114 

119 

124 

129 

894 

134 

139 

143 

148 

153 

158 

163 

168 

173 

177 

895 

182 

187 

192 

197 

202 

207 

211 

216 

221 

226 

8% 

231 

236 

240 

245 

250 

255 

260 

265 

270 

274 

897 

279 

284 

289 

294 

299 

303 

308 

313 

318 

323 

898 

328 

332 

337 

342 

347 

352 

357 

361 

366 

371 

899 

376 

381 

386 

390 

395 

400 

405 

410 

415 

419 

900 

424 

429 

434 

439 

444 

448 

453 

458 

463 

468 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

Logarithms  of  Numbers. 


S05 


Num.  900  to  939.  Log.  954  to  973. 


95  424  429  434  439  444 

472  477  482  487  492 
521  525  530  535  540 
569  574  578  583  588 
617  622  626  631  636 

665  670  674  679  684 

713  718  722  727  732 

761  766  770  775  780 

809  813  818  823  828 

856  861  866  871  875 

904  909  914  918  923 

952  957  961  966  971 

999  *004  *009  *014  *019 

96  047  052  057  061  066 
095  099  104  109  114 

142  147  152  156  161 

190  194  199  204  209 

237  242  246  251  256 

284  289  294  298  303 

332  336  341  346  350 

379  384  388  393  398 

426  431  435  440  445 

473  478  483  487  492 
520  525  530  534  539 
567  572  577  581  586 

614  619  624  628  633 

661  666  670  675  680 

708  713  717  722  727 

755  759  764  769  774 

802  806  811  816  820 

848  853  858  862  867 

895  900  904  909  914 

942  946  951  956  960 

988  993  997  *002  *007 

97  035  039  044  049  053 

081  086  090  095  100 

128  132  137  142  146 

174  179  183  188  192 

220  225  230  234  239 

267  271  276  280  285 

313  317  322  327  331 


448  453  458  463  468 

497  501  506  511  516 

545  550  554  559  564 

593  598  602  607  612 

641  646  650  655  660 

689  694  698  703  708 

737  742  746  751  756 

785  789  794  799  804 

832  837  842  847  852 

880  885  890  895  899 

928  933  938  942  947 

976  980  985  990  995 

*023  *028  *033  *038  *042 

071  076  080  085  090 

118  123  128  133  137 

166  171  175  180  185 

213  218  223  227  232 

261  265  270  275  280 

308  313  317  322  327 

355  360  365  369  374 

402  407  412  417  421 

450  454  459  464  468 

497  501  506  511  515 

544  548  553  558  562 

591  595  600  605  609 

638  642  647  652  656 

685  689  694  699  703 

731  736  741  745  750 

778  783  788.  792  797 

825  830  834  839  844 

872  876  881  886  890 

918  923  928  932  937 

965  970  974  979  984 

*011  *016  *021  *025  *030 

058  063  067  072  077 

104  109  114  118  123 

151  155  160  165  169 

197  202  206  211  216 

243  248  253  257  262 

290  294  299  304  308 

336  340  345  350  354 


SOU 


LOGARITHMS    OP    NUMBERS. 


Num. 

940  to  979. 

Log. 

973  to  991. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

940 

97   313 

317 

322 

327 

331 

336 

340 

345 

350 

354 

941 

359 

364 

368 

373 

377 

882 

387 

391 

396 

400 

942 

405 

410 

414 

419 

424 

428 

433 

437 

442 

447 

943 

451 

456 

460 

465 

470 

474 

479 

483 

488 

493 

944 

497 

502 

506 

511 

516 

520 

525 

529 

534 

539 

945 

543 

548 

552 

557 

562 

566 

571 

575 

580 

585 

946 

589 

594 

598 

603 

607 

612 

617 

621 

626 

630 

947 

635 

640 

644 

649 

653 

658 

663 

667 

672 

676 

948 

681 

685 

690 

695 

699 

704 

708 

713 

717 

722 

949 

727 

731 

736 

740 

745 

749 

754 

759 

763 

768 

5 

950 

772 

777 

782 

786 

791 

795 

800 

804 

809 

813 

1 

0.5 

951 

818 

823 

827 

832 

836 

841 

845 

850 

855 

859 

2 
3 

4 

1.0 
1.5 
2.0 

952 

864 

868 

873 

877 

882 

886 

891 

8% 

900 

905 

953 

909 

914 

918 

923 

928 

932 

937 

941 

946 

950 

5 

2.5 

954 

955 

959 

964 

968 

973 

978 

982 

987 

991 

996 

6 

7 

3.0 
3.5 

955 

98   000 

005 

009 

014 

019 

023 

028 

032 

037 

041 

8 
9 

4.0 
4.5 

956 

046 

050 

055 

059 

064 

068 

073 

078 

082 

087 

957 

091 

096 

100 

105 

109 

114 

118 

123 

127 

132 

958 

137 

141 

146 

150 

155 

159 

164 

168 

173 

177 

959 

182 

186 

191 

195 

200 

204 

209 

214 

218 

223 

960 

227 

232 

236 

241 

245 

250 

254 

259 

263 

268 

961 

272 

277 

281 

286 

290 

295 

299 

304 

308 

313 

962 

.  318 

322 

327 

331 

336 

340 

345 

349 

354 

358 

963 

363 

367 

372 

376 

381 

385 

390 

394 

399 

403 

964 

408 

412 

417 

421 

426 

430 

435 

439 

444 

448 

965 

453 

457 

462 

466 

471 

475 

480 

484 

489 

493 

4 

966 

498 

502 

507 

511 

516 

520 

525 

529 

534 

538 

1 

0.4 

967 

543 

547 

552 

556 

561 

565 

570 

574 

579 

583 

2 

0.8 
1.2 
1.6 
2.0 

968 

588 

592 

597 

601 

605 

610 

614 

619 

623 

628 

3 
4 
5 

969 

632 

637 

641 

646 

650 

655 

659 

664 

668 

673 

970 

677 

682 

686 

691 

695 

700 

704 

709 

713 

717 

6 

7 

2.4 

2.8 

971 

722 

726 

731 

735 

740 

744 

749 

753 

758 

762 

8 

3.2 

972 

767 

771 

776 

780 

784 

789 

793 

798 

802 

807 

9 

3.6 

973 

811 

816 

820 

825 

829 

834 

838 

843 

847 

851 

974 

856 

860 

865 

869 

874 

878 

883 

887 

892 

8% 

975 

900 

905 

909 

914 

918 

923 

927 

932 

936 

941 

976 

945 

949 

954 

958 

963 

967 

972 

976 

981 

985 

977 

989 

994 

998  *003  *007 

*012  *016  *021  *025  *029 

978 

99   034 

038 

043 

047 

052 

056 

061 

065 

069 

074 

979 

078 

083 

087 

092 

0% 

100 

105 

109 

114 

118 

980 

123 

127 

131 

136 

140 

145 

149 

154 

158 

162 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

Logarithms  op  Numbers. 


807 


Num. 

980  to  1000. 

Log 

.  991  to  999. 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9, 

P.  P. 

980 

99   123 

127 

131 

136 

140 

145 

149 

154 

158 

162 

981 

167 

171 

176 

180 

185 

189 

193 

198 

202 

207 

982 

211 

216 

220 

224 

229 

233 

238 

242 

247 

251 

983 

255 

260 

264 

269 

273 

277 

282 

286 

291 

295 

984 

300 

304 

308 

313 

317 

322 

326 

330 

335 

339 

985 

344 

348 

352 

357 

361 

366 

370 

374 

379 

383 

986 

388 

392 

3% 

401 

405 

410 

414 

419 

423 

427 

987 

432 

436 

441 

445 

449 

454 

458 

463 

467 

471 

988 

476 

480 

484 

489 

493 

498 

502 

506 

511 

515 

'  989 

520 

524 

528 

533 

537 

542 

546 

550 

555 

559 

4 

990 

564 

568 

572 

577 

581 

585 

590 

594 

599 

603 

1 

0.4 

991 

607 

612 

616 

621 

625 

629 

634 

638 

642 

647 

2 
3 

4 

0.8 
1.2 

1.6 

992 

651 

656 

660 

664 

669 

673 

677 

682 

686 

691 

993 

695 

699 

704 

708 

712 

717 

721 

726 

730 

734 

5 

2.0 

994 

739 

743 

747 

752 

756 

760 

765 

769 

774 

778 

6 

7 

2.4 
2.8 

995 

782 

787 

791 

795 

800 

804 

808 

813 

817 

822 

8 
9 

3.2 
3.6 

996 

.   826 

830 

835 

839 

843 

848 

852 

856 

861 

865 

997 

870 

874 

878 

883 

887 

891 

896 

900 

904 

909 

998 

913 

917 

922 

926 

930 

935 

939 

944 

948 

952 

999 

957 

961 

965 

970 

974 

978 

983 

987 

991 

996 

1000 

000   000 

043 

087 

130 

174 

217 

260 

304 

347 

391 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

Logarithms  of  Important  Numbers. 


Number. 

Logarithm. 

It 

= 

3.141  593 

0.497  150 

If 

= 

4.188  790 

0.622  089 

fr 

= 

0.523  599 

1.718  999 

l 

= 

0.318  310 

"1.502  850 

7r2 

= 

9.869  604 

0.994  300 

1 

= 

0.101  321 

1.005  700 

vz 

= 

1.772  454 

0.248  575 

1 

= 

0.564  190 

1.751  425 

fm 

= 

1.464  592 

0.165  717 

1 

= 

0.682  784 

1.834  283 

- 

1.240  701 

0.093  667 

INDEX. 


a,  8,  45,  47,  49,  54 
Acacia,  679 

Accommodation  ladders,  472 

Acres  in  hectares,  731 

Adjustable   terminal,   exhaust   pipes, 

555    556 
Admiralty  cables,  615-618 
"  constant,  262 

knot,  701 
"  turnbuckles,  527 

Agriculture,  dept.  of  regulations,  171 
Air,  679 
Alder,  679 
Algebraical  signs,  ix 
Alleyways,  cattle,  172 
Allowances  for  splices,  577 
Alteration  in  trim  through  shipping 

a  weight,  20 
Aluminum,  cast,  679 
sheet,  679 
bronze,  679 
Analysis  data,  Kirk's,  153-157 
Anchor  gears,  431 
Anchors,  394-400 

mooring,  624,  625 
Angle-steel,  weight  of,  232-237 
Angle-bulb,  weight  of,  236 
Animals,  space  allotted  to,  172 
Antimony,  679 
Anthracite,  679 
Apple  wood,  679 

Approximate  rule  for  C.  of  B.,  12,  45 
rule  for  L.  B.  M.,  17 
"  rule  for  M",  19 

Area  of  circles,  697,  744-750 
"  of  lightening  holes,  246 
"    of  L.  W.  L.  and  coefficient  a,  8, 

45,  47,  48,  54 
"    of   midship   section  and  coeffi- 
cient/3, 10 
"    of  propeller  brackets,  169,  170, 

362 
"    of  water  plane,  7 
Armor,  weight  of,  245 
Asbestos  board,  679 
Ash,  679 
Asphalt,  679 

Awning  decked  vessel,  99,  110,  133 
Axes,  fire,  654 


8,  10,  45,  47,  48,  57 
Babbit  metal,  679 
Balanced  rudders,  166,  357 


Bar  keel,  351,  352 

Barley,  679 

Barrels,  654 

Basalt,  679 

Battening  bar,  381 

Beam  bending  moments,  286,  287 

"     camber,  51,  371 

"     collars,  376 

"    -knees,  372,  373,  375 
Beams,  371-376 
Beckets,  592 
Beech,  679 

Belay  pins,  size  of,  414 
Bell,  metal,  679 
Bells,  proportions  of  ship's,  413 

"     size  and  weight  of,  414 
Bending  moments  of  pins,  322,  323 

"      moments  of  stress,  280 
Bevel  gear,  formula  for,  405 
Bilge  diagonal  coefficient,  45,  47,  48, 

55,  57 
Bethlehem  guns,  570,  571 
Birch,  679 
Bismuth,  679 
Bitts,  towing,  504 
Bituminous  coal,  679 
Bitumastic  cement,  370 

"  cement  solution,  679 

Blake  stopper,  613 
Block  coefficient,  8,  7,  45,  47,  48 
Blocks,  590-597 

25-ton,  424 

"       cat  and  fish,  591 

"       cargo,  597 

"       clump,  591 

"       cheek,  591 

"       fiddle,  590 
gin,  591 
snatch,  419,  590 

"       wrecking,  591 

"       sheaving  for,  591 

"       shackles  for,  591 

standard  iron,  422,  423 

"       weight  of,  595 

u       U.  S.  Navy,  596 
Board  of  Trade  Regulations,  634-645 
Boat  crane,  navy,  432 

"    davits,  432-449 
Boats,  626-634 

"      proportions  of,  627 

"      scantlings  of,  628,  630,  631 

"      rules  and  regulations,  634-655 

"      weight  of,  449 


809 


810 


Index 


Body  plan  of  "Oceanic,"  57 

"     poet,  354 
Boilers,  U.  S.  law,  655 
Bollards,  proportions,  417 
Bollards,  size  and  weight  of,  418 
Bolts  and  nuts,  U.  S.  Standard,  427, 
428 
"     and  nuts,  Whitworth  Standard, 

688 
"     and  nuts,  weight  of,  426,  427, 
689 
B.  M.,  13 

Boom  mountings,  514-516 
Boss  barrel,  59,  170,  362 
Bossing  around   shafts,    58,    59,    170, 
363,  364 
"      fairing  the,  58,  59,  170 
Bottom  half-breadth,  5 
Boxes,  stuffing,  523 
Boxwood,  679 
Braces,  355,  361 
Bracket  knees,  372,  373,  375 
Brackets,  area  of  propeller,  169,  170, 

362 
Brake,  friction,  for  cranes,  542-548 
"      cone,  for  gantry  crane,  544 
Brass,  679 

"     sidelights,  weight  of,  513 
"      wire,  679 
Breaking  strength  of  chains,  3 10,  311 
Brick,  679 
Brickwork,  679 
Bridge  house,  87,  110,  376 
Bridle  beams,  381 
British  Corporation,  rudder  formula, 

168 
British  Board  of  Trade  regulations, 

634-645 
Bronze,  679 
Buckets,  fire,  654 
Builders'   old  measurement  tonnage, 

678 
Built  columns,  377 
Bulb  angle,  weight  of,  215-220 
"     plate,  weight  of,  221-224,  241 
"     section,  Lloyd's,  247 
"     tee,  weight  of,  223-230,  240 
Bulkhead  collars,  365,  383 
"         collision,  384 
liners,  383 
plating,  384 
"         stiff eners,  384 
Bulkheads,  383,  384 
Bullivant's  thimbles,  524 
Burton,  Spanish,  599 
Butts,  plating,  386 
"      shift  of,  386 
Buttstraps,  Lloyd's  table  of,  336,  337 
"  strength  of  riveted,  343 

U.  S.  Navy,  table  of,  334 


Tables,  admiralty,  615-618 
Calculation  of  (i.  Z„  40,  41 
Calculations,  ship,  1-280 
Calories  into  thermal  units,  737 
Camber  of  ways,  162 
Camphor,  680 
Capacities  of  circular  tanks,  692 

of  lifeboats,  639,  648,  652 
"  of  rectangular  tanks,  690, 

691 
Carlings,  376 
Cast  steel  rudder,  356 

"    steel,  weight  of,  680 
Cat  and  fish  blocks,  591 
Cattle  alleyways,  172 

"      fittings,  weight  of,  172 
"      transport  of,  171 
Catting  hooks,  430 
Caulking,  384 
Cedar,  680 
Ceiling  on  tanks,  370 
Cement,  bitumastic,  370 
Louisville,  680 
Portland,  680 
Roman,  680 
Centimetres  to  inches,  726 
Centre  keelson,  351,  352 

"      of  buoyancy,  11,  17,  26,  27,  45, 
"      of  buoyancy  by  Tchibyscheff 's 

rule,  26,  27 
"      of    buoyancy    longitudinally, 

12,  18,  25 
"      of  flotation,  16,  18,  29 
"       of  gravity,  251-253 
"       of  gravity  coefficient  "g,"  45, 

48 
"       vertical  girder,  351,  352,  368 
Chafing  pieces,  384 
Chain  plates,  428 

"     slips,  proportions,  513 
"     rigging,  593 
"     swivel,  622 
Chalk,  680 
Change  of  trim,  18 
Channel  bars,  weight  of,  238 

floors,  367 
Characteristic  of  logarithm,  782 
Charcoal,  680 
Cheek  blocks,  591 
Cherry,  680 
Chestnut,  680 

Cheval-vapeur  into  horse-power,  736 
Circle,  formulae  for,  743 
Circles,    circumference   and   area   of, 

697,  698 
Circumference    and    area   of    circles, 

744-750 
Clay,  680 
Cleats,  belay,  425 
"      hatch,  380 
Clips,  wire  rope,  584 


Index 


811 


Club  shackle,  621 
Clump  blocks,  591 
Coal,  680 

Coefficient  a,  8,  45,  47,  48,  54 
0,  10,  45,  47,  48,  57 
5  (fineness),  7,  45,  47,  48, 

75 
g  (gravity),  48 
"        i  (inertia),  49 
Coir  rope,  589 
Collars,  beams,  376 

"  bulkhead,  365,  383 
Collision  bulkhead,  383 
Columns,  built,  377 

"      strength  of,  302-311 
Compressive  stress,  280 
Cone  brake  for  gantry,  544-548 
Constants,  admiralty,  262,  263 
Corner  angles,  hatch,  380 
Correction  for  variations  (freeboard) , 

93 
Cotton  rope,  589 
Countersink,  Lloyd's,  335 

"  point  rivets,  487 

Coupling  bolts,  355,  361 

"      palm  (rudder),  355,  356,  361 
Covers,  hatch,  381 
Cowl  ventilators,  557-558 
Cowls,  weight  of,  559 
Crane  hooks,  429 

Cranes,  dimensions  of   anchor,    406- 
411 
"      notes  on  anchor,  412 
"      stresses  on,  402—404 
Cross  curves  of  stability,  42 
Cubic  centimetres  into  cubic  inches, 
732 
"      decimetres  into  cubic  feet,  732 
"      feet  into  cubic  decimetres,  732 
"      inches  into  cubic  centimetres, 

732 
"      metres  into  cubic  yards,  730 
"      yards  into  cubi«  metres,  730 
Cut  frames,  365 
Cypress,  680 

S,  coefficient,  7,  45,  47,  48,  72 
Davit  heads,  448 
Data,  Kirk's  analysis,  153-157 
"      launching,  161,  162 
"      steamers,  276,  277 
Davits,  Board  of  Trade  Rules,  445- 
447 
"       diameters  of,  449 
"       mallory,  433,  436,  437 
"       mine,  440, 
"       rotating,  433 
"       screw  gear,  442 

swan-neck,  437,  438 
*'       Welin,  443 
Deck  girders,  376 


Deck  seats,  509-511 

"      line,  86 
Declivity  of  ways,  162 
Deductions  for  erections  (freeboard), 

93 
Deep  framing,  366 

Department    of    agriculture    regula- 
tions, 171 
Derrick  rigging,  604,  605 
Design,  44-63 

Designing  the  bossing,  58,  59 
Details  of  fittings,  389 

of  standardizing,  389 
"      of  structure,  350 
Details,  the  preparation  of,  391 
Diagram  of  bilge  diagonals,  55 
Diagram  of  L.  W.  L.  half-breadths,  56 
Diamond  wire  rope  blocks,  420,  421 
Dimensions  for  freeboard,  73 
"  for  tonnage,  667 

Disc  friction  brake,  547 
Displacement,  1,  6,  24,  25 
"  sections,  4 

sheet     by     Tchiby- 
scheff's  rule,  24 
Displacement  table,  6,  24 
Distances  from  colon,  721 
Division  boards,  cattle,  172 
Donkey  boiler,  655 
Doubling  plates,  379,  388 
Doublings  at  breaks,  388,  389 
"        at  hatchways,  379 

e,  relation  coefficient,  47,  48 
Earth,  680 
Ebony,  680 

Effect  of  form  of  waterline,  34-37 
Effective  horse-power,  270-271 
Elasticity,  280 
Elements  of  angles,  313-314 
"       of  bulb-angles,  315 
'*       of  circular  sections,  293 
"       of   coefficients   for   various 
types,  44,  47,  48 
of  deck  beams,  316,  317 
"       of  marine  engines,  60,  61 
of  sections,  284,  285 
of  tee  bars,  318,  319 
of  zee  bars,  320,  321 
Elm,  680 

Elswick  guns,  560-562 
Emergency  chains,  356 
Emery,  680 
End  floors,  367 
Engine  room  lengths,  63 
Engines,  elements  of  marine,  60,  61 
Equipment,  607-625 

Lloyd's,  607,  610 
numerals,  608,  609 
Explanation  of  tables  of  metacentres, 
31-33 


812 


Index 


Exponent  of  logarithm,  783 
Eyebolts,  standard,  454 
Eyes,  pad,  468 
"      worked,  603 

Factors,  useful,  powers  and  roots,  700 

"       of  safety,  282,  283 
Fairing  the  bossing,  58,  59 

"     the  oxter,  62 

"     plate  lines,  384,  385,  387 
Fairleads,  proportions  of,  455 

"         weight  of,  455 
Falls,  cargo  and  purchase,  580,  604, 

605 
Feet  to  metres,  726 
Fiddle  blocks,  590 
Figureheads  and  lacing  pieces,  52 
Fir,  680 

Fitting  of  pillars,  379 
Fittings,  details  of,  389 

"        weight  of  cattle,  172 

"        weight  of  horse,  173 
Fixed  terminals,  exhaust  pipes,  554 
Flagging,  680 
Flanges,  lead  pipe,  456 

standard  pipe,  457 

"      ventilation,  458 
Flanged  floors,  368,  369 
Flat  plate  keels,  351,  352 
Flexible  steel  wire  ropes,  578-580 
Flint,  680 

Floor  brackets,  369,  370 
Floors,  368,  369 
"      at  ends,  369 
"      channel,  369 
"      flanged,  368,  369 
"      in  inner  bottom,  370 
"      ordinary,  369 
"      watertight,  369 
Flush  deck  vessel,  109,  112 
Footboards,  cattle,  172 
Footlocks,  cattle,  172 
Footpounds  into  kilogrammetres,  736 
Foot  tons  into  tonnes-metres,  737 
Foreign  weights  and  measures,  706- 

710 
Formulae  for  the  circle,  744-750 
Fractions,  squares,  cubes  and  fourth 

powers,  699,  700 
Frame  doublings,  363,  364,  365 

"      riveting,  347 
Framing,  364,  365 

"  of  superstructure,  364,  365 
Franklin  Institute  standard  bolts,  427 
Freeboard,  73-152 

"  examples,  77 

"  marks,  111 

"  tables,  note  on,  86 

tables,  87,  115 
Freeboards  for  awning   deckers,    99, 
133 


Freeboards  for  freighters,  114 

"         for  sailing  vessels,  101,  142 

for  shelter  deckers,  105 
"         for  spar  deckers,   77,   89, 

127 
"         for  turret  steamers,  102 
"         for  winter  North  Atlantic, 
93 
Freeing  port  area,  91 
Freestone,  680 
French  measures,  725 
Friction  brake  for  cranes,  542-548 
Froude's  Law  of  Comparisons,  187 
Functions,    natural    trigonometrical, 

738-742 
Furnaced  plates,  387 

Gaff  mountings,  519-522 

Garboard  strake,  350,  351 

Germanischer    Lloyd's,    rudder    for- 
mula, 168 

Gin  blocks,  591 

Glands,  stuffing  boxes  and,  523 

Glass,  681 

Gold,  681 

Grains  into  grammes,  735 

Grammes  into  grains,  735 
"         into  ounces,  735 

Granite,  681 

Graphite,  681 

Greenheart,  681 

Gudgeons,  352,  353,  359 

Gum,  681 

Gun  tackle  purchase,  599 

Guns  and  mountings,  weight  of,  560- 
573 

Gunmetal,  681 

Guys,  604,  605 

Guy  purchase,  604,  605 

Gypsum,  681 

Hall  anchors,  296,  397 
Hand  wheels,  standard,  459,  460 
Hatch,  balanced  armor,  415,  416 
cleats,  380 

"       corner  doublings,  380 

"       covers,  381 
edges,  381 

"       fore  and  afters,  381 

"       lashing  rings,  381 

"       wedges,  381 
Hatches,  379 

Hatching,  standard  sectional,  392 
Hawse  pipes,  proportions  of,  462 

"    ■  pipes,  weight  of,  463 
Hawthorn,  681 
Hay,  681 
Hazel,  681 

Headboards,  cattle,  172 
Hectares  into  acres,  731 
Heel  bearing  of  rudders,  356 


Index 


813 


Heels,  stanchion,  379 
Hemlock,  681 
Hemp  cordage,  588 

"      rules  for  strength  of,  588 
Hold  pillars,  377-379 
Holes  through  shell,  386,  387 
Hollow  pillars,  weight  of,  231 
Hood  end  plates,  353,  389 
Hooks,  various,  464 

cargo,  465 

swivel,  466 

trip,  467 

for  blocks,  592 

for  catting,  430 

crane,  429 

match,  592 

sister,  592 
Hornbeam,  681 
Horse  fittings,  weight  of,  173 

"     stalls,  172 
Horse-power  into  cheval  vapeur,  736 
Houseline,  589 

I  section,  weight  of,  205-210 
Ice,  681 

Immersion,  passing  from  salt  to  fresh 
water,  9 
"  tons  per  inch,  8 

Inch,  graphic  division  of  the,  393 
Inches  to  centimetres,  726 
India  rubber,  681 
Indicated  horse-power,  271,  277. 
Inertia  coefficient,  17,  44 

"      moment  of,  281,  284,  285,  287, 

288,  291,  292,  293 
"      moment  of  for  circular   sec- 
tions, 292,  293 
Inglefield  anchors,  400 
Inner  bottoms,  370 
Inspection  laws,  American  and  British, 

634-655 
Intercostal  plates,  382 
Interlocking  rubber  tiling,  681 
International  rules,  1897,  656-662 
Iron,  cast,  681 

"      wrought,  681 
Ironwood,  681 
Ivory,  681 

Jackwood,  681 

Jogging,  387 

Johnson's  formula  for  columns,  296 
"         formula  for  steel  hulls,  176 

Keel  doublings,  353 

"     scarphs,  351 
Keels,  351,  352 
Keelsons,  382,  383 
Kenter  shackle,  623 
Keys  and  key  ways,  461 

"     plug  cock,  476 


Kilogrammes  into  pounds,  734 

per  sq.  cm.  into  lbs.  per 
sq.  inch,  733 
Kilogrammetres  into  foot-pounds,  736 
Kilometres  into  sea  miles,  727 

"         into  statute  miles,  727 
Kirk's  analysis,  153-157 
Knees,  beam,  372,  373,  375 

"      bracket,  373 
Krupp  guns,  568,  569 

Laburnum,  681 

Lacing  pieces,  52 
Lancewood,  681 
Landings,  388 
Larch,  681 
Lashing  rings,  381 
Launching,  159,  161 

curves,  159,  161 
data,  160,  161 
"  periods,  159 

L.  W.  L.  area  of,  8,  45,  47,  48,  54 
Lead,  cast,  681 

"      sheet,  681 
Least  radius  of  gyration  of  various 

sections,  284,  285,  295 
Ledges,  hatch,  381 
Lewis  bolt,  471 
Lifeboats,  633-655 
Life-floats,  650 
Life-preservers,  644,  645,  651 
Life-rafts,  643,  650 
Lifting  rings,  381 
Light  screens,  657 
Lightening  holes,  246 
Lignum  vitae,  681 
Lime,  681 
Limestone,  681 
Lime  wood,  682 
Liners,  370 

"       at  overlaps,  388 
bulkhead,  384 
Linoleum,  682 

Litres  into  U.  S.  gallons,  729 
Lloyd's  equipment  rule,  607 
"       riveting  table,  336 
"       rudder  formula,  166 
L.  M.  C.  by  Tchibyscheff's  rule,  28,  29 
Load  draught  diagrams,  108,  113 
"     line  diagram,  56 
"     line  half  breadths,  53 
Logarithms  of  numbers,  782-807 

"  of    important     numbers, 

807 
Longitudinal  metacenter,   16,   17,   28, 

29,  31,  34,  45 
Longitudinals,  383 
Lucania,   Tchibyscheff    sections    for, 

23 
Luff  tackle  purchase,  599 


814 


Index 


Mahogany,  682 
Manholes  in  inner  bottoms,  370 
Manila  ropes,  586-589 
Mantissa  of  logarithm,  783 
Maple,  682 
Marble,  682 

Margin  plate  in  tanks,  388,  389,  390 
Marine  engines,  elements  of,  60,  61 
Marline,  589 

Mathematical  tables,  724-807 
Metacentre,  longitudinal,  16,   17,   28, 
29,  31,  34,  35 
transverse,  13,  30,  33,  36, 
37.  45 
Metres,  into  feet,  726 

into  yards,  730 
Metric  system,  725 

"       tons  into  tons,  734 
Mica,  682 

Middendorf's  method,  271 
Midship  section  area,  10 
Mid.  area  coefficient  /3,  10,  45,  47,  48 
Millimetre,  725 
Mitre  gear,  formula  for,  406 
Modulus  of  elasticity,  280 
Moment  of  inertia,  256,  281,  284,  285, 
287,  288,  291,  292,  293 
"       of   inertia    of    circular    sec- 
tions, 292,  293 
"       of  inertia  of  waterline  coeffi- 
cients, 49 
"       of  inertia  of  water  plane,  14 
of  resistance,  282,  284,  285, 
287,  289,  291,  292 
"        to  alter  trim  one  inch,  19 
"        to  change  trim,  17 
Monkey  forecastle,  109 
Mooring  anchors,  624,  625 
"        pipes,  474 
"       swivel,  612 
Mortar,  682 

Multipliers  for  subdivided  intervals,  3 
for  Tchibyscheff's  rule,  22 
Mushroom  mooring  anchors,  624,  625 
Muntz  metal,  682 

Natural  sines,  738-742 

"      trigonometrical       functions, 
738-742 
Nautical  mile,  701 
Neutral  surface,  282,  283 
New  York  Yacht  Club  racing  rules, 

672-678 
Nickel,  682 
Nitric  acid,  682 
Norman  head,  354 
Notes  on  wire  rope,  308,  309 
Numbers,  logarithms  of,  782-807 

"         powers  and  roots  of,   751- 
782 
Nuts,  U.  S.  standard,  426,  427 


Oak,  682 

"Oceanic"  body  plan  of,  57 
Oil  fuel  chart,  685 

"  fuel  data,  686 

"  linseed,  682 

"  olive,  682 

"  petroleum,  682 

"  whale,  682 
Openings,  tonnage,  105 
Ordered  lengths  of  rivets,  488-492 
Ore,  red  iron,  682 
"    brown,  682 
"    Clydesdale,  682 
Oregon  pine,  682 
Ounces  into  grammes,  735 
Oxter,  fairing  the,  62 


x,  744 

Pad  eyes,  standard,  468,  469 

"    eyes,  reversible,  470 
Paper,  building,  682 
Parcelling  and  serving,  585 
Parson's  turbines,  60 
Pens,  cattle,  171 
"     sheep,  172 
Permanent  set,  281 
Petroleum,  refined,  682 
Texas,  682 
Pewter,  683 
Phosphor  bronze,  682 
Physical  properties  of  timber,  305 
Pillar  heads  and  heels,  378 
Pillars,  hold,  377-379 

"      pipe,  299 

"      weight  of  tubular,  244 
Pins,  belay,  414 

'     moments  on,  322,  323 
"     standard  toggle,  525 
Pine,  Georgia,  683 
Pintles,  353,  355,  360 
Pipe,  300-303,  378,  379 
Pitch,  682 
Pitch  pine,  683 
Plate  lines,  385 
Plating,  shell,  384-389 
Platinum,  683 
Plough  steel,  575 
Plug  cock,  keys,  476 
Plumbago,  683 
Poop,  109 
Poplar,  683 

Pounds  per  sq.  inch  into  atmospheric 
pressure,  733 

"       per  sq.  inch  into  kilogrammes 
per  sq.  cm.,  733 

"       into  kilogrammes,  734 
Powers  and  roots  of  numbers,   751- 

782 
Pressed  plate  chocks,  365 
Pressure  on  dog-shores,  164 


Index 


815 


Pressure  of  water  at  various  heads, 

693 
Prismatic  coefficient,  10,  45,  47,  48 
Proof  load  for  chain,  310 
"      of  Simpson's  rule,  3 
"      of  strength,  279 
Propeller  brackets,  area  of,  169,   170, 
362 
struts,  168-170,  362,   363 
"        struts,    Simpson's   formula, 
168 
Proportions  of  chain  slips,  513 
of  towing  bitts,  504 
"  of  ventilating  cowls,  558 

of  ship's  bells,  413 

Quartz,  683 

Radius  of  gyration,  282 
Rail  half  breadths,  53 
Raised  quarter  deck,  109 
Range  lights,  658 
Ratlines,  585 
Reels,  length  of,  589 
Regulations,  Board  of  Trade,  634-645 
Dept.  of  Agriculture,  171 
"  U.   S.    Inspection,    646- 

655 
Relation  coefficient,  45,  47,  48 

"        of    the    coefficients    to    one 
another,  47 
Resilience,  280 
Resistance  of  framing,  364 

moment  of,  282,  284 
of  ships,  262-275 
form  of  least,  271-275 
skin,  264-266,  271 
"  wave-making,  264-266, 

271 
Reverse  frames,  365-366 
Rigging,  derrick,  604,  605 
"        and  ropes,  575-605 
"        standing,  575 
"        chain,  593    . 
ropes,  578-581 
screws,  526,  527 
Ring  plates,  493 
Rings,  proportions  of,  479-487 

"      wrought  iron,  478 
Riveting  of  boss,  353 

U.  S.  Navy  standard,  328 
Lloyd's,  340 
strength  of,  342-347 
Rivets,  standard,  338 

ordered  lengths  of,  488-492 
Roots  and  powers  of  numbers,   751- 

782 
Rope,  coir,  589 

"      hemp,  586,  588 
"      manila,  586,  587 
"      small  stuff,  589 


Rope,  cotton,  589 
wire,  575 
"      end  fittings,  584,  585 
Ropes,  586-589 

rigging  and,  575-605 
Round  bar,  weight  of,  211 

"       of  beam  (freeboard),  97 
Rudder,  area,  165,  166 
arms,  355 
balanced,  166,  357 
cast  steel,  356 
coupling  bolts,  355,  361 
coupling  palm,  355,  356,  361 
carriers,  358,  359,  360 
emergency  chains,  356 
heel  bearing,  356 
tail  plates,  360 
trunks,  360 
post,  354 

stock,  166,  167,  168,  355 
Rule  for  moment  to  alter  trim,  19 
"     for  moment  to  change  trim,  17, 

18 
"     for  ordering  rivets,  345 
"     for  pressure  on  dog  shores,  164 
"     for  pressure  on  rudder,  165 
'     for  prismatic  coefficient,  10,  45 
"     for  propeller  struts  (Simpson's), 

169 
"     for  radius  of  gyration,  282,  284, 

285,  291,  294 
"     for  racing  yachts  (N.  Y.  Y.  C), 

672-678 
"     for  relation  coefficient,  45 
"     for  riveting  (Lloyd's),  340 
"     for  row  boats,  626 
'     for  rudder  area,  165 
"     for  rudder  stocks,  165-168 
"     for  sail  area,  628 
"     for  sea  anchors,  495,  650 
"     for  size  of  blocks,  591 
"     for  shackles,  325,  326 
"     for  spectacle  frames,  170 
"     for  speed  and  power,  263,  266, 

267,  268,  269,  270,  271 
"     for  strength  of  hemp,  588 
"     for  strength  of  manila,  587 
"     for   steamships    (British),    634- 

645 
"     for  steamships  (American),  646- 

655 
"     for  stresses  on  anchor'cranes,  411 
"     for  tackles,  602,  603 
"     Tchibyscheff's,  21,  25,  41 
"     for  tons  per  inch,  8 
"     for  twisting  moments   on  rud- 
ders, 166 
'     for  wetted  surface,  157,  158 
"     for  area  of  water  plane,  7 
"     for  B.  M.,  16,  45 


816 


Index 


Rule  for  bending  moments  on  beams, 
287,  289 
"     for  bending  moments  on  pins, 

322,  323 
'     for  bilge  diagonal  coefficient,  47 
"     for  bollards,  417 
"     for  bottom  breadth,  6 
"     forC.  B.,  11,  12,  45 
"     for  centre  of  gravity,  251-253 
"     for  centre  of  gravity  coefficient, 

45,  48 
"     for  centre  of  pressure  on  rud- 
ders, 165 
'     for  chain  cable  links,  619 
'     for  catting  hooks,  430 
"     for  columns    (Johnson's),   302- 

311 
"     for  crane  hooks,  429 
"     for  davits,  433 
"     for  end  links  on  cables,  619 
"     for  fairleads  or  chocks,  455 
'     for  finished  steel  weight,  175 
'     for  freeing  port  area,  76 
'     for  hawse  pipes,  462 
'     for  inertia  coefficient,  17,  45 
'     for  iron  rings,  478 
"     for  Johnson's  for  steel  columns, 

302 
"     for  Johnson's  for  steel  weights, 

175 
"     for  L.  B.  M.,  17 
"     for  L.  C.  B.,  12 
"     forL.  M.  C,  16 
"     for  maximum  bending  moment 

on  hull,  261 
"     for  mid.  area,  10 

Sailing  vessels,  freeboard,  101,  143 

Salt,  683 

Sand,  683 

Sandstone,  683 

Satinwood,  683 

Scantlings  for  small  boats,  628,  630, 

631 
Scarphing  of  landing  edges,  388 

of  keels,  352 
Schneider  guns,  566-567 
Screens,  light,  657 
Screws,  dimensions  of  wood,  494 

rigging,  526,  527 
Sea  anchors,  areas  of,  495 
"    anchors,  detail  of,  496 
"    miles  into  kilometres,  727 
Section  modulus,  282 
Sellers'  standard  bolts  and  nuts,  426, 

427 
Senhouse  slip,  614 
Serving  twine,  589 
Shackles  for  blocks,  591 
lashing,  592 
special,  325-327 


Shackles  standard,  497,  501,  502 
Shade  deck  vessel,  1 10 
Shearing  and     bearing     values     for 
m      rivets,  349 
stress,  280 
Sheaves,  577 

for  blocks,  591,  593 
Sheep  pens,  1 72 
Sheer,  50,  82 

"     for  boats,  626 
'     for  freeboard,  95 
"     poles,  585 

"     strake,  384,  386,  388,  389 
Shell  plating,  386-389 
"      plate  lines,  387 
"     riveting,  388 
Shelter  deck  vessel,  105,  112 
Shift  of  butts,  386 
Shingle,  683 
Ship's  bells,  413,  414 
Shoe  for  wire  rope,  584 
Side  girders  in  tanks,  368 
"     lights,  weights  of  brass  framed, 

513 
"     stringers,  382,  386 
Signs,  algebraical,  ix 
Silver,  683 
Simpson's  first  rule,  1 

"         formula  for  struts,  168 
Single  plate  rudders,  354 
Sisterhooks,  498 
Size  of  hatches,  379 
Slate,  683 

Slip  shackles,  499,  500 
Slips,  proportions  of  chain,  513 
Snatch  blocks,  419,  590 
Snow,  683 
Space,  crew,  672 
Spanish  Burton,  599 
Spar  deck  vessel,  97,  110,  127 
Spars  for  small  boats,  626 
Specification  headings,  64-72 
Specifications,  the  preparation  of,  64 
Spectacle  frames,  170,  363 
Speed  and  power,  262,  263 

"      tables,  701-705 
Spider  bands,  517 
Spirketting  plate,  365,  366 
Splices,  576 

"        allowances  for,  577 
Spruce,  683 
Square  bar,  weight  of,  211 

"  centimetres   into    square 

inches,  728 
"  foot     into     kilogrammes 

per  sq.  metre,  732 
"  inches  into  square  centi- 

metres, 728 
"  kilometres     into     square 

miles,  731 


Index 


817 


Square  bar,  metres  into  square  yards, 
730 
"  metres  into   pounds   per 

sq.  foot,  732 
"  miles    into    square    kilo- 

metres, 731 
"  yards  into  square  metres, 

730 
Squares,    cubes    and   fourth   powers, 

699,  700 
Square  of  numbers,  751-782 

roots  of  numbers,  751-782 
Stability  calculation,  38,  43 

"         curves,  43 
Staggered  pillars,  379 
Stalls,  cattle,  171,  172 

"       horse,  172 
Standard  pipe  elements,  304,  305 
Standard  rivets,  328 
"         shackles,  502 

thimbles,  582,  583 
"         toggle  pins,  525 
"         ventilator  cowls,  557,  558 
Stapled  collars,  365 
Statute  miles  into  kilometres,  727 
Statutory  deck  line,  86 
Stealers,  385 
Steamers  data,  276,  277 
Steel,  weights  of,  180-230. 
plough,  575 
"      wire  rope,  578-580 
Steering  chain  springs,  505,  506 

gears,  screw,  507,  508 
Stem,  contour  of,  51 
"       scarph  of,  353 
Stems,  353,  354 
Stern  frames,  354,  355 
Stowage  of  merchandise,  711-719 

of  oil,  687 

Strakes,  arrangement  of,  385 

Strength  of  chain  cables,  310 

"  of  columns,  294 

"         of  guard  chains,  311-349 

of  materials,  279-349 
"         of  metals  and  alloys,  304 
"  of  rings,  477 

of  special  shackles,  325,  326 
of  tackles,  602,  603 
of  timber,  305-307 
W.  I.  pipe,  475 
Stress  and  strain,  279 
Stresses  on  floors,  366 
Strong  beams,  375 
Strops  for  blocks,  592 
Structural  details,  350 
Stuffing  boxes  and  glands,  523 
Swivel  jaws,  592 
Sycamore,  683 
Symbols,  vii 


Table  of  logarithms  of  numbers,  782- 
807 
of  powers  and  roots,  751-782 
"      of  strength  of  rivetting,    342- 
347 
Tack  rivets  in  keels,  350 
Tackle,  gun,  599 
luff,  599 
Tackles,  598-606 

relieving,  600 
strength  of,  602,  603 
Tail  plates,  362 
Talc,  683 
Tallow,  683 

Tank  bleeders,  670,  671 
Tanks,  circular,  692 

rectangular,  690,  691 
Tar,  683 
Tchibyscheff's  rule,  22 

sections,  39 
sections     for     "Luca- 
nia,"  23 
Teak,  Burmese,  683 
Tee  steel,  weight  of,  185-189 
Tees  as  struts,  324 
Temperatures,  cold  storage,  720,  721 
Tensile  stress,  280 

Terminals  for  exhaust  pipes,  554-557 
Thames  measurement  tonnage,  678 
Thermal  units  into  calories,  737 
Thimbles  for  wire  rope,  524,  576,  581- 

583 
Threefold  purchase,  599 
Tile,  683 
Tiling,  683 
Timber,  305 
Tin,  683 
Toggle  pins,  525 
Tons  into  metric  tons,  734 
Tonnes-metres  into  foot  tons,  737 
Tonnage,  667-671 

B.  O.  M.,  678 
"         openings,  105 
"        Thames  measurement,   678 
schedule,  668-669 
Tons  per  inch  immersion,  8 
Topgallant  forecastle,  109 
Topping  lifts,  601,  604,  605 
Torpedo  net  details,  518 
Torsional  stress,  280 
Towing  machine,  steam,  611 
Towing  bitts,  504 

Transverse  metacentre,  13,  30,  33,  36, 
37,  45 
"         metacentre     by    Tchiby- 
scheff's rule,  30 
Trap,  683 

Trial  trip  tables,  701 
Triangles,  lashing,  473 
Trigonometrical    functions,    natural, 
738-742 


SIS 


Index 


Trim,  alteration  to,  20 

moment  to  alter  one  inch,  19 
"      moment  to  change,  17 
Trolley  block,  528 
Trunk  deck  vessel,  1 10 
Tube  end  castings,  363,  364 
Turbines,  Parsons  marine,  60 
Turnbuckles,  585 

Admiralty,  527 
Turret  deck  vessel,  110 
Twine,  serving,  589 
Types  of  rudder  carriers,    358,   359, 
360 
"      vessels  (freeboard),  109,  110 

Ultimate  strength,  279 

U.  S.  Dept.  of  Agriculture,  171 

U.  S.  Inland  Rules,  662-666 

U.  S.  gallon  into  litres,  729 

U.  S.  inspection  laws,  646-655 

U.  S.  naval  ordnance,  572,  573 

U.  S.  standard  bolts  and  nuts,  426, 

427 
Unit  equivalents,  694,  695,  696 
Universal  bar,  354 

"         joints,  529 

Values  for  Johnson's  formula, 
Valves,  low  pressure,  530-535 

"       heavy  pressure,  536-541 
Various  stresses  and  their  factors,  283 
Ventilation,  548-558 

"  pipes,  551 

Ventilator  cowls,  557,  558 
Ventilators,  cattle,  172 
Vickers  guns,  563-565 

Walnut,  683 

Water,  683 

notes,  697 
plane,  area  of,  7 
Watertight  compartments, 

doors,  details  of,  453 
doors,  hinged,  452 
"  doors,  sizes  of,  450 

"  doors,  sliding,  451 

floors,  367 
Ways,  length  of,  162 
Web  frames,  381,  382 
Weights  and  measures,  foreign,  706- 

710 
Wedges,  hatch,  381 
Weight  of  Acacia,  679 
of  alder,  679 
"       of  aluminum,  679 

of  anchors,  624,  625 
**       of  angle  steel,  180-184,  233- 

237 
"        of  antimony,  679   \ 

of  anthracite  coal,  679 
"       of  armor,  245 


Weight  of  ash,  679 
"        of  asphalt,  679 
"       of  asbestos  board,  679 

of  Babbit  metal,  679 

of  bars,  211-213 

of  bells,  414 

of  bitts,  504 
"        of  blocks,  595 

of  boats,  449 

of  bollards,  418 

of  bolts,  426,  427,  689 

of  brick,  679 

of  brass,  679 
"        of  bronze,  679 
"        of  bulb-angle,  215-220 

of  bulb-plate,  221,  222,  241 

of  bulb  tee,  223-230,  240 

of  cables,  312 
"        of  camphor,  680 
"        of  canvas,  684 
"        of  cement,  680 
"        of  chain,  312 

of  channel,  195-204,  238,  239 
"        of  coal,  680 
"        of  copper,  680 
"        of  cowl  ventilators,  559 

of  deals,  Riga,  680 

of  elm,  680 

of  fir,  680 

of  glass,  681 
"        of  greenheart,  681 
"        of  gunmetal,  681 

of  hemlock,  681 
"        of  hemp  rope,  588 

of  hollow  pillar,  231 
"  of  India  rubber,  681 
"        of  I-section,  205-210 

of  iron,  681 

of  larch,  681 

of  lead,  681 
"        of  lignum  vitae,  681 

of  lime,  681 

of  linoleum,  682 
"        of  mahogany,  682 
"        of  manila  rope,  587 

of  maple,  682 

of  Muntz  metal,  682 

of  nickel,  682 

of  oak,  682 

of  oil,  682,  687 

of  ore,  682 
"        of  Oregon  pine,  682 

of  paper,  682 
"        of  petroleum,  682 
"        of  phosphor  bronze,  682 

of  pine,  683 

of  pitch,  683 
"        of  pitch  pine,  683 

of  poplar,  683 
"        of  punchings,  246 

of  rope,  587,  588 


Index 


819 


Weight  of  rope  wire,  578 
of  round  bar,  211 
of  sand,  683 
of  satinwood,  683 
of  shapes,  180-230 
of  sheaves,  577 
of  sheet  steel,  214 
of  sidelights,  513 
of  spruce,  683 
of  steel  plating,  243 
of  square  bar,  211 
of  tallow,  683 
of  tar,  683 
of  teak,  683 
of  tee  bar,  185-189 
of  tee  bulb,  223-240 
of  thimbles,  577 
of  tiling,  inlaid  rubber,  683 
of  tiling  vitrified  brick,  683 
of  tiling,  white,  683 
of  timber,  305 
of  tin,  683 

of  tubular  pillars,  244 
of  walnut,  683 
of  water,  683 
of  white  pine,.  684 
of  yew,  684 

of  zee  bars,  190-194,  242 
of  zinc,  684 


Weights  and  measures,  foreign,  706— 
710 

Welded  beam  knees,  372,  373,  375 

Well  decked  vessel,  93,  109 

Wetted  surface  formula,  157 

Wheat,  684 

Whip,  598 

"       upon-whip,  599 

White  metal,  684 
pine,  684 

Whitworth  bolts  and  nuts,  688 

Willow,  684 

Windlasses,  611 

Wire  ropes,  flexible  steel,  578-580 
"     ropes,  end  fittings  for,  584 
"     ropes,  thimbles  for,  581 
"     rope,  notes  on,  308,  309 

Worked  eyes,  standard,  503 

Working  load,  279 

Wrecking  blocks,  591 

Yacht's  launches,  632 
Yacht  racing  rules,  672-678 
Yards  into  metres,  730 
Yew,  684 

Zee  bar,  weight  of,  190-194,  242 
Zinc,  684 


ISHERWOOD  SYSTEM 

OF 

SHIP  CONSTRUCTION 

MEANS 

Increased  Strength 

Increased  Capacity  for  Bale  Goods 

Increased  Deadweight  Carrying  Capacity 

Improved  Ventilation 

Reduced  Cost  of  Maintenance 

Reduced  Vibration 


Suitable  for  all  types  of  vessels         Specially  advantageous  for  oil  steamers, 
Passenger  and  lake  steamers 

For  Particulars  Apply  to 

J.  W.  ISHERWOOD 

4  LLOYD'S  AVENUE,  LONDON,  E.  C. 

Tel.  Add.  "Ishercon,  London" 

OR    TO 

S.  C.  Chambers  &  Co.,  3  King  St.,  Liverpool 


PARKS    PNEUMERCATOR" 


^Bt^1 

OKrT 

WiWKm 

"Parks  Pneumercator"  In  Captain's  Office  of 
New  England  Coaf  &  Cpke  Co's  steamer  "Newton 


INDICATES  AND 
REGISTERS 
FORWARD,  AFT 
and  MEAN  DRAFTS 
of  vessels.alongside  Dock, 
at  Anchor  or  Under-way, 
in  either  salt  or  fresh 
water. 

Shows  TRIM  and  LIST 
of  vessel  under  the  same 
conditions. 


WEIGHS  AND  MEASURES 
BULK  CARGOES, 
such  as  coal,  oil,  grain, 
ore,  lumber,  molasses  etc. 
BUNKERS,  either  coal 
or  oil,  checking  consump- 
tion of  same. 

MEASURES  AND 

INDICATES 

DEPTH,      HEIGHT 

and  VOLUME  of  any 
liquid  or  semi-liquid  in 
Tanks,  Reservoirs,  Dry- 
docks  etc. 


"PARKS  PNEUMERCATOR" 


The  Indicating  and  Registering  portion 
of  the  instrument  can  be  installed  at  any  dis- 
tance  either  above  or  below  the  part  of  the 
apparatus  connected  to  the  source  of  press- 
ure. 

In  marine  work,  this  is  preferably,  The 
Captain's  Office,  Chartroom  or  Pilot  House, 
(see  photograph) 

Operating  and  control  valves  are  an  in- 
tegral part  of  the  instrument  itself  and  the 
accuracy  of  the  readings  can  be  instantly 
checked. 

Various  models  are  manufactured  for 
Marine,  Submarine  and  Stationary  service. 

Estimates  furnished  and  booklet  con- 
taining full  details  of  the  instrument,  its  op- 
eration and  installation  sent  on  application. 

Address: 
GARDNER  GORNETT  QUIMBY  ENGINEERING  CO, 

118  Liberty  St.         or  Philadelphia 

New  York,  N.  Y.  Pennsylvania,  U.  S.  A. 


CONSULTING  ENGINEERS 

GEORGE  SIMPSON  JACOBS  &  BARRINGER,  Ltd. 

17  Battery  Place  78  Gracechurch  St. 

New  York  London 


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REILLY  MULTICOIL  FEED 
WATER   HEATER 


REILLY  MULTICOIL  NAVY 
TYPE  EVAPORATOR 


G-R    MULTISCREEN 
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REILLY 

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THE   GRISCOM-RUSSELL 

(Formerly  THE  JAMES  REILLY  REPAIR  &  SUPPLY  CO.) 

ENGINEERS-MANUFACTURERS  LAND-MARINE 

2119  West  St.  Bldg.  New  York 


''Watch  the   Thermometer" 

ECKLIFF 
CIRCULATORS 

FOR  SCOTCH  MARINE   BOILERS 

,      Fully  protected  b$  U.  S.  and  Foreign  Patents 

Have  achieved  results — have  established  records,  that  most 
Marine  Engineers  and  Constructors  believed  impossible  of  accom- 
plishment. In  every  installation,  they  are  creating  and  maintain- 
ing perfect  circulation,  are  equalizing  temperatures  at  top  and 
bottom  of  boilers  and  eliminating  all  boiler  troubles  arising  from 
imperfect  circulation.  They  are  guaranteed  to  do  that.  Eckliffs 
are  now  in  use  by  the 

U.  S.  Revenue  Cutter  Service 

U.  S.  Naval  Department 

U.  S.  War   Department 

and   by 

Many  of  the  largest  Steamer* 

on    Salt    and    Fresh    Water. 

A  large  Dredging  Company  recently  installed  an  Eckliff  in 
one  of  its  12  ft.  6  in. — 3  furnace  boilers;  120  pounds  steam  press- 
ure was  raised  in  forty  five  minutes,  from  cold  water — tempera- 
tures at  top  and  botton  of  boiler  the  same — have  saved  from  1 50 
pounds  to  1 80  pounds  of  coal  per  hour  since  installation — haven't 
had  to  clean  boiler  since,  except  to  remove  previously  deposited 
scale  which  the  action  of  the  Eckliff  loosened.  No  wonder  this 
company  is  now  pushing  the  installation  of  seventeen  more 
Eckliffs;  it'll  mean  a  saving,  in  coal  alone,  of  twenty-fine  tons  a 
day.  This  is  but  one  typical  instance  of  Eckliff  Service.  There 
are  many  more. 

Write  or  phone  our  representative. 
He  will  satisfy  you  on  every  point 
and  refer  you  to  Eckliff  users  you  know. 

ECKLIFF    AUTOMATIC 

Boiler  Circulator  Co. 

DETROIT  47  Shelby  St.  MICHIGAN 

New  York:  Philadelphia: 

33  Broadway  Bullitt  Bldg. 


LIDGERWOOD  MARINE  SPECIALTIES 

The  Lidgerwood  Mfg.  Co.  has  for  40  years 
held  foremost  place  in  its  line  of  products. 

(Incorporated  1873,  virtual  successor  to  Speedwell  Iron 
Works,  founded  1802,  where  engines  of  SAVANNAH,  first 
steamer  to    cross  the  ocean,  were  built.) 

Special  attention  of  ship  designers  and  own= 
ers  is  called  to  the  following  products  for  use  on 
vessels  and  wharves: 

Steam  and  Electric  Hoists 

Ships  Winches 

Steering  Engines 

Telemotors 

Marine  Transfer  for  Bulk  Cargo 

Package  Cargo  Handling  Devices 

Marine  Breeches  Buoy  for  Life  Saving 
at  Sea 

Marine  Cableways   for  Coaling    War- 
ships at  Sea 

Cableways  for  Transporting  Cargo  be- 
tween Ship  and  Shore 

For  catalogues  and  full  information  address: 

LIDGERWOOD  MANUFACTURING  CO., 

96  LIBERTY  STREET, 
NEW  YORK  CITY. 


Wire  Rigging 

Roebling  ships'  rigging  and  guy  ropes  are  all  treat- 
ed by  double  galvanizing  process,  insuring  a  tenacious 
coating  of  zinc  which  forms  an  excellent  protection 
for  the  wire. 

We  make  also  galvanized  mooring  lines,  wire  tiller 
ropes,  wire  ropes  for  hoisting,  galvanized  hawsers 
and  high  strength  wire  for  defence  against  attack  by 
torpedo. 

In  addition  to  the  above  we  make  iron,  steel  and 
copper  wire  both  bare  and  insulated,  also  insulated 
electrical  cables. 

John  A.  Roebling's  Sons  Go. 

TRENTON,  N.  J. 

Branches:   Chicago,  Philadelphia,  Pittsburg, 
Cleveland,  Atlanta. 

John  A.  Roebling's  Sons   Co.  of   New  York 
117=119=121  Liberty  St.,  N.  Y. 

John  A.  Roebling's  Sons  Co.  of  California 
San  Francisco  Los  Angeles 

Seattle  Portland,  Oregon 


"BITUMASTIC" 
COATINGS 


f/ — n — \\ 


Solution   /   /^g\   \  Cement 

REGISTERED 

Enamel 
Permanent  Protection  Against  Corrosion 

Water  Ways,  Decks,  Tanks,  Bilges, 
Tank  Tops,  Coal  Bunkers,  Inner  Bottom 
Tanks,  Floors,  Peaks,  Refrigerating  Spaces 


Inquire  for  full  particulars  and   estimates 


American  Bitumastic  Enamels  Go. 

JAMES  HERMISTON  &  SON 

322  So.  Delaware  Ave.      17  Battery  PL 
Philadelphia,  Pa.  New  York 


WAILES,  DOVE  &  CO.,  Ltd, 

5  St.    Nicholas  Buildings 
NEWCASTLE-ON-TYNE 


Cables"  BITUMASTIC"  Newcastle-on-Tyne 


PATENTEES    AND    MANUFACTURERS    OF 

'BITUMASTIC"    SPECIALTIES 

FOR 

PREVENTING    CORROSION 


Patent   "BITUMASTIC"  Deck   Coverings 

FOR  LEVELLING  AND  FLUSHING  UP  DECK  PLATING 

ADOPTED  BY  THE  LEADING  OWNERS  IN  LIEU  OF 

WOOD  FOR  ALL  DECKS  IN  WAY  OF  ACCOMMODATION 

PERMANENT    PROTECTION    FOR    STEEL    WORK 
CORTICENE  OR  RUBBER  TILING  EASILY  LAID  ON 


Patent  "BITUROS"  Enamel  for 

Protecting  fresh  water  tanks  from  corrosion 

Does  not  taint  the  water 

Thousands  of  tanks  coated 


Send  for  Particulars 


De  RUSETT'S  Patent  Hatch  Covers 

ADVANTA6ES 

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get  cut.  No  cor- 
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bunch. 

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lodge  on  the  cover 
ana  soak  through. 

There  is  nothing 
to  get  out  of  order. 

Hatch  is  clear  to 
work  directly  the 
cover  is  lifted. 

No  hatch  beams  or  girders  to  be  removed. 

No  side  projection  inside  the  coaming  on  which  cargo 
can  be  damaged.    . 

For  full  particulars  apply  to 

CHARLES   SKENTELBERY 

111    Devonshire  St.  Boston,  Mass.,  U.  S.  A. 


D.  C.  REID 

18  Broadway  New  York  City 

Broker  for  the  sale  of  steam- 
ers of  all  descriptions 

Representative  of 

SWAN,  HUNTER  and 
WIGHAM  RICHARDSON,  Ltd. 

Wallsend-on  Tyne,  England 

Ship,  Engine,  Boiler  and  Floating 
Dock  Builders  and  Repairers 

Inquiries   Solicited 


Cable  Address  "Huntreid"  New  York 
Telephone  2172  Broad 


HOLZAPFELS 

INTERNATIONAL 

Compositions  for  bottoms  of 
Steel  and   Iron  Vessels 


Obtainable   at  all  parts  of  the  world  and  in  use  by 

the  fastest  and  most  important  vessels  of  the  United 

States  and  foreign  navies. 

TOTAL  TONNAGE  PAINTED  IN  1912 

16.784.906  Gross  Tons 

Manufactured  by 

Holzapfels    American    Composition    Co. 

John  A.  Donald,  President 

John  Crowe  Harland,  General  Manager 

18  BROADWAY  NEW  YORK,  U.  S.  A. 


"BITUCOAT"  COMPOSITIONS 

SOLUTION,  ENAMEL,  COVERING  AND  CEMENT 

Are  unequalled   for 

Goal  Bunkers,  Floors,  Tanks  under  Boilers 
and  Engines,  Cold  Storage  Chambers,  Peaks, 
Decks,  Inside  Holds,  Deep  Tanks,  etc. 

Specially  recommended  for  pontoon  docks 

SPECIFY  CAIL'S 
"BITUCOAT"  COMPOSITION 


The  WILLIAM  CAIL  BITMO  CO. 

E.  McDERMOTT  HOWE,  Manager 
18  Broadway  -  -  New  York,  U.  S.  A. 


STRATFORD 
OAKUM 

Quality  guaranteed 
Is  standard  everywhere. 

Made  in  Jersey,  City,  U.  S.  A. 
GEORGE  STRATFORD   OAKUM  CO. 


MORRIS  METALLIC  PACKINGS 


The 

Standard 

Packing 

for 

Marine  use 


AN  our  Pack- 
ings tested,  be- 
fore shipment, 
to  50%  above 
boiler  pressure 


Records    of 

Six  Years' 

Service 

Without 

Attention  or 

Repairs 


Morris  Metallic  Packing  Co. 


NEW  YORK 


PHILADELPHIA 
LONDON 


NORWAY 


VON    HOVELING'S    COMPOSITIONS 


FOR 

STEAMERS   AND    SHIPS 

Largely   used    by   the  different  Navies  of   the    World,    and 
by  most  of  the  steam   and   sailing  Ship   and  Yacht  owners. 

Agencies  in  all  the  principal  ports  of  the  world. 

SOLE  MANUFACTURERS  IN  THE  UNITED  STATES 

The  VON  HOVELING 
AMERICAN  COMPOSITION  CO.,  Ltd. 

Office,  Whitehall  Building,  17  Battery  Place,  New  York. 

Factory,  41st  Street,  South  Brooklyn,  N.  Y. 

Cable  Address,  "GLISSADE."  New  York  Tel.  41 46-41 47  Rector 


FOR 

BITUMINOUS   WORK 

IN 

BUNKERS,    HOLDS,    BALLAST    TANKS, 
PEAKS,    BILGES,    BOILER   ROOMS.  &c. 

SPECIFY  "BRIGGS" 

SOLUTION  AND  ENAMELS 

Briggs  Bituminous  Composition  Co.,  Inc. 

17  Battery  Place,  New  York,  U.  S.  A. 

Cable  Address  "CEMENT,  N.  Y."  Telephone  4146-4147  Rector 


ROSS  SCHOFIELD  SYSTEM 

OF  CIRCULATION  IN 
SCOTCH  MARINE  BOILERS. 

NOW  USED  BY  THE  PRINCIPAL 
STEAMSHIP  LINES  of  the  WORLD. 


3,000,000  H.  P.  NOW  IN  USE. 


Ross  Schofield  Company 

17  BATTERY  PLACE, 
NEW  YORK. 

The  Parsons  Marine  Steam 
Turbine  Co.,  Ltd. 

TURBINIA  WORKS. 

Wallsend-on-Tyne, 
England. 

Total  Horsepower  afloat 
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approximately  10,000,000. 

6EARED  TURBINE  INSTALLATIONS  450,000  S.  H.  P. 
OFFICE:   97  Cedar  Street,  New  York. 


RElPADD 

BITUMINOUS 
SOLUTION,  ENAMEL,  CEMENT 


For  the  protection  off  interior  steel 
surfaces,  bunkers,  bilges,  ballast 
tanks,  double  bottoms,  etc.,  etc. 
RELPACO  has  been  applied  to  sur- 
faces off  U.  S.  battleships  NEVADA, 
TEXAS,  ARKANSAS;  Argentine  bat- 
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Chinese  cruiser  FEI-HUNG  and 
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RELIANCE  COMPOSITIONS 

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RELIANCE  PAINT  COMPANY 

16  Coenties  Slip  New  York 


►»     .S         JS 


175  Pages       4^X7^       Illustrated       Cloth,  NET  $2.00 

MARINE  ENGINE  DESIGN 

Including  the  Design  of 
Turning  and  Reversing  Engines 

By  E.  M.  BRAGG 

Assistant  Professor  of  Naval  Architecture  and  Marine 
Engineering,  University  of  Michigan. 

CONTENTS 

The  Heat  Engine.  Calculations  for  Cylinder 
Diameters  and  Stroke.  Strength  of  Materials 
and  Factors  of  Safety.  Cylinders.  Pistons. 
Cylinder  Covers.  Calculations  for  Cylinders 
and  Pistons.  Maximum  Load  on  Reciprocating 
Parts.  Piston  Rods.  Allowable  Pressure  on 
Bearing  Surfaces.  Crosshead  Blocks.  Slipper. 
Calculations  for  Piston  Rod,  Crosshead  and 
Slipper.  Connecting  Rod.  Crank  Shaft  For- 
mula. Lloyd's  Rules  for  Shafting.  Bureau 
Veritas  Rules  for  Shafting.  American  Bureau 
of  Shipping  Rules  for  Shafting.  Crank  Shaft 
Proportions.  Maximum  Loads  on  Main  Bear- 
ing. Engine  Bed.  Main  Bearing  Caps.  En- 
gine Frame.  Calculations  for  Crank  Shaft 
and  Main  Bearings.  Steam  Speeds  and  Valve 
Diagrams.  Location  of  Center  Lines  of  Cyl- 
inders. Calculations  for  Steam  Speeds,  Valves, 
Receiver  Pipes  and  Distance  between  Cylinder 
Centers.  Piston  Valve,  Slide  Valves  and 
Valve  Gear.  Calculations  for  Drag  Rods. 
Eccentric  Rods,  Links,  Eccentrics,  Eccentric 
Straps  and  Reverse  Shafts.  Turning  Engine 
Design.     Reversing  Engine  Design. 

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102   Illustrations  NET  $1.50 

Marine  Gas  Engines 

Their  Construction  and  Management 

BY 

CARL  H.  CLARKE,  S.B. 

Naoal  Architect  and  Engineer 

CONTENTS 

Types  of  Engines: — Principles  and  Operation  of  Each  Type. 
Advantages  of  Each  Type.  Two-Cycle  Engines: — General 
Construction.  Description  of  Some  Standard  Types.  Pumps. 
Four-Cycle  Engines: — General  Construction.  Description 
of  Standard  Types.  Vaporizers  and  Carburetters: — Va- 
porization of  Fuel.  Principles  of  Operation  and  Description  of 
Standard  Types.  Ignition  Devices: — Principles  of  Ignition. 
Mechanisms  of  Igniters.  Timers.  Spark  Coils.  Plugs.  Bat- 
teries. Dynamos.  Magnetos.  Ignition*  Wire: — Diagrams 
for  Wiring.  Spark  Coils.  Distributor.  Lubrication: — Meth- 
ods of  Lubricating  the  Several  Parts.  Multiple-Cylinder 
Engines: — Description  and  Construction  of  Standard  Types. 
Reversing  Mechanisms: — Reversing  Propeller.  Reversing 
Gears.  Reversing  Engines.  Propellers: — Definitions.  Ef- 
ficiency. Measuring  Propellers.  Calculations.  Installation: 
Foundation.  Piping.  General  Considerations  and  Description. 
Operation  and  Care  of  Engines: — General  Instructions. 
Hints  on  Finding  Troubles.  Care  of  Engine  and  Outfit.  Power 
of  Engines: — Horse  Power.  Formulas  for  Power.  Methods 
of  Finding  Power.  Brakes.  Selecting  an  Engine: — Gen- 
eral Considerations  as  to  Type,  Size  and  Construction. 

Does  not  deal  with  the  matter  from  a  theoretical 
standpoint.  The  idea  is  rather  to  describe  the  con- 
struction and  principles  of  operation  of  the  standard 
types  in  a  plain  and  simple  and  well  illustrated  form. 

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Cloth,  $7.50  Net.        Half  Morocco,  $9.00  Net. 

MODERN    SEAMANSHIP 

By  REAR  ADMIRAL  AUSTIN  M.  KNIGHT,  U.  S.  N. 

Sixth  Edition,  Rewritten  and  Enlarged 

In  the  present  edition  about  one-half  of  the  material 
retained  from  earlier  editions  has  been  entirely  re- 
written and  a  large  part  of  the  remainder  entirely 
revised.  Three  entirely  new  chapters  have  been 
added.  All  of  the  chapters  in  the  previous  editions 
dealing  with  sailing  ships  have  been  discarded,  but  a 
brief  description  of  such  vessels  is  Included  in  the 
appendix. 

CONTENTS 

The  Hull  and  Fittings  of  a  Ship.  Rope.  Knotting 
and  Splicing.  Mechanical  Appliances  on  Shipboard. 
Blocks  and  Tackles.  Handling  Heavy  Weights. 
Compass.  Log  and  Lead.  Submarine  Signals. 
Boats.  Handling  Boats  in  a  Surf.  Ground  Tackle. 
Carrying  Out  Anchors.  The  Steering  of  Steamers, 
The  Rules  of  the  Road.  Manoeuvring  to  Avoid 
Collission.  Piloting.  Handling  a  Steamer  Alongside 
a  Dock.  Placing  a  Ship  in  Dry  Dock.  Weather 
and  the  Laws  of  Storms.  Handling  Steamers  in 
Heavy  Weather.  The  Handling  of  Torpedo  Vessels. 
Keeping  Stations  and  Manoeuvring  in  Squadron. 
Towing.  Rescuing  the  Crew  of  a  Wreck.  Man 
Overboard.  Stranding.  Hints  for  Junior  Officers 
Doing  Line  Duty.     Appendix. 

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FOURTEENTH  EDITION,  ENLARGED 

With  a  New  Chapter  on  Electric  Lighting 

8vo.  Cloth     404  Illustrations     507  Pages     NET  $2.00 
THIRTY-SECOND  THOUSAND 

LESSONS  IN 

PRACTICAL   ELECTRICITY 

PRINCIPLES,  ARITHMETICAL  PROBLEMS. EXPERIMENTS 

AN  ELEMENTARY  TEXT  BOOK 

With  Numerous  Tables,  Formulas,  and 
Two  Large  Instruction  Plates. 

By  C.  WALTON  SWOOPE 

Associate  Member,  American  Institute  of  Electrical  Engineers. 

I«ate  Instructor  of  Applied  Electricity  at  the 

Spring  Garden  Institute,  Philadelphia. 


CONTENTS 

1. — Magnetism.  2. — Magnetisation.  3. — Magnetic  Fields. 
4. — Theory  of  Magnetism.  5. — Magnet  Induction.  6. — Mag- 
netic Circuits.  7. — Earth's  Magnetism.  8. — Voltaic  Electricity. 
9 — Batteries.  1 0. — Electrolysis.  1 1 .  — Measurement  of  Current 
Strength.  12. — Resistance.  13. — Ohm's  Law  and  Battery 
Connections.  14. — Circuits  and  Their  Resistance.  1 5. — Electro- 
magnetism.  16. — Galvanometers.  17. — Electromagnets.  18. 
Ammeters.  19. — Electrical  Work  and  Power.  20. — Meas- 
urement of  Pressure.  21. — Measurement  of  Resistance.  22. 
Electrical  Development  of  Heat.  23. — Electrodynamics.  24. 
Electromagnetic  Induction.  25. — The  Induction  Coil.  26. 
Dynamo  Electric  Machines.  27. — Armatures  28.  — Direct 
Current  Dynamos.  29.  Direct  Current  Motors.  30. — Electric 
Lighting.     31.     Alternating  Currents.     Tables.     Formulas. 


This  book  combines  the  principles  of  electricity  upon  which 
the  practical  applications  of  to-day  depend,  with  the  experimental 
demonstration  of  these  principles  and  the  elements  of  the  arith- 
metic of  electricity  used  in  making  practical  electrical  measure- 
ments and  calculations. 

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275  Pages       5^x8       Illustrated       Cloth,,  NET  $2.00 

Cold  Storage,  Heating 
and  Ventilating  on  Board  Ship 

By    S.    F.    WALKER 

CONTENTS 

COLD  STORAGE.  The  Cold  Storage  Prob- 
lem. Methods  of  Cooling  the  Cold  Chambers. 
Methods  of  Cooling  the  Air.  Leading  the 
Cooled  Air  into  the  Cold  Chambers.  How  the 
Low  Temperature  of  the  Brine  or  Refrigerant 
is  Produced.  The  Condenser.  Lubrication 
and  Stuffing  Boxes  of  Compressors.  Absorption 
Machines.  Circulating  Pumps.  How  Refrig- 
erating Apparatus  is  Measured.  Power  Required 
for  Refrigerating  Apparatus.  Cooling  Water. 
Form  of  Apparatus  for  Use  on  Board  Ship. 
Other  Applications  of  Refrigeration  on  Board 
Ship.  Cooling  Magazines  and  Officers'  and 
Men's  Quarters.  Faults.  HEATING.  Special 
Requirements  on  Board  Ship,  Difficulties. 
Methods  of  Heating  Available.  Hot  Water, 
Steam,  Air,  Combined  Air  and  Steam  Radiator. 
The  Thermotank  System.  The  System  Applied 
to  the  S.  S.  Lusitania.  Heating  by  Electricity. 
Regulating  Heat  Delivered  by  Electric  Heaters. 
VENTILATING.  Ventilation  by  Heating 
and  Cooling.  Ventilation  of  Laboratories  and 
Cattle  Spaces.  Fans.  Size  and  Power  Re- 
quired. Testing  Air  Current.  Estimating 
Heat  Required.  Apparatus  Estimated  to  be 
Required  for  Heating  the  Different  Saloons, 
State  Cabins,  etc.  Cost  of  Furnishing  Heat 
Required. 

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SECOND  E 


312  Pages    5x6^    124  Illustrations    NET  $2.00 

Handbook  for  the  Care  and  Operation  of 
NAVAL  MACHINERY 

BY 

Lieut.  H.  C.  Dinger,  U.  S.  N. 


{Being  an  Extended  and  Enlarged  Form  of  a  Series 

of  Articles  Published  in  the  "Journal  of  the 

Amer.  Society  of  Naval  Engrs." 


CONTENTS 

Operation  of  Naval  Machinery.  Getting  Underway. 
Running  Engines  Underway.  Accidents  Underway. 
Care  and  Overhaul  of  Main  Plant.  General  Rules 
for  Overhauling  Machinery.  Cylinders.  Valves  and 
Valve  Gear.  Engine  Adjustments.  Oiling  Gear, 
Friction  and  Lubrication.  Condenser  and  Pumps. 
Fittings  and  Auxiliaries.  Joints  and  Packings.  Stuff- 
ing-Boxes. Lagging  and  Clothing.  Feed  and  Filter 
Tanks.  Feed  Water  Heaters.  Evaporators  and 
Distillers.  Heating  System.  Steam  Launches.  Re- 
frigerating Plant.  Gauges  and  Thermometers.  Rev- 
olution Counters,  Telegraphs  and  Revolution  Indica- 
tors. Piping.  Valves  and  Cocks.  Cleaning, 
Painting,  and  Points  in  Doing  Work.  Care  and 
Subdivision  of  Hull.  Special  Auliliary  Engines. 
Steam  Steering  Gear,  Air  Compressors.  Blowers 
and  Blower  Engines.  Ash  Hoists  and  Ejectors. 
Workshop  Machinery.  Spare  Parts  and  Tests. 
Spare  Parts  and  Outfit  of  Accessories.  Tests  of 
Machinery  and  Piping. 

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We  carry  a  complete  stock  of  the 
publications  of  all  other  publishers 
and  are  especially  well  fitted  to  fill 
your  orders  for  books  on  marine  and 
naval  engineering — All  inquiries  are 
given  prompt  and  careful  attention 


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Practical  Mathematics  for  Young  Engineers. 

F.  HOVENDEN 
144  Pages  B#  x  7  h  Illustrated  Net  $1.00 

Hints  to  Engineers  for  the 

Board  of  Trade  Examinations. 

W.  D.  MARTIN 

141  Pages  Sx7%  Illustrated  Net  $1.00 

Marine  Engineers'  Drawing  Book  for 

Board  of  Trade  Examinations. 

W.  C.  McGIBBON 

Seventh  Edition  137   Pages  \2%  x  9% 

Flexible  Cloth 59  Plates  Net  $2.00 

Indicator    Diagrams   for  Marine    Engineers. 

W.  C.  McGIBBON 
196  Pages        1%  x  9%       197  Illustrations       Net  $3.00 

Mechanical  and  Marine  Engineering  Science. 

A.  N.  SOMERSCALES 

Fourth  Edition  544  Pages  £%  x  8^ 

216  Illustrations Net  $5.00 

Lessons  in  Mechanics  for 
Marine  Engineers  and  Engineering  Students. 

A.  N.  SOMERSCALES 
280  Pages         5  x  7lA         149  Illustrations         Net  $1.50 

Simple  Problems  in 

Marine  Engineering  Design. 

J.  W.  M.  SOTHERN  and  R.  M.  SOTHERN 

Third  Edition  202  Pages  5^x7^ 

Flexible  Cloth Net  $1.00 

"Verbal"  Notes  and  Sketches 

for  Marine  Engineers. 

J.  W.  M.  SOTHERN 

Eighth  Edition,  Enlarged  and  Rewritten, 

709  Pages       6y2  x9'A        545  Illustrations        Net  $5.00 

Elementary  Mathematics 

for  Marine  Engineers 

J   W.  M.  SOTHERN  and  R.  M.  SOTHERN 

180  Pages  5^x7^  Illustrated  Net  $1.00 

Marine  Engineers  B.  of  T.  Examinations. 

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